Nicolas Hernandez
email: hernandez@limsi.fr

Brigitte Grau
email: grau@limsi.fr

What Is This Text About? Combining topic and meta-descriptors for text structure presentation

Keywords: H.3.1 [Information storage and retrieval]: Content Analysis and Indexing-Abstracting methods, Linguistic processing, H.5 [Information interfaces and presentation]: Miscellaneous, I.2.7 [Artificial intelligence]: Natural Language Processing-Discourse, Text analysis Dynamic summarization, Text visualization, Meta-descriptors and topical descriptors identification, Text structure

Most work in text retrieval aims at presenting the information held by several texts in order to give entry clues towards these texts and to allow a navigation between them. Besides, a lesser interest is dedicated to the definition of principles for accessing content of single documents. As most information retrieval systems return documents from an initial request made of words, a usual solution consists of presenting document titles and highlighting words of the request inside a passage or in the whole document. Such a presentation does not allow a rapid reading and systems cannot satisfy themselves with it. Our studies lead us to provide indicative and informative view of texts as in summarization systems. We offer the user different levels of abstraction of a text: the first is a global overview, where global topics are indicated and positioned in the text. The second level of abstraction goes deeper in the topic description by adding local topics and information about the argumentative role of the segments. In this paper, we will detail the extraction of thematic descriptors and meta-descriptors that relies on recurrence -respectively in a text or in the corpus-and how their characterization provides the segment structuring.

INTRODUCTION

What is this text about? Which descriptors are relevant for indexing it and further retrieving its topics? Is this text relevant for my purpose, does it contain the answer I am looking for and in which part?

Even if these questions often characterize user's needs, answering them often requires a lot of times, as information retrieval systems seldom offer means for a rapid reading and a guided exploration of a document. Most work in text retrieval aims at presenting the information held by several texts [START_REF] Cutting | Scattergather: A cluster-based approach to browsing large document collections[END_REF][START_REF] Wise | Visualizing the non-visual: Spatial analysis and interaction with information from text documents[END_REF][START_REF] Chen | Internet browsing and searching: user evaluations of category map and concept space techniques[END_REF] in order to give entry clues towards texts and to allow a navigation between them. Besides, less interest is dedicated to the definition of principles for accessing content of single documents. Jacquemin et al. [START_REF] Jacquemin | Multi-dimensional and multi-scale visualizer of large xml documents[END_REF] offer a 3D visualization of large documents, as PhD thesis, that encounters for the overall document logical organization and for the similar parts from a topic point of view. It remains to characterize each part of the documents more precisely in order to inform about their content, and this problem is mainly tackled in automatic summarization [START_REF] Saggion | Concept identification and presentation in the context of technical text summarization[END_REF][START_REF] Teufel | Argumentative classification of extracted sentences as a first step towards flexible abstracting[END_REF]. Apart from the size and the number of documents they deal with, all these systems face up the same major problem: it is difficult, in textual information presentation, to represent text but with text [START_REF] Hearst | User interfaces and visualization[END_REF]. The abstract view commonly assumed relies on the organization of the information according to a thematic criterion. Multi-document presentation systems visualize thematic classes of documents in 2D or 3D paradigms [START_REF] Hearst | User interfaces and visualization[END_REF]. Nevertheless, the deeper an application has to examine single documents of relatively small size (10 to 20 pages), the more graphical means are difficult to use for abstracting text.

As most information retrieval systems return documents from an initial request made of words, a usual solution consists of presenting document titles and highlighting words of the request inside a passage or in the whole document (KWIC). Such a presentation does not allow a rapid reading and systems cannot satisfy themselves with it. If the TileBars interface of [START_REF] Hearst | Improving full-text precision on short queries using simple constraints[END_REF] entails a user to target relevant passages by adding to the document a graphical bar indicating the text segments that contain the request words, it is not enough for giving an idea of the whole text. Thus the fundamental problem consists in defining what information has to be shown so that a user will rapidly get rid of irrelevant texts or irrelevant passages and will be guide towards relevant ones. Our studies lead us to provide indicative and informative view of texts as in summarization systems [START_REF] Saggion | Concept identification and presentation in the context of technical text summarization[END_REF]. In these approaches, the indicative part corresponds to eliciting text topics, and the informative part to a summary obtained by extracting the prominent descriptive sentences. However whether such a static view of texts is relevant in a first approach of the texts in order to decide of keeping them or not, it has to be refined for guiding the reading.

This remark leads us to offer the user different levels of abstraction of a text. The first level is a global overview, where global topics are indicated and positioned in the text. We not only show the different segments as in [START_REF] Boguraev | Salience-based content characterisation of text documents[END_REF][START_REF] Kan | Linear segmentation and segment relevence[END_REF], but we place them in a thematic structure [START_REF] Salton | Automatic text decomposition using text segments and text themes[END_REF][START_REF] Yaari | Segmentation of expository texts by hierarchical agglomerative clustering[END_REF][START_REF] Moens | Generic topic segmentation of document texts[END_REF][START_REF] Hernandez | Analyse thématique du discours : segmentation, structuration, description et représentation[END_REF]. The second level of abstraction goes deeper in the topic description by adding local topics and information about the argumentative role of the segments. This last information is given by selecting argumentative and rhetorical cue phrases in each segment, i.e. their meta-descriptors [START_REF] Hernandez | Extraction et typage de termes significatifs pour la description de textes[END_REF][START_REF] Saggion | Concept identification and presentation in the context of technical text summarization[END_REF][START_REF] Teufel | Argumentative classification of extracted sentences as a first step towards flexible abstracting[END_REF]. The third level gives the detail of chosen segments. In addition, the links between each entity are kept so that they allow navigating from a level to another, or, inside a same level, from a topic to another.

In this paper, after presenting an overview of our system, we will compare it to related works (section 3). Then we will detail how thematic descriptors and meta-descriptors are extracted (section 4) and how their characterization and they combination provides the segment structuring (section 5). We develop our model for scientific or technical texts, avoiding any handmade database and any restriction on the text domains. Finally, we present results we obtained with our approach in section 6, and make a conclusion.

SYSTEM OVERVIEW

Figure 1 shows the architecture of our system. A text is first pre-processed by a POS tagger because the segmentation task and the extraction phase rely on lemmatized words in order to bypass word inflections. The tagging also provides the morpho-syntactic category of each word.

The segmentation process leads to decompose the text in consecutive segments that are cohesive and coherent. As in [START_REF] Hearst | Texttiling: Segmenting text into multi-paragraph subtopic passages[END_REF], our method ( [START_REF] Masson | Méthodes pour une génération variable de résumé automatique : vers un système de réduction de texte[END_REF]) relies on the repetition of same words when a same topic is developed, and on the concentration of these words in a part of text if they are typical of this local topic. Thus, it finds breaks between two basic units if they do not share enough words that mainly appear in these units. We will see in section 5.1 that we do not always interpret a cohesive segment as a topic segment. We only consider content words as unit descriptors (noun, verb and adjective), and we weight them according to the TF.IDF scheme, with tf the occurrence number of the word in the text, and idf the number of paragraphs that contain this word. We then evaluate the proximity of two units by computing the Dice coefficient between their two vectors and by applying a threshold relative to the variation of this value to the mean of all the coefficient values for each two consecutive units.

Scientific texts are generally structured in rather equilibrated paragraphs, and a paragraph tends to develop only one topic. Thus we chose them as basic units and text segment are then made of several consecutive paragraphs.

In order to exhibit the text structure, we identify in each segment their topic descriptors and their meta-descriptors. Topic descriptors are dynamically recognized, without any a priori on what are potential topics and which relations they may entertain. Topic descriptors are the noun phrases that are the most prominent at the segment level (local topics), and at the multi-segment level (global topics). At the multi-segment level, descriptors correspond to topics that are developed along several segments. As two consecutive segments differ in their local topics (by construction), we consider each segment develops a different point of view on the same global topic. Topic descriptors are mainly recognized by their occurrence number, incorporating in this computing an anaphora resolution process.

Meta-descriptors are recognized in texts from a list we acquired automatically from the whole corpus, considering all the expressions that are used in all the texts, independently of the domains, are those cue phrases of the general language that are used for highlighting a passage, or for making a link explicit. We will describe here the acquisition phase. These descriptors will play an explicative role in the visualisation phase, by specifying the argumentative role of the topic or the segment in the global text structure.

This global structure relies on the thematic segments and the links we found between them. These links come from the global topics they share. These topics can also be viewed as constituents of lexical chains that cover parts of texts made of several segments. Their distribution on the text leads to propose a text structure, and we will show we can exhibit different kinds of text structure.

The last process makes use of all this information, represented in XML format, and proposes a dynamic visualization of a text in different abstraction levels, with relations between all the entities our system recognizes: segments, global and local topics descriptors. This visualization allows the user a rapid reading of the whole text by presenting topics and their repartition in the thematic structure. If the user wants details about a specific part, she can request a summarization of a segment (or of linked segments) with the printing of local topics and meta-descriptors, or request the whole segment content(s).

BACKGROUND

For years, advantages of taking into account structures of texts have been shown in several areas such as information organization, summarization, and access to information.

Text Description

Boguraev et al. [START_REF] Boguraev | Salience-based content characterisation of text documents[END_REF] introduce the notions of "capsule overview" -topically homogeneous text segment -and of "topic stamp" -most salient phrases of a segment under considerationin order to offer slight but intelligible text overviews. They adopt a TextTiling-like algorithm [START_REF] Hearst | Texttiling: Segmenting text into multi-paragraph subtopic passages[END_REF] for text segmentation and based the phrase salience definition on linguistic heuristics such as predominant grammatical roles, privileged positions in the sentence, phrase recurrence, etc.. Similarly, Kan et al. [START_REF] Kan | Linear segmentation and segment relevence[END_REF] perform a linear segmentation, but this time by using lexical chains. They do not intend to describe segment contents but to locate significant segments presenting key information about the article as a whole. For each segment, significance is computed by summing the relevance of terms occurring in it; it means the TF*SF (term frequency * how many segments does the term occur in) of each term and its coverage (a score following a harmonic series is added for each term occurrence) -both are normalized by the maximum value. In addition to segment significance, segment function is determined by text-genre cues such as global position, segment significance, lexical markers, etc.. In a sense, the two following approaches [START_REF] Saggion | Selective analysis for automatic abstracting: Evaluating indicativeness and acceptability[END_REF][START_REF] Teufel | Argumentative classification of extracted sentences as a first step towards flexible abstracting[END_REF] are similar to the previous one. Indeed, both of them aim at providing indicative information about text content, in particular about the argumentative structure of texts.

SumUM, [START_REF] Saggion | Selective analysis for automatic abstracting: Evaluating indicativeness and acceptability[END_REF], is an automatic two-steps summarizer for scientific documents based on selective text analysis. The selection is based on lexical and syntax recognition patterns such as goal of author + define + [GOAL]1 . First, it provides an indicative view of the document, proposing major themes of the text, and then, an informative view by expanding a particular aspect selected by the user. Though this system obtained the best results in the evaluation program DUC 2002, it requires costly knowledge development.

The second approach [START_REF] Teufel | Argumentative classification of extracted sentences as a first step towards flexible abstracting[END_REF] takes also interest in global rhetorical organization of scientific articles in order to make more coherent automatic summarization. They propose a learning-based method to identify and classify new "indicator markers". So used, those indicator markers permit to retrieve abstract-worthy sentences. But even if their results are encouraging, their approach to extract indicator phrases requires costly manual pre-processing.

Text Structure and Topic Hierarchy

Dominant discourse analysis theories [START_REF] Mann | Rhetorical structure theory: A theory of test organisation[END_REF][START_REF] Grosz | Centering: A framework for modeling the local coherence of discourse[END_REF][START_REF] Charolles | L'encadrement du discours -univers, champs, domaines et espaces[END_REF] do not permit simple computational way to determine the detailed discourse structure of texts.

Starting from the definition of topicality based on lexical recurrence [START_REF] Halliday | Cohesion in English[END_REF], some authors have proposed two kinds of robust approaches: the automatic construction of topic hierarchies and the topic text structure detection. The former are based on relations between terms like subsumption or lexical relations. A thorough review of automatic methods to build topic hierarchies is described in [START_REF] Lawrie | Discovering and comparing hierarchies[END_REF]. Although topic hierarchies provide good corpus overviews, they need to integrate more information for single text presentation in order to take more into account the text linearity and segment embedding.

Salton et al. [START_REF] Salton | Automatic text decomposition using text segments and text themes[END_REF] are one of the first work that observes topic structure by automatic means. They computed a graph of lexical similarities between paragraphs. Lexical homogeneity between contiguous paragraphs defines text segments and sets of mutually related paragraphs (more than 3) generate text themes. Text structure classification is defined by observing the congruence between text segments and text themes, and text traversal strategies are so defined according to.

In comparison with this system, the following two systems have been designed to detect specific text structure. Even if they present correct results they remain text-genre dependant.

Yaari [START_REF] Yaari | Segmentation of expository texts by hierarchical agglomerative clustering[END_REF] proposes a method for segmenting expository texts based on bottom-up hierarchical agglomerative clustering (HAC). More than a linear segmentation, the algorithm identifies a nested outline of the text. Based on paragraphs as elementary segments, the HAC algorithm merges iteratively the two most lexically similar consecutive segments while more than one segment remains.

In [START_REF] Hernandez | Analyse thématique du discours : segmentation, structuration, description et représentation[END_REF] we got interested in nested thematic structures of scientific texts. In order to detect them, we sought for the two most lexically similar non-consecutive segments -this permit us to localize the theme inside those passages -and we reproduced the same process recursively on embedded segments. This algorithm presents correct results over texts where announcements and resumptions are common.

Moens et al. [START_REF] Moens | Generic topic segmentation of document texts[END_REF] propose to observe generic topical cues, amongst which the content terms, to automatically detect the thematic structure of any given text. They argue that combination of information about lexical chains and topically coherent passages -consecutive sentences sharing the same topical term recognized thanks to cues such as the position in the sentence, the persistency with previous sentence, bound pronouns, etc. -helps in finding the most probable thematic structure (detecting topic shifts, nested topics, sequential topics, topic returns). The authors give one example of heuristic they used: topic returns can be detected as large gaps in the positions of two members of a lexical chain that are into topical focus. Their approach goes further by generating a table of contents of the text by selecting most informative terms in the lexical chain of dominent sentences of each segment.

TEXT DESCRIPTORS

We said that a text is fully described if the topics of each of its parts are identified, if the role of each segment can be understood and if the overall organization is made explicit. For this purpose, we defined two kinds of descriptors, topic descriptors and meta-descriptors, for characterizing functional or argumentative roles of segments.

Meta-descriptors

Meta-descriptors are those expressions an author uses to make explicit an argumentative link between parts of text, in order to indicate which role plays a segment or a topic in the global discourse. These roles are such as introduction, result, conclusion. Meta-descriptors are also those rhetorical expressions that enable to highlight an important passage.

Meta-descriptors correspond to formulaic phrases, either fixed phrases as in the same way or in particular, or flexible phrases, as have to be implemented or the goal of that can be found in text with slight variations. These expressions do not depend on text topics and are recurrent in all the documents of a scientific corpus. This last characteristic leads us to extract them automatically from our corpus rather than building a list manually. The automatic process entails to collect expressions without any a priori about their validity as meta-descriptor, and, as we will see further, without any a priori about the form of the meta-descriptor.

As shown by the previous examples, meta-descriptors do not correspond to a fixed category of phrase and their ex- traction cannot be achieved by the application of syntactic patterns. So we choose to work with n-grams, i.e. sequences of n consecutive tokens, made of 1 up to 5 tokens. Tokens are those provided by a POS tagger, the TreeTagger [START_REF] Helmut | Probabilistic part-of-speech tagging using decision trees[END_REF].

F
The extraction process follows two phases: i) the collecting phase, ii) the selection phase. The collecting phase consists of making a list of unique instances of n-grams from each text, and to count the number of documents that hold each of them. A threshold allows the system to eliminate the less frequent expressions, thus the words linked to the text domain. This first step produces a first list that is sufficiently relevant for a manual selection. Nevertheless, the second step aims at selecting automatically the right length of each expression. We assume that if two expressions, with one enclosing the other, are in the same neighborhood in term of frequency, they both refer to the same meta-descriptor. The smaller expression corresponds to a variation of the longest expression that is then chosen. We made several tests (see [START_REF] Hernandez | Extraction et typage de termes significatifs pour la description de textes[END_REF]), and we finally retained expressions with a frequency equal or greater to 7 after the first step. Closeness of two expressions is stated when their difference of frequency is less than 20% of the greater number. Table 1 shows the filtering step with F for the frequency of the expression, N for the inferior boundary of the interval that defines the neighborhood. One can see that example, is embodied in for example, and as they are in the same neighborhood (135 belongs to the interval [126, 158]), example, is no more considered as a candidate. By applying this principle gradually, we finally select the longest expression along all the embodied expressions in the same neighborhood (by transitivity). In the series shown in table 1, we finally keep . for example,. It does not signify that we always select the longest expression; if two of them are not close enough, they are both kept. We can note the important role played by the punctuation when defining an expression. Punctuation translates a constraint on the position of the meta-descriptor in a sentence.

The final list we obtained contains 1063 markers from a corpus of 80 scientific articles containing each one about 5000 tokens. Table 2 shows an excerpt of the list (words of the meta-descriptors are lemmatized). Another interest of our approach is the possibility of considering some tokens as flexible depending on their part-of-speech assignation (determiner, pronoun, adverb, etc.). This permits us to generalize forms and to bring together several variants of a same form.

When analyzing a text, we recognize all the meta-descriptors in it. They represent a great part of its total vocabulary (between 30% and 40%). Then, we will present in section 6 some heuristics leading to filter them, according to their contextual use.

Topic Descriptors

Topic descriptors aim at identifying both the topics the whole text is about, and the topics parts of texts are about. This becomes essential when considering different application tasks, as indexing a text or searching for information either by searching documentation about some topics or looking for a precise information. Text topics are extracted from the text currently analyzed for presentation and typically correspond to noun phrases of the text, considering these expressions are the better descriptors for topics, as in [START_REF] Boguraev | Salience-based content characterisation of text documents[END_REF]. The topic extraction is not based on a pre-built list of selected topics, as for meta-descriptors, as a topic can be relevant in some text and not in other texts, according to the global thematic and the discourse organization. Thus, it is a dynamic process, based on the recurrence and the distribution of the noun phrases inside the thematic segments. Recurrence is the main criterion for deciding of the relevance of a term as for segmenting texts [START_REF] Hearst | Texttiling: Segmenting text into multi-paragraph subtopic passages[END_REF]. It is justified when dealing with scientific texts where developing topics needs to make use of a specific vocabulary without synonyms or ambiguities. The distribution criterion is not used for weighting the selected terms as in text segmentation. However, the interpretation given to a topic distributed over several segments remains the same. Thus, frequent terms mainly present in one segment are characterized as local topics. When they appear in several segments, they are considered as global topics, i.e. topics that typify a greater passage. These characterizations will lead us to propose a discourse structure that links non consecutive segments in a same thematic (see section 5). As we just saw it, term recurrence is a strong criterion for deciding which noun phrase identifies a topic. For this reason, recurrence is not only computed by counting identical terms and the system also accounts for their anaphoric references.

Topic extraction follows the steps illustrated in figure 2. The first step aims at retrieving topic referring expressions that denote the text entities by applying syntactic patterns. These patterns identify simple noun phrases (a noun with eventually adjectives), complex noun phrases (phrases with the preposition of) and pronouns (personal, reflexive and demonstrative pronouns). Among these expressions, the system tries to solve the anaphoric expressions made of pronouns and demonstrative noun phrases. We chose to work only on the non ambiguous anaphoric expressions, as our purpose is to reinforce the pregnancy of some entities when they are used again and not to solve all the co-references of the text. So, we prefer precision over recall in order to avoid noisy results.

The anaphora resolution process was inspired from [START_REF] Boguraev | Salience-based content characterisation of text documents[END_REF][START_REF] Mitkov | Robust pronoun resolution with limited knowledge[END_REF]. It first selects the potential antecedents for a given anaphora in the current sentence and its prior sentence. The system keeps all the noun phrases that are present or referred in these sentences. Then, candidates are ranked according to several criteria that lead to give them a weight: i) morphological criterion (gender and number agreement); ii) lexical indicators (identical head of noun phrases); iii) syntactic criteria (parallel grammatical relations, kinds of grammatical relations); iv) discursive criterion (the distance between a candidate antecedent and the anaphora in scope). Most of these criteria are computed by robust heuristics, as the relative position of the words for deciding their grammatical role for example.

The last step consists in labelling the salient entities with a topic stamp. The topic label is chosen according to a threshold that states as topical the recurrent entities and the entities which are at least one time subject, object, or which are coming along with demonstrative. These topical entities are all considered to be local topics except those occurring in several segments which are named global or hyper-global if they are repeated throughout a text.

TOPICAL TEXT STRUCTURE

We propose a general framework to analyze topic structure of scientific and technical texts. This framework should be refined to handle particular text segments.

Text Segmentation

In traditional text segmentation methods based on lexical recurrence [START_REF] Halliday | Cohesion in English[END_REF][START_REF] Hearst | Texttiling: Segmenting text into multi-paragraph subtopic passages[END_REF], cohesive segments are considered coherent from a thematic point of view and different because of the theme they carry. Less cohesive text parts are considered as topic shift.

Ferret [START_REF] Ferret | Segmenter et structurer thmatiquement des textes par l'utilisation conjointe de collocations et de la rcurrence lexicale[END_REF] interprets the various cohesive parts as different degree of topic shifting: new topic detection, topic development, topic shift detection and topic shift.

In this paper we argue that lexical cohesion does not always stand for topical assignment. Indeed, an example can lexically differ from the topic it aims to instance. So we will consider segments obtained by lexical cohesion simply as coherent segments for which the role remains to specify. In addition, we argue that less cohesive segments can stand for articulation between topic segments.

Model and Basic Structures

Popular theories of discourse structure model the document as a hierarchical structure of text segments, e.g. the nucleus-satellite relation in rhetorical structure theory [START_REF] Mann | Rhetorical structure theory: A theory of test organisation[END_REF] and the dependence relation in [START_REF] Grosz | Centering: A framework for modeling the local coherence of discourse[END_REF].

We start from this axiom and we distinguish two kinds of segments: the topical segments and the meta-discursive ones. The former class represents topic contents and the latter acts as an articulation between topics. The articulation segments are divided into two subclasses: the announcement and the conclusion segments. An announcement segment announces explicitly or implicitly the themes or aspects which are going to be dealt with, and a conclusion segment summarizes or concludes one or several previous topic segments.

From our corpus observations, we identified two basic structures in which the various kinds of segments are related. The detection of these structures and the interpretation of their combination permit to describe the topic structure of the texts.

Contiguous topic segments stand for items of a list which should be analyzed in respect of a more global structure. In our approach, we always consider them as explicitly or implicitly introduced by a subsuming structure.

Nested segment(s) are used to specify a dependence relation. A segment is said dependent to another if it requires that the other exists in the text. We make the distinction between the recursive nesting of single segments and the nesting of several segments. This lead us to define the following text grammar rules 2 :

• Str → Sa Str+ Sc?

• Str → St A text structure can be parsed as a list of nested structures beginning by an announcement and potentially finishing by a conclusion. Figure 3 shows some example of basic structures. For examples, (a) can stand for elaboration or instantiation of a single topic as well as the reprise of the focus of a segment as the theme of the following; (b) concerns various aspects of a same topic, or distinct topic developments. 2 With Sa for announcement segment, Sc for conclusion segment, St for topic segment and Str for the structure symbol.

Structure Detection

Identification of the segment roles is performed by the detection of some intrinsic and extrinsic properties. We noticed that topic segments are much more lexically homogeneous than articulation segments in which global themes are more likely combined (at least two of them) and in which meta-descriptors presence is higher. Thanks to metadescriptive lexicons and works of [START_REF] Minel | Résumé automatique par filtrage sémantique d'informations dans des textes. présentation de la plate-forme filtext[END_REF], we defined heuristics and patterns to detect announcements, conclusions and topic segments.

The structure algorithm is based on the correct assignment of announcement and conclusion segments with the topic segments. This is done by matching the same global topics between topics segments and announcement or conclusion segments respectively to the previous and following text parts. We suppose the text structure follows the text linearity so the text is back-parsed from the end to the beginning of the text.

Single nested segments are identified in the situation of two adjacent segments with the first one linked to an announcement (by having a common global theme): if the second segment has the same global theme or if it is not related to any announcements, then it is considered as a single nested segment of the previous one.

Going further...

In practice, roles of text segment are not so easily identified. It is the major problem of text segmentation methods based on lexical cohesion. Many segments are ambiguous and regularly we encounter segments concatenating both a conclusion and an announcement, or series of segments in which the first one contains the announcement of the series.

Text segmentation needs finer-grained observation. Our approach is dedicated to provide a generic model to analyze topic text structure. We argue that most of the ambiguous segments follow the same hierarchical structure that we have defined in previous sub-section. So the enhancement of the system consists of observing new ambiguous segments and setting heuristics to recognize them in order to consider respectively announcement, conclusion and topic parts. Combination of statistical and linguistic methods [START_REF] Ferret | Repérage de structures thématiques dans des textes[END_REF] also seems to be an interesting approach to decompose texts into segments and to assign them more accurate roles.

EXAMPLE AND DISCUSSION

The main issue for short text presentations is to combine both abstract and textual representations of documents. In order to limit cognitive processes and make easier the users's task, the interface should provide all and only the needed information on a same screen and provide ways of linking the different information sources.

Our corpus is composed of articles extracted from the Computation and Language (cmp-lg) collection, developed by the TIPSTER SUMMAC project (http://xxx.lanl.gov/cmplg), from French proceedings of TALN conference and from the French scientific news paper called "la Recherche".

Currently, due to our running task for adapting the process to English, we do not have a full text description in English. The example in figure 4 is an article of "la Recherche". The article deals with "vin jaune" or "yellow wine". The author wonders which molecule is responsible of its specific flavor. In particular, the fragment presents the most straight method of wine analysis.

Our current presentation is a prototype. The left part of the screen stands for an abstract view of the text. It corresponds to the text topic structure in which global terms are mentioned. Each level presents the global terms from segments which are not embedded (nominal expressions, laying in context several global terms, are preferred). This structure offers accesses to the text content.

The right part of the screen refers to the segment under consideration. Thanks to our term labelling process, we identify in this text segment "wine/vin" as playing a global thematic role, which sounds as normal because the entire text is about wine. In the same way, we identify mixture/mélange and element/composé as playing local theme role. Both reinforce the role played by expressions identified as indicative label, it means analysis/analyse and technique/technique. As a note, we point out that a global theme and a meta-descriptor occur in the first sentence of the segment and that they describe correctly the text fragment since we can type it as a description of technical analysis of wine. Combination of meta-descriptors with topic descriptors within a same linguistic expression, position in topic segments, etc. can be used as clues to select some significant meta-descriptors among others.

It is difficult to evaluate this kind of systems. In general either each sub-system is evaluated separately or the whole system is used for a retrieval task to determine whether it facilitates searching tasks.

Our system is composed of many parts. The main dependency risk relies on genre-dependent text. Text segmentation by lexical recurrence shows some limitations with journalistic text-genre documents. Nevertheless Ferret et al. [START_REF] Ferret | Utilisation d'un réseau de cooccurrences lexicales pour améliorer une analyse thématique fondée sur la distribution des mots[END_REF] have shown that using a co-occurrence network can solve this kind of problem. Concerning topic identification, Mitkov [START_REF] Mitkov | Robust pronoun resolution with limited knowledge[END_REF] shows correct results for robust pronoun resolution in scientific texts. The problem should be more difficult for other text genre. Indeed journalistic documents do not use words repetition but synonymous and metaphors. It is known that some semantic knowledge resources are required to deal with this kind of documents. We just have started to test our meta-descriptor extractor over different sets of scientific documents. Analysis requires more data, but in comparison with scientific meta-descriptor lists, a list obtained from a journalistic corpus seems to prefer some specific parts of speech like adjectives and adverbs.

CONCLUSION AND PERSPECTIVES

Our system aims at facilitating visualization of documents and navigation intra-documents. Our approach is supported by automatic text analysis to identify topic descriptors and meta-descriptors, which are used to detect the topical structure of texts. Moreover we propose a generic framework to detect text topic structures.

Future developments will concern on one hand to enhance our text structure detection by integrating more markers to identify correctly the various segments, and on another hand to set an evaluation framework to test how significant our analysis can help a user in retrieval task.

Figure 1 :

 1 Figure 1: System overview.

Figure 2 :

 2 Figure 2: Identification of topic descriptors.

Figure 3 :

 3 Figure 3: Various examples of basic text structure composition.

Figure 4 :

 4 Figure 4: Example of segment description.

Table 1 :

 1 Automatic filtering.

		Expressions	N	Comment
	158 example ,	126 Not a candidate term
	142 for example	113 Not a candidate term
	135 for example ,	108 Not a candidate term
	130 . for example	104 Not a candidate term
	127 . for example ,	101 Is a candidate term !
	102 example of	81	Is a candidate term !
	84	example , the	67	... ?
	76	an example	60	... ?

Table 2 :

 2 Excerpt of our final list of fixed phrases

"GOAL" is the retrieved expression marked by "goal of author + define"


M Eletta Negretti

David Z Zhu

Gerhard H Jirka

The effect of bottom roughness in two-layer flows down a slope

Keywords: Stratified flows, Bottom roughness, Topographic effects, Interfacial waves, Entrainment, Vorticity

Laboratory experiments were conducted to study the effect of locally enhanced bottom roughness in a density-stratified two-layer flow down a slope. Three bottom roughness configurations were investigated, a smooth bed and two artificially roughened beds, employing sparse and dense roughness elements, respectively. The bottom roughness elements have shown to affect differently the generation and collapse mechanisms of large-scale two-dimensional structures observed at the interface between the two layers: dense bottom roughness inhibits the generation of large-scale structures while sparse bottom roughness inhibits their collapsing mechanism. Both bottom roughness configurations cause a reduction of the size of the large structures at the interface as compared to the smooth case. Two main sources of entrainment have been identified, namely the observed large-scale structures at the interface and enhanced bottom roughness. Sparse bottom roughness gives the lowest entrainment coefficients among the three cases due to the low interaction between the bottom boundary layer and the interface.

Introduction

Two-layer density stratified flows are commonly observed in the oceans, in lakes and in the atmosphere. Examples of such flows in the oceanographic context include the two-layer flow in the Strait of Gibraltar exchanging the water mass between the Mediterranean sea and the North 1 Atlantic [START_REF] Armi | Maximal two-layer exchange through a contraction with barotropic net flow[END_REF] and that in the Faroe Bank channel connecting the Greenland-Iceland-Norwegian Seas to the North Atlantic [START_REF] Hansen | North Atlantic-Nordic Seas exchanges[END_REF]. The two-layer flows in these channels play a crucial role in determining the distribution of water masses in the global ocean. Two-layer flows are also important in many hydraulic/environmental applications (e.g. lakes and reservoirs with interconnections and side arms) and in metereology (e.g. downslope windstorms in mountains areas). At the interface of two-layer flows small-scale instabilities, like Kelvin-Helmholtz instabilities as well as large-scale instabilities have been observed [START_REF] Sherwin | Mixing and advection of a cold water cascade over the Wyville Thomson Ridge[END_REF][START_REF] Negretti | Barotropically induced interfacial waves in stratified two-layer flows over a sill[END_REF]. Understanding of these flow processes is crucial in predicting vertical transport of heat, oxygen, nutrients and pollutants in inland water bodies, oceans, and the atmosphere. In metereology for example, it has been estimated that instability and mixing causes a 50% increase in the drag of atmospheric flows and thus the study of shear instabilities in these flows is important also for atmospheric flow modeling and weather forecasting [START_REF] Afanasyev | On breaking internal waves over the sill in Knight Inlet[END_REF].

The effect of bottom roughness on the entrainment processes has been studied by [START_REF] Hebbert | Collie river underflow into the Wellington reservoir[END_REF], [START_REF] Dallimore | Entrainment and turbulence in saline underflow in Lake Ogawara[END_REF], [START_REF] Fernandez | Bed roughness induced entrainment in a high Richardson number underflow[END_REF]. Other studies on two-layer stably-stratified flows considering the effects of bottom roughness have mostly been devoted to investigate how the bottom generated turbulence affects the two-layer hydraulics [START_REF] Zhu | Non-hydrostatic effects in layered shallow water flows[END_REF][START_REF] Zaremba | Frictional two-layer exchange flow[END_REF][START_REF] Gu | Analytical solution for maximal frictional two-layer exchange flow[END_REF]. A general review of past studies on these investigations not including the effect of rotation is given in the following.

A series of papers by Armi and Farmer in the 1980s [START_REF] Farmer | Maximal two-layer exchange over a sill and trough a combination of a sill and a contraction with barotropic flow[END_REF] analyzed the hydraulics of two-layer flows over a smooth bottom topography. [START_REF] Pratt | Rotating shocks in a separated laboratory channel flow[END_REF] reported that due to frictional effects, the location of a control, located originally at the crest of a bottom sill, could be shifted away from the crest point. [START_REF] Zhu | Non-hydrostatic effects in layered shallow water flows[END_REF] extended the two-layer hydraulic theory by incorporating the non-hydrostatic pressure distribution due to streamline curvature and friction. [START_REF] Anati | Laboratory models of sea straits[END_REF] examined the relative importance of frictional and inertial forces in exchange flows in constant-width channels. [START_REF] Zaremba | Frictional two-layer exchange flow[END_REF] developed a numerical model to study effects of friction on the steady stratified exchange flow which revealed three viscous flow regimes for a converging-diverging connecting channel and further three flow regimes when a sill is introduced (see also the numerical studies of [START_REF] Assaf | Sea starits: a dynamical model[END_REF][START_REF] Ogˇuz | Modeling of hydraulically controlled exchange flow in the Bosphorus Strait[END_REF]. More recently, [START_REF] Gu | Analytical solution for maximal frictional two-layer exchange flow[END_REF] developed a one-dimensional analytical solution to the fully nonlinear problem of two-layer frictional exchange flow within the context of internal hydraulics in a rectangular channel of constant width.

Studies on the interaction between the bottom generated turbulence and the sheared interface include the numerical study of [START_REF] Skyllingstad | Large-eddy simulation of flow over two-dimensional obstacles: high drag states and mixing[END_REF], who used a three-dimensional large-eddy simulation (LES) model to examine how uniformly stratified flow interacts with bottom obstacles in the coastal ocean. [START_REF] Thorpe | A laboratory study of stratified accelerating shear flow over a rough boundary[END_REF] performed experiments of linearly stratified flows down a slope over a rough floor, where the roughness elements were represented by square bars set at regular intervals, studying both the configurations of k-type and d-type as defined in [START_REF] Perry | Rough wall turbulent boundary layers[END_REF]. In his experimental study, [START_REF] Thorpe | A laboratory study of stratified accelerating shear flow over a rough boundary[END_REF] observed the generation of radiating internal gravity waves at the initial stage of the flow and reported turbulent mixing behind the bars due to flow separation but low interaction with the interface between the two layers. He showed that this turbulent layer spread vertically less rapidly than the internal waves and that the rate of spread depends on the separation of the bars. [START_REF] Negretti | Barotropically induced interfacial waves in stratified two-layer flows over a sill[END_REF] showed that in a two-layer stably-stratified flow with pulsating barotropic flow over smooth topography, large-scale structures are generated at the interface between the two layers. Similar structures have been also observed previously by [START_REF] Morin | Supercritical exchange flow down a sill[END_REF] and [START_REF] Fouli | An experimental study of interfacial waves and instabilities in exchange flows over a smooth sill[END_REF]. [START_REF] Negretti | Barotropically induced interfacial waves in stratified two-layer flows over a sill[END_REF] explained these large-scale structures as plunging density currents in the lower layer triggered by the barotropic oscillation. They observed that these structures were generated with roughly the same period as the barotropic oscillation.

Continuing the work in [START_REF] Negretti | Barotropically induced interfacial waves in stratified two-layer flows over a sill[END_REF], this paper is aimed at investigating the effect of enhanced bottom friction on the generation and growth mechanism of these surge-like structures and the related entrainment and mixing processes. Experiments are conducted employing two enhanced bottom roughness strategies. Following the definition of [START_REF] Perry | Rough wall turbulent boundary layers[END_REF], the first strategy is of the d-type, adopting sparse, coarse but tall bottom roughness elements above the sill, while the second strategy corresponds to the k-type, employing dense fine short bottom roughness elements. These experiments will allow us to examine the effect of enhanced bottom friction and both baroclinic and barotropic vorticity generation. Thus the results presented in this paper will deliver novel contributions more representative for natural flow conditions. In particular, the understanding of the flow interaction between the bottom generated turbulence (influenced by bottom friction) and interfacial two-dimensional surge-structures (triggered by the unsteady barotropic flow) will help to develop control methods for influencing the circulation of nutrients and pollutants in inland and coastal waters and in the atmosphere. These flow phenomena are commonly observed in nature as demonstrated by the field observations of [START_REF] Scinocca | Pulsating downslope windstorms[END_REF] and [START_REF] Sherwin | Mixing and advection of a cold water cascade over the Wyville Thomson Ridge[END_REF].

The paper is organized as follows. In Section 2, the experimental design is described. A brief qualitative description of the flow is given in Section 3. In Section 4 the different mechanisms of vorticity production are discussed and specific parameters are defined. Section 5 gives an estimation of the bottom roughness coefficients through comparison to two-layer hydraulic theory. In Section 6 the experimental results are presented and discussed. Section 7 summarizes the paper.

Experiments

Experiments were conducted in a 12 m long and 0.6 m wide basin shown in Fig. 1, which is divided in the middle into two basins, and connected by a channel of reduced width (14.5 cm). A bottom sill has been placed in the channel. The sill shape is described by: z(x) = h s cos 2 (πx/(2L)), for -40 <x<0, and z(x) = h s -x/5, for 0 <x<100, where h s = 20 cm is the height of the sill crest and L = 100 cm is the length of the sill on the right hand side of the sill crest (see Fig. 1). The tank was first filled with fresh water to the desired depth H = 40 cm. A plexiglas barrier was then placed at the sill crest to divide the tank into two reservoirs. A density difference ρ/ρ ≈ 0.4% was produced by adding salt to the water in the left reservoir. The density of the salty water was measured with a density-meter (Anton Paar, DMA 5000). To minimize effects of wave reflections at the end of the reservoirs, two grid plates were built at each end of both reservoir (see Section 3 for a qualitative description of the flow).

Measurements of velocity and concentration fields were obtained using Particle Image Velocimetry (PIV) and Planar Laser induced Fluorescence (PLIF) techniques, respectively. Essential details are given in the following.

Polyamide particles with a mean diameter of 200 m and a density of 1.061 g/cm 3 , were added in both reservoirs as tracer particles for the velocity measurements with PIV. A 10 W Argon-Ion laser operating in multimode (λ 1 = 488 nm, λ 2 = 514 nm) was used as continuous light source. The beam was transmitted through a fiber optic cable to a line generator with spherical lenses. Images of roughly 70 cm × 55 cm were grabbed with a CCD camera (1024 × 1024 pixels), at a frame rate of 10 Hz. The raw image pairs were then processed using a PIV cross-correlation algorithm (software package DaVis, LaVision) to compute the velocity fields, starting with an interrogation window of 32 × 32 pixels and a final window size of 16 × 16 pixels with 50% overlap. Each vector of the resulting vector field represents an area of roughly 0.6cm× 0.6 cm. Given the velocities encountered in the experiments, the error for the instantaneous velocity is approximately 4%.

In concentration measurements Rhodamine 6G was used as dye and was added to the salt water. Its concentration was kept under 70 g/l to assure minimal attenuation [START_REF] Daviero | Refractive Index Matching in Large-Scale Stratified Experiments[END_REF]. Images of 70 cm × 55 cm were grabbed simultaneously with the PIV images with a CCD camera (1280 × 1024pixels) at a frame rate of 10 Hz.

Table 1 lists the experimental conditions. The smooth case was conducted using a smooth bottom, while the sparse and dense cases were performed with two different bottom roughness configurations. In the sparse roughness case, screw anchors were used (see Fig. 2(a)), with sparse spacing of coarse, tall roughness elements. This bottom roughness is similar to d-type [START_REF] Perry | Rough wall turbulent boundary layers[END_REF]. In the dense roughness case, artificial turf was used (see Fig. 2(b)), with a dense close spacing of fine, short roughness elements. This bottom roughness is similar to k-type [START_REF] Perry | Rough wall turbulent boundary layers[END_REF].

Qualitative description of the flow

For a purely baroclinic exchange flow the net flow rate should be zero but as outlined in [START_REF] Negretti | Barotropically induced interfacial waves in stratified two-layer flows over a sill[END_REF], with the experimental set-up described above, an additional unsteady barotropic flow component is superimposed on the baroclinic exchange flow. This is clearly shown in Fig. 3, where the net flow rate time series at the sill crest for each experiment are plotted, normalized with the flow rate scale

q ref = H √ g ′ H,
showing that it oscillates periodically around zero. These normalized net flow rates also give the ratio between the relative magnitudes of the baroclinic exchange currents (q ref ) and the superimposed barotropic oscillation ( H h u dz). Fig. 3 shows that the barotropic contribution is much smaller (about 8-10% for all the experiments) than the baroclinic contribution. Also, the barotropic oscillation period is smaller than the transit time of the flow across the region, which can be estimated with the internal seiche period T s = 2L B /c, with L B being the total basin length and c = √ g ′ z 1 z 2 /(z 1 + z 2 ) the propagation speed of the internal interfacial wave, with z 1 and z 2 being the water depth in the upper and lower layer, respectively (cf. Fig. 1). With a total length of L B = 12 m this gives periods of 359, 375 and 381 s for the smooth, sparse and dense cases, respectively. The flow development at the interface for the three experiments is presented in Fig. 4 by a series of images taken during the maximal exchange regime. In the smooth case the flow is characterized by the generation of two-dimensional structures, generated at the interface due to the superimposed barotropic flow [START_REF] Negretti | Barotropically induced interfacial waves in stratified two-layer flows over a sill[END_REF] leading to large billow-like structures. The interfacial fronts pass right to the sill crest (Fig. 4(a), first and second image) and the flow in the lower layer begins to accelerate down the sill. In the third and fourth images, the growth of the large structure can be clearly observed, while in the following image, it starts to collapse. In this smooth case, the wake behind the surge-like flow can fully develop resulting in significant entrainment. This behavior is periodic and the phenomenon starts again from the beginning (Fig. 4(a), image 8) [START_REF] Negretti | Barotropically induced interfacial waves in stratified two-layer flows over a sill[END_REF].

The dense roughness case shows a different behavior (see Fig. 4(c)): the increase in the water depth of the lower layer is still present at the interface as a result of the pulsating barotropic flow. But the growth and subsequent roll-up mechanisms of the structures can not be observed anymore, because of the enhanced turbulence dissipation due to friction. Without roll-up of the two-dimensional structures, no wake zone is generated. However, the turbulent fluctuations are increased in this case as is discussed more in detail further below.

The sparse roughness case (see Fig. 4(b)) lies in between the behavior of the smooth and the dense roughness case: it behaves like the smooth case in the initial accelerating region near the sill crest (images 1 to 4 in Fig. 4(b)), where a growing two-dimensional structure can be observed. However, in this case, the collapse mechanism does not occur and therefore, no wake region is generated in the lee of the surges. The sparse distributed bottom roughness with tall roughness elements inhibits the roll-up mechanism of the large-scale structures when they reach a certain size and interact with the roughness elements.

Vorticity production

The definition diagram for vorticity generation in a gradually evolving two-layer flow over downslope is given in Fig. 5. Quantities in the upper layer are denoted with the index 1 while quantities in the lower layer with the index 2. In such a flow, different mechanisms are responsible for vorticity production: (1) the vortex stretching due to the variation in height of the channel. (2) The baroclinic generation of vorticity, given by the inclination of the interface. (3) The bottom generated turbulence due to the enhanced bottom roughness. Depending upon the intensity of the interaction between the bottom boundary layer and the interface between the two layers, this results possibly in an accelerated dissipation process of the turbulence produced at the interface. In the following, some parameters are defined, which can express the ratio between the magnitude of each contribution in order to relate the bottom generated turbulence with the turbulence produced by the density and velocity gradients. The starting point for the estimation of these contributions is the vorticity equation [START_REF] Baines | Topographic Effects in Fluids[END_REF]

) Dζ Dt = ζ •∇u + ∇ρ ×∇p ρ 2 + ν△ζ, (1)
where D/Dt denotes the Lagrangian derivative, u = (u, v, w) is the velocity vector, ζ =∇×u the vorticity vector, ρ(x, y, z) the density, p(x, y, z) the pressure, ν the kinematic viscosity, △ the Laplacian operator.

The vorticity production related to the enhanced bottom roughness can be included in Eq. ( 1) through the boundary conditions and can be expressed in the form of the viscous term ν△ζ.

To model the friction source of vorticity it is assumed that the friction arises essentially due to tangential (shearing) forces and that vertical gradients are much larger than horizontal. In fact, the effects related to horizontal gradients are more important for the processes occurring at the interface between the two layers and these are taken into account with the dimensional analysis of the term ζ∇u. Thus, the boundary layer assumptions can be used without any loss of generality, namely that the horizontal gradients are much smaller than the vertical (∂/∂x ≪ ∂/∂z) and that the vertical velocity is small compared to the streamwise velocity (i.e. w ≪ u). Moreover, the transverse velocity v and the transverse velocity gradients ∂/∂y can be assumed negligible as the flow can be treated as two-dimensional in first approximation.

As a starting point to model the bottom friction, the bottom shear stress τ b can be written as follows

τ b ρ 2 = f w 8 u 2 = ν ∂u ∂z , (2)
where ρ 2 is the density of the lower layer fluid, u 2 is the velocity in the lower layer, ∂u/∂z is the streamwise velocity gradient due to the bottom generated shear stress. The relation

√ τ b /ρ = u √
f w /8 has been used, where f w = 4c f , with c f being a quadratic-law friction coefficient. To introduce this term into Eq. ( 1) the Laplacian operator has to be applied on both hand sides of Eq.

(2), leaving to

ν△ ∂u ∂z ∼ ν△ζ ≈ f w 4 ∂u ∂z 2 + ∂ 2 u ∂z 2 u , (3)
where the streamwise and cross-stream variation of the velocity u has been neglected, since ∂ /∂ y<∂ /∂x≪ ∂/∂z. The viscous term in Eq. ( 1) can thus be replaced with the right hand side of Eqs. ( 1) and (3) reads finally as follows

Dζ Dt = ζ •∇u + ∇ρ ×∇p ρ 2 + f w 4 ∂u ∂z 2 + ∂ 2 u ∂z 2 u . (4)
It is noted that by integrating the last term on the right hand side of Eq. (4) in the z direction, the bottom boundary condition reduces to Eq. (2). We recall that Eqs. ( 2) and (3) are only a model which is defined in order to include the bottom friction term in the vorticity Eq. ( 1) and are not used to derive analytically new equations: Eq. ( 4) will be used below to perform an order of magnitude analysis of the single terms.

In the following, the different production terms on the right hand side of Eq. ( 4) are scaled separately.

The generation of y-vorticity due to vortex stretching is given by:

(ζ •∇u) y = ∂u ∂z - ∂w ∂x ∂v ∂y . (5)
Using the continuity equation ∇•u = 0 and applying the boundary layer assumptions Eq. ( 5) gives

(ζ •∇u) y = ∂u ∂z - ∂w ∂x - ∂u ∂x - ∂w ∂z ∼- ∂u ∂z ∂w ∂z . (6)
To evaluate the term ∂w/∂z we note that the variation of the velocity w in the vertical direction is expected to be related to the acceleration down the slope, i.e. ∂w/∂z ∝ u 2 /z 2 d(z 2 + h)/dx (see Fig. 5). The scaling arguments for the estimation of the vortex stretching term are chosen under the assumption that the related vorticity production is mainly caused by the velocity shear at the interface. Taking the vorticity thickness δ ν (a more precise definition of δ ν will be given in Section 6.1) as vertical scale and the velocity difference between the two layers U as velocity scale to estimate the vertical velocity gradient ∂u/∂z, the vortex stretching term is finally approximated as follows

(ζ •∇u) y ∼ ∂u ∂z u 2 z 2 d(z 2 + h) dx ≈ Uu 2 δ ν 1 z 2 sin θ. ( 7
)
where θ denotes the angle of inclination of the slope with respect to the longitudinal direction x. Thus, the contribution to the vorticity due to vortex stretching is a result of both the vertical gradient of the streamwise velocity and the acceleration down the slope. We note that Eq. ( 7) has been written under the assumption that the interface is approximately parallel to the sill slope, d(z 2 + h)/dx ≈ sin θ (see Fig. 5).

The baroclinic production of y-vorticity reads

∇ρ ×∇p ρ 2 = 1 ρ 2 ∂ρ ∂x ∂p ∂z - ∂ρ ∂z ∂p ∂x . ( 8
)
Assuming the horizontal pressure gradient is negligible and using the Boussinesq approximation for small density variations [START_REF] Pawlak | Vortex dynamics in a spatially accelerating shear layer[END_REF]

it follows ∇ρ ×∇p ρ 2 ∼ g ρ ∂ρ ∂x ∼ g ρ ∂ρ ∂n sin θ, (9)
with ρ being the mean density between the two layers. The relation ∂ρ/∂x = ∂ρ/∂n sin θ derives from the flow geometry, in which n is the direction of density gradient (see Fig. 5). For dimensional analysis the vertical length scale δ ρ represents the shear layer thickness and Eq. ( 9) can be approximated as follows

∇ρ ×∇p ρ 2 ≈ g ′ δ ρ sin θ, (10)
Taking as velocity scale the velocity in the lower layer u 2 , the contribution of y-vorticity production due to the bottom roughness can be evaluated as

f w 4 ∂u ∂z 2 + ∂ 2 u ∂z 2 u ∼ f w 4 u 2 δ b 2 + 1 δ b u 2 δ b u 2 , (11)
where δ b = z 2 /2 is assumed to be the vertical scale for the bottom velocity gradient, with z 2 and u 2 being the water depth and velocity in the lower layer, respectively (cf. Fig. 5). The vertical gradient ∂u/∂z is here scaled using the velocity scale u 2 and the vertical length scale δ b ,asfor the friction production of vorticity the vertical velocity gradient is expected to be mainly caused by the shear generated by friction.

Assuming that the vorticity and density gradients are constant across the interfaces, integrating Eqs. ( 10) and ( 11) to obtain the total vorticity produced at a given x-location, amounts to multiplying by δ ν , δ ρ and δ b , respectively. The following interaction parameter can be defined

Baroclinic production

Vortex stretching

= Z v ≡ |δ ρ (∇ρ ×∇p/ρ 2 ) y | |δ ν (ζ •∇u) y | ≈ F -2 u 2 U , (12a)
Friction production Baroclinic production

= Z r ≡ |δ b ((f w /8)△(u 2 ))| |δ ρ (∇ρ ×∇p/ρ 2 ) y | ≈ F 2 ℓ (sin θ) -1 , (12b)
Friction production Vortex stretching

= Z rv ≡ |δ b ((f w /8)△(u 2 ))| |δ ν (ζ •∇u) y | ≈ z 2 ℓ sin θ u 2 U , (12c)
where we recognize that F 2 = (u 2 ) 2 /(g ′ z 2 ) is the single layer Froude number. The length scale ℓ = 2δ b /f w represents a "roughness scale" and F 2 ℓ = (u 2 ) 2 /(g ′ ℓ) is a "frictional Froude number", which can be reinterpreted as a measure of the limiting effects of buoyancy on the velocity acceleration in the lower layer, hindered by friction.

Eq. ( 4) shows that the vorticity related to vortex stretching is balanced by the stabilizing vorticity contribution related to the stratification and to bottom friction. Moreover, while the vorticity generated by the stratification as well as by the vortex stretching are "intrinsic" contributions related directly to the fluid properties, the term resulting from the bottom friction represents an "external" source of vorticity and is built from the boundary conditions. In this sense, the interaction parameters containing the relative contribution of "intrinsic" and the "external" vorticity source are the most interesting parameters. Because there are three parameters defined using three vorticity contributions, they are related to each other and one of them is redundant, i.e.

Z v = Z rv /Z r .
The vorticity parameters Z r and Z rv are plotted in Fig. 6(a) and (b), respectively. In the smooth case the only restoring force is given by buoyancy, while in the rough cases the gap between frictional and baroclinic production is smaller and they both work for stabilization: this explains why in Fig. 6(a) the curves become nearly horizontal in the rough cases earlier compared to the smooth case.

The parameter Z rv is plotted in Fig. 6(b) and it shows to increase very fast for (-0.2 < x/L < 0) for the smooth experiment and for (-0.2 < x/L < 0.2) and then the growth decreases. This change in the slope of the curves is given by the effects of the acceleration down the sill, so that right to the sill crest, vortex stretching increases faster than the friction production of vorticity. Moving downstream the curves become almost horizontal for the two rough experiments as the friction contribution becomes more important, while for the smooth case a growth is still present.

Estimation of roughness coefficients

In this section, results from the PIV measurements are used to estimate the effect of friction. The vertical and horizontal length scales are given by the total water depth H and the sill length L on the right hand side of the sill crest, respectively. As the interfacial instabilities are primarily dominated by the unsteady barotropic flow component and scale with the total water depth, we choose as velocity scale √ g ′ H. The bottom roughness coefficients were estimated using the measured flow rates in the upper layer for all three experiments at positions near the sill crest, where the entrainment between the two layers can be neglected [START_REF] Morin | Supercritical exchange flow down a sill[END_REF]. We expect the flow rates to be decreased in the rough cases, as the bottom roughness effectively results in an increased height of the sill. The normalized flow rate in the upper layer of the rough experiments was thus compared to that of the smooth experiment to obtain the ratio q c,r /q c,s , where q c,r and q c,s are, respectively, the flow rate in the upper layer at the sill crest for the rough (index r) and the smooth (index s) experiments. The ratio gives a value of 97% for the sparse roughness case and 93% for the dense roughness case as shown in Fig. 7, a value averaged between -0.05 < x/L < 0.05. This average has been done because it is well known that the bottom friction, as well as the interfacial friction, cause the internal hydraulic controls to be shifted from the theoretical positions at the sill crest and the channel exit. However, the determination of this location is not easy because of entrainment and friction effects [START_REF] Pratt | Rotating shocks in a separated laboratory channel flow[END_REF][START_REF] Gu | Analytical solution for maximal frictional two-layer exchange flow[END_REF] as well as due to streamline curvature [START_REF] Zhu | Non-hydrostatic effects in layered shallow water flows[END_REF] and so is omitted within the scope of this study.

An equivalent sill height can be estimated with the help of internal hydraulic theory. Our flow is controlled by two hydraulic control located at the sill crest and the channel exit [START_REF] Armi | Maximal two-layer exchange through a contraction with barotropic net flow[END_REF]. We adapt the control curve in Fig. 3 in [START_REF] Zhu | Control curves for two-layer flows[END_REF] for the sill crest control by changing the value of h s to obtain the above estimated ratios q 1c,r /q 1c,s for the critical flow rate (correspondent to the intersection between the curve of the sill crest control and the channel exit control). The so obtained equivalent sill heights are h ′ = 0.510 and h ′ = 0.517 for the sparse and dense roughness configurations, respectively. With the water depth of 40 cm used in all the performed experiments, this corresponds to heights of 20.4 cm and 20.7 cm for the sparse and dense configuration, respectively (see Table 1).

The internal hydraulic energy was defined as E = h + z 2 + q 2 /g ′ (1/z 2 2 -1/z 2 1 ) and calculated using the measured flow rate and interface position and is plotted in Fig. 8, with the continuous line representing the inviscid hydrostatic prediction of E/H = 0.75, which can be calculated following the method outlined in [START_REF] Zhu | Control curves for two-layer flows[END_REF]. While the internal hydraulic predictions are in very good agreement for experiment 1, it overestimates the internal energy for experiments 2 and 3 on the right of the sill crest, from x/L = 0.1onward. In these experiments internal energy is obviously dissipated due to frictional effects and this is the reason for the poor matching between experimental data and theoretical predictions. [START_REF] Zhu | Hydraulics of exchange flows[END_REF] gave a relation to estimate the energy loss in longitudinal direction due to wall and interfacial friction. Considering only the contribution given by the bottom boundary, an estimation of its friction coefficient can be made using the rearranged relation given in [START_REF] Zhu | Hydraulics of exchange flows[END_REF]:

f w = 2 u 2 2 z 2 d(E/H) dx H L c -τ * I (z 1 + z 2 ) z 1 z 2 (13)
where (dE/H)/dx is the measured slope of the energy decrease in longitudinal direction (cf. Fig. 8), L c is the length of the connecting channel (cf. Fig. 1(a)) and τ * I =-ρu ′ w ′ is the measured interfacial shear stress between the two layers normalized with ρgH , calculated using the measured values for u ′ w ′ (averaged over time) at the interface positions and using the mean measured densities in the lower layer ρ. The water depths z 1 and z 2 are normalized with the water depth H and the velocity u 2 with the velocity scale √ g ′ H. The interfacial shear stress along the longitudinal direction is plotted in Fig. 8(c) showing the largest values for the dense roughness case, followed by the smooth case and finally the sparse roughness case. The so obtained estimated friction coefficients are f w = 0.024 and f w = 0.018 for the sparse and dense roughness configuration, respectively.

At first glance this seems to be in contradiction with the estimated equivalent sill heights: in the dense roughness case a higher equivalent sill height h ′ is calculated, however resulting in a reduced friction coefficient f w . This is principally due to the fact that in the dense roughness case the interfacial shear stress τ * I is larger as compared to the sparse roughness case (cf. Fig. 8(c)) because the interaction between the bottom boundary layer and the interface is considerably larger in the dense roughness case compared to the sparse case. On the other hand, the depth of the lower layer z 2 is reduced in the dense case as compared to the sparse roughness case and thus also the flow rate. All these effects result in reduced bottom roughness coefficients (cf. Eq. 13) and flow rates for the dense roughness case. This demonstrates that in a two-layer flow the magnitude of bottom roughness is also influenced by the interaction between the bottom boundary layer turbulence and that at the interface.

Discussion

Mean flow characteristics

In Fig. 9, the averaged velocity fields U = √ u 2 + w 2 (left column) and the Reynolds-stress u ′ w ′ distribution (right column) are shown for all three experiments. In the rough cases the velocity difference between the two layers is lower and as bottom roughness inhibits acceleration down the slope. The Reynolds stresses are significantly higher in the two rough experiments in a thinner shear layer. The vorticity and density thicknesses, first mentioned in Section 4, were obtained from the inverse slope of the best-fit line through the normalized velocity profile between the 15 and 85% values [START_REF] Pawlak | Mixing and entrainment in developing stratified currents[END_REF]: respectively, where ū and ρ are the normalized velocity and density, ranging from 0 to 1. These parameters are plotted for all the experiments in Fig. 10.

δ ν = dū dz | ū=0.
The vorticity thickness shows a faster increase in the smooth case (see Fig. 10(a)), followed by the dense roughness case and, finally, the sparse roughness case. The density layer thickness (Fig. 10(b)) is larger right to the sill crest for the smooth case while it shows smaller values for the rough cases. The wake behind the pulsating surge-like currents observed for the smooth experiment can not develop right to the sill crest, which results in a reduced increase of the shear and density layer thickness downstream of the sill crest. It is worth noting that in the dense roughness case the growth of the vorticity thickness fits between the other two experiments, while density thickness has the smallest values for this experiment. This can be explained by the fact that in the sparse roughness case the velocity gradients in the velocity shear layer are much larger than those in the dense roughness case thus resulting in reduced values as compared to the dense roughness case. However, density gradients in the density shear layer are larger for the dense roughness case resulting in the smallest values observed in Fig. 10(b).

The configuration with dense roughness elements is more effective in damping the formation of the two-dimensional structures at the interface compared to the sparse configuration. Sparse spacing of coarse, tall roughness elements act almost as single disturbance bodies and the turbulence produced between the elements is not interacting so intensively with the interface as compared to the dense configuration.

Due to the larger height of the roughness elements in the sparse roughness case the growth process of the large-scale surges generated at the interface is disturbed and the collapse of these surges is hindered, so that no wake zone can be observed behind them. In the dense roughness case, the velocity gradients in the lower layer are much stronger than in the sparse roughness case (cf. Fig. 11(a) and(b)) and also the mixing layer is growing faster and becomes larger in the dense roughness case than in the sparse roughness case (cf. Fig. 10): this suggests that the interaction between the boundary layer and the velocity shear interfacial is more intensive for the dense roughness case than for the sparse roughness case. In the sparse roughness case the turbulent bottom layer spreads vertically less rapidly than the two-dimensional structures generated at the interface due to baroclinic/barotropic effects. The effect of the roughness can also be noted on the density layer properties. The normalized concentration profiles are plotted in Fig. 12(a): the concentration profiles become sharper when the roughness increases. This is also demonstrated in Fig. 12(b)-(d), where the concentration at the density interface is compared to the mean concentration in the density layer for the smooth, the sparse and the dense roughness case, respectively. As the roughness increases, the gap between the data increases remarkably. We note that in fact, if one looks at the instantaneous density profiles, they show sharper density interfaces in the smooth case as compared to the rough cases, but in the average the results show the contrary.

In Fig. 13 the vertical profiles of the Richardson numbers Ri =-g ρ (∂ρ/∂z) (∂u/∂z) 2 ( 14) are plotted at three different longitudinal sections. The first noticeable difference is that the highest Richardson numbers are observed at higher vertical positions z/H in the smooth case as compared to the bottom roughness cases at all longitudinal sections. This suggests that in the bottom roughness cases the strongest density gradients, or the most unstable regions, are found at lower vertical positions as compared to the smooth case. Also interesting to note is that the thickness of the region with non-zero Ri is increasing in the longitudinal direction for the smooth and the dense roughness case, indicating a growing mixed layer, while it decreases in the sparse roughness experiment (cf. Fig. 10). These results are also consistent with those presented in Figs. 12 and 17. The averaged horizontal (left column) and vertical (right column) Reynolds transports, u ′ c ′ and w ′ c ′ , respectively, are plotted in Fig. 14 normalized using the velocity scale √ g ′ H and with the maximal concentration. Positive values represent mass transport from the lower salty layer into the upper fresh water layer, while negative values represent the transport of fresh water into the lower layer. The largest values of the buoyant transport in both directions are observed in the smooth experiment, due to the large concentration fluctuations in the lower layer at the density interface originated by the periodic passing of the large-scale surges. The dense roughness case presents a similar buoyant transport as the smooth case, due to the intensive interaction between the bottom turbulence and the interface. The concentration fluctuations are strongly reduced in the sparse roughness case as the collapse of the surges is hindered, consequently resulting in a reduced turbulent transport. This also explains why the thickness of the region with the highest turbulent transport is much larger in the smooth case as compared to the rough cases. However, bottom roughness causes larger Reynolds stresses at the sheared interface, as demonstrated in Fig. 9, right column. This is also consistent with the results presented in Fig. 10. It is also worthwhile noting that the turbulent transport increases moving to the right of the sill crest for the smooth bottom case, while they are decreasing in the longitudinal direction in the rough cases. In the rough cases the surge structures initially grow, but further downstream the collapsing mechanism and the further growth in the sparse and dense bottom roughness experiments are hindered by friction, thus resulting in reduced concentration fluctuations. This is also consistent with the results presented in Fig. 16(a). These results relative to the turbulent transport distribution are also consistent with the entrainment rates presented in Section 6.3(Fig. 17 the flow moves down the slope, the rough experiments show an opposite behavior, with the standard deviation decreasing in longitudinal direction. In the sparse roughness case there is an initial increase in the region 0 < x/L < 0.15, and then a continuous decrease can be observed, indicating an initial growth, but a rapid collapse of the large-scale structures at the interface. In the dense roughness case there is a constant decrease, suggesting that no two-dimensional structures are generated at the interface. Moreover, the standard deviation for the rough experiments is higher as compared to that of the smooth case in the initial developing region x/L < 0.3, while in the growing region of the large scale structures, the fluctuations of the density interface in the smooth case become larger than those of the rough experiments. This is also consistent with the visual observations described above.

The effect of locally enhanced bottom roughness on interfacial large-scale structures

Fig. 16(b) shows an estimation of the horizontal (empty symbols) and vertical (filled symbols) length scales of the large, two-dimensional structures at the interface. They were calculated using the time scale T I obtained from the temporal autocorrelation functions of the horizontal and vertical velocity fluctuations at the interface for x/L = 0.24, and the mean velocity shear U/2 as convective velocity scale, e.g. L I = T I U/2. For the dense roughness case, both the horizontal and vertical sizes of the large-scale structures at the interface are reduced, while for the sparse roughness case only the vertical scale is reduced, as compared to the smooth case, and the horizontal scale is roughly the same.

The effect of locally enhanced bottom roughness on mixing and entrainment

Given the velocity field data, estimates of the entrainment coefficient can be obtained. Following [START_REF] Ellison | Turbulent entrainment in stratified flows[END_REF], the entrainment coefficient is defined as

α e = 1 V dq dx with V = u 2 dz u dz ( 15
)
where q is the flow rate per unit width in the layer of interest and V is a representative velocity for the layer. Here, we also use the relation proposed by [START_REF] Dallimore | Entrainment and turbulence in saline underflow in Lake Ogawara[END_REF], where the entrainment coefficient is defined as follows

E D = C k C 3/2 D + C s Ri + 10(C k C 3/2 D + C s ) (16)
where C k and C s are coefficients measuring the efficiency of the boundary-introduced turbulent kinetic energy and of the local shear production, respectively. Past experimental data examined by [START_REF] Sherman | Turbulence and mixing in stably stratified waters[END_REF] suggested universal values for C k = 2.2 and C s = 0.2. Ri = g ′ z 2 /u 2 2 is the Richardson number as defined also in [START_REF] Ellison | Turbulent entrainment in stratified flows[END_REF] and C D is the bottom drag coefficient. Fig. 17(a) shows the entrainment coefficients for all the performed experiments and the higher values are found in the region 0 < x/L < 0.15. The overall higher entrainment coefficients are observed for the dense roughness case, which are of the same order of magnitude of the entrainment coefficients found by [START_REF] Pawlak | Mixing and entrainment in developing stratified currents[END_REF], [START_REF] Morin | Supercritical exchange flow down a sill[END_REF] and [START_REF] Fouli | An experimental study of interfacial waves and instabilities in exchange flows over a smooth sill[END_REF], approaching the value 0.1. The entrainment coefficients for the smooth case are similar to those observed for the dense roughness case, while the sparse roughness case has the lowest values. This is somehow contradictory, because bottom roughness normally increases the mixing [START_REF] Dallimore | Entrainment and turbulence in saline underflow in Lake Ogawara[END_REF][START_REF] Fernandez | Bed roughness induced entrainment in a high Richardson number underflow[END_REF]. However, in the flow treated in this study, there are two main sources for mixing between the upper and lower layer: the first one is given by the wakes developed by the large-scale structures periodically generated at the interface and triggered by the barotropic oscillation, while the second one is given by the small-scale, bottom generated turbulence. In the smooth experiment the main source of entrainment is given by the wake region developed in the collapsing phase of the large-scale surges mechanism. In the dense roughness case the main source of entrainment is given by the bottom generated turbulence due to the intensive interaction between the bottom boundary layer and the interface. In the sparse roughness case, the bottom roughness inhibits the collapsing phase of the large-scale barotropic surges and thus, the wake region in which entrainment normally takes place. Moreover, the bottom generated turbulence interacts less intensively with the interface in this case as compared to the dense roughness case. Both these effects result in reduced entrainment coefficients as compared to the other two experiments. These results are also briefly summarized in Table 2. lence. In the sparse roughness case the bottom roughness inhibits the collapsing phase of the large-scale structures and thus the wake region in which entrainment normally takes place. Moreover, the interaction between the bottom boundary layer and the interface is weak. Both these behaviors result in reduced entrainment coefficients as compared to the other two configurations (see Table 2).

Fig. 1 .

 1 Fig. 1. Sketch of the experimental set-up. (a) Plan view and (b) side view.

Fig. 2 .

 2 Fig. 2. Sketch of the roughness used in the rough experiments. (a) The sparse roughness case with sparse spacing of coarse, tall roughness elements (screw anchors). (b) The dense roughness case with a dense close spacing of fine, short roughness elements (artificial turf).

Fig. 3 .

 3 Fig. 3. Time series of the normalized net flow rate at the sill crest showing to oscillate around a zero value. This results in an unsteady barotropic flow component on the baroclinic exchange flow.

Fig. 4 .

 4 Fig. 4. Series of instantaneous images of the smooth case (a), the sparse roughness case (b) and the dense roughness case (c) with dye (Rhodamine 6G) mixed in the lower layer (salt water). The time lag between the images is 2 s. The image size is 55 cm (vertical) ×70 cm (horizontal). Dashed lines follow the development of the large-scale interfacial structures.

Fig. 5 .

 5 Fig. 5. Definition diagram for vorticity production in a gradually evolving two-layer flow over downslope.

Fig. 6 .

 6 Fig. 6. Vorticity parameters expressing the ratio between the three main contribution of vorticity production in a two-layer stratified flow down a slope with enhanced bottom roughness. (a) Z r as ratio between the friction and the baroclinic sources and (b) Z rv as ratio between the friction and the vortex stretching sources vs. x (cf. Eqs. (12b) and (12c)).

Fig. 7 .

 7 Fig. 7. Normalized flow rate for the rough experiments compared to that of the smooth experiment.

Fig. 8 .

 8 Fig. 8. Comparison between experimental data (symbols) and theoretical prediction using the hydraulic inviscid hydrostatic prediction (continuous line) (a and b) and experimental interfacial friction (c). (a) Total internal hydraulic energy E vs. x, (b) mean interface positions calculated as z 2 + h where z 2 = (z| ū=0.15 -z| ū=0.85 )/2 and (c) dimensionless interfacial friction τ * I = ρu ′ w ′ estimated using the measured mean values for u ′ w ′ at the interface positions and using the mean measured densities in the lower layer ρ, normalized with ρgH .

Fig. 9 .

 9 Fig. 9. Mean flow characteristics in the measured flow field. Normalized averaged velocity field U = √ u 2 + w 2 (left column) and normalized Reynolds stresses u ′ w ′ distribution (right column).

Fig. 10 .

 10 Fig. 10. Time averaged quantities for the performed experiments. (a) Vorticity thickness vs. the longitudinal direction and (b) density layer thickness.

Fig. 11 .

 11 Fig. 11. Measured velocity profiles at different longitudinal sections averaged over 10 barotropic cycles for (a) the sparse roughness case and (b) dense roughness case. The velocity gradients in the lower layer are larger in the dense bottom roughness configuration (b) as in the sparse configuration (a).

Fig. 12 .

 12 Fig. 12. Concentration characteristics for the performed experiments. (a) Averaged density profiles at different sections: smooth case (continuous line), sparse roughness case (dotted line) and dense roughness case (dashed line). Averaged concentration at the density interface and averaged concentration in the density layer δ ρ for the smooth case (b), the sparse roughness case (c) and the dense roughness case (d).

Fig. 13 .

 13 Fig. 13. Vertical distribution of the Richardson number (Eq. (14)) at three different longitudinal sections.

  (a)).

Fig. 15

 15 Fig. 15 shows the interface fluctuation record for a time series of 400 s duration, constructed from a vertical cut at a fixed location in the spatial image, i.e. at x/L = 0.24. The vertical fluctuations of the density interface as well as the horizontal size of the large-scale structures are visibly reduced for the rough cases as compared to the smooth case. Fig. 16(a) shows the standard deviation of the density interface fluctuations shown in Fig. 15 as a measure of the growth rate of the large-scale two-dimensional structures. It is worth noting that while for the smooth experiment there is a constant increase of the standard deviation as

Fig. 16 .

 16 Fig. 16. (a) Standard deviation of the normalized density interface fluctuations; (b) estimated horizontal (empty symbols) and vertical (filled symbols) length scales of the large, two-dimensional structures at the interface.

Fig. 17 .

 17 Fig. 17. (a) Entrainment coefficients of the upper-layer fluid along the longitudinal direction and (b) entrainment coefficients compared with the relation proposed by Dallimore et al. (2001) vs. the Richardson number Ri. Symbols represent averaged entrainment coefficients of the performed experiments (smooth case •, sparse case , and dense case ⋆), while the curves represent Eq. (16) for different bottom drag coefficients c D .

Table 1

 1 Details of the performed experiments

	Experiment properties	Smooth	Sparse	Dense
	g ′ (cm s -2 )	4.47	4.1	3.97
	Bottom configuration	Smooth	Sparse	Dense
	Mean height of roughness elements (cm)	-	3.5	1.6
	Mean spacing (cm)	-	3.0	0.1
	Equivalent sill height, h ′ H (cm)	20.0	20.4	20.7
	Roughness coefficient, f w	0.01	0.024	0.018
	g ′ is the reduced gravitational acceleration, h ′ is the equivalent sill height. The roughness coefficient f w was calculated
	using Eq. (13).

Acknowledgement

The authors would like to thank the German Research Foundation (DFG Ji 18/12-1) for its support in conducting this research.

In Fig. 17(b), the averaged entrainment quantities reported in all the experiments are plotted (symbols) versus the Richardson number Ri as defined in [START_REF] Ellison | Turbulent entrainment in stratified flows[END_REF]. The lines represent the prediction proposed by [START_REF] Dallimore | Entrainment and turbulence in saline underflow in Lake Ogawara[END_REF] as in Eq. ( 16) for different values of the drag coefficient. Increasing the drag coefficient should also increase the entrainment. This is only partially valid for the dense roughness case, as compared to the smooth experiment. For the sparse roughness case the entrainment is lower than in the other two cases, given the same Richardson number. The prediction by [START_REF] Dallimore | Entrainment and turbulence in saline underflow in Lake Ogawara[END_REF] overestimates the entrainment coefficients observed here.

Summary and conclusions

Results of an experimental study on stratified exchange flows down a submerged slope were presented. Three different types of bottom roughness configurations have been used in the experiments, namely a smooth bottom and a sparse and a dense distribution of bottom roughness. By dimensional analysis of the vorticity equation, three parameters have been defined (one of them redundant), in order to analyze the weight of each contribution of vorticity.

Bottom friction coefficients and an equivalent sill height have been estimated through comparison of experimental data with the internal hydraulic theory. Internal energy was found to decrease in the longitudinal direction if bottom roughness is present, while the internal hydraulic theory predictions agree well with the experimental data in the smooth case. The sparse bottom configuration presents the largest bottom friction coefficient f w however having a smaller equivalent sill height as compared to the dense configuration. This demonstrates that in a two-layer flow the value of the bottom roughness coefficient strongly depends on the interfacial friction which is related to the interaction between the bottom boundary layer and the overlying interface.

The different bottom roughness elements have been shown to behave differently with respect to the interfacial wave activity: enhanced bottom roughness has shown to intensify the interaction between the lower layer and the sheared interface, resulting in hindering the growth (in the dense roughness case) or the collapse (in the sparse roughness case) of large-scale surge-like flows (see Table 2). These behaviors also causes the Reynolds stresses to increase in a thinner sheared interface as bottom roughness increases, while the turbulent transport decreases in the sparse roughness case. The length scales of the large-scale surges has been estimated revealing a reduction of their size if enhanced bottom roughness is present.

Finally, two main sources for mixing have been identified: the first one is given by the wakes developed in the lee of the large-scale structures, while the second one is given by the smallscale, bottom generated turbulence. The entrainment in the smooth experiment is predominantly caused by the wake region developed in the collapsing phase of the large-scale surges. In the dense roughness case, the main source of entrainment is given by the bottom generated turbu-