Claudine Chamoreau
email: [claudine@vjf.cnrs.fr

Purepecha

Background

Purepecha (p'orhépecha o tarascan) is classified as an isolated language, spoken by around 110,000 people (10% of them monolingual), in the state of Michoacan, in the west of Mexico. Spanish was introduced in the 16 th century, and became the official language of Mexico, where more than about a hundred languages are still spoken. It gained more importance with the linguistic policies of the Mexican Independence and Revolution, in the 19 th and in the 20 th centuries respectively. Spanish functions as a prestigious language, and is connected to education, a better standard of living, oral and written media, religion, administration, commerce, and employment.

Nevertheless, Purepecha, in 2003, acquired (like the other indigenous languages spoken in Mexico) the status of official language. In general, Purepecha is used only orally; it having been established as a written language very recently, and only used in that mode by a few individuals (specifically, the intellectual-speakers or the teachers). The language is spoken by 28% of the Purepecha children aged between 5 and 14, this data indicating that Purepecha is not generally transmitted to the younger generation, who prefer to learn and use Spanish. Moreover, the situation is not homogeneous in all the communities. In some villages, the language functions for communication among all family members and friends (salutations and discussions at home, in the streets, in the shops or markets, and in children's games). In other communities, only the middle-aged and older people speak Purepecha.

Spanish has been the principal contact language for many centuries, however, before the Conquest, there were speakers of other languages in the area -mostly Nahuatl (Uto-Aztecan family), and Otomi (Otopamean family). The influences of these languages in Purepecha has not been studied in detail, but one hypothesis has been proffered regarding constituent order. Purepecha exhibits all the traits of an SOV language: a) tense, aspect and modal markers follow the verb, b) postpositions, c) suffixes almost exclusively, d) case markers, e) main verbs precede inflected auxiliaries, f) genitives can precede the head noun, and g) relative clause can precede the head noun. Nevertheless, in the Lake Patzcuaro area, Purepecha has become SVO [START_REF] Capistran | Variaciones de orden de constituyentes en p'orhépecha. Topicalización y focalización[END_REF]. This order has been attested since the 16 th century, and has become progressively more widespread since that time [START_REF] Villavicencio | P'orhépecha kaso sïrátahenkwa: desarrollo del sistema de casos del purépecha[END_REF]. Considering that Nahuatl -and Otomi-present a verb-initial structure, this change probably has its roots in areal contact prior to the 16 th century, with the subsequent influence of Spanish, an SVO language, continuing the process.

In the present chapter, I will concentrate on the influence of Spanish contact on Purepecha, specifically, on the grammatical structure. related to this contact are found in the areas of phonology, morphological typology, nominal and verbal structures, other parts of speech, constituent order, and syntax. This paper deals with the dialect of Jaracuaro (denoted Jr), a peninsula in Lake Patzcuaro, however, when necessary, I use data from other varieties. Purepecha varieties are more or less mutually intelligible, nevertheless, great sociolinguistic differences exist between them (Chamoreau 2005). Most of the data considered for this paper are the result of my own field research projects carried out over a period of fifteen years.

Phonology

In the phonological system of Purepecha, two phonemes -that are not shared with Spanish -have been influenced by Spanish: the retroflex /ɽ/, a consonant, and the high central vowel /ɨ/. In some varieties (for example, Cuanajo), Purepecha has a phonological opposition between the retroflex /ɽ/ and the flap /r/ (e.g. jurani 'to make somebody cough'/ juɽani 'to come'), however, in certain varieties, this opposition no longer exists; the retroflex becomes either a flap, losing the retroflex/flap opposition, or a lateral, a phoneme probably borrowed from Spanish. Purepecha conserves an opposition, but shows a new lateral/flap feature. In general, the lateral only appears in Spanish loanwords such as azuli 'blue' (from Spanish 'azul'), or limoni 'lemon' (from Spanish 'limon'). However, in some varieties (for example, Comachuen, Arantepacua), young and middle-aged speakers use the lateral (jolempiri 'teacher'), while the older generation uses the flap (jorempiri), or the retroflex (joɽempiri). The use of the lateral in Purepecha words reveals the replacement of the Purepecha phoneme by the Spanish phoneme. Currently, Purepecha is acquiring a new phonological opposition (Chamoreau 2002a).

The high central vowel /ɨ/ is used after /ts/, /tsh/ and /ʃ/, and a phonological opposition appears between /ɨ/ and the high front vowel /i/ (e.g. tsiriri 'rib'/ tsɨriri 'paste'; kheʃi 'shoulder'/ khaʃɨ 'shape').

Nevertheless, particularly in the varieties which have lost the retroflex /ɽ/, and have transferred the lateral /l/, and in other varieties, in the case of the young and middle speakers, the high central vowel /ɨ/ is no longer used, and /i/ replaces /ɨ/ (tsiriri 'paste', khaʃi 'shape'). The phonological system of these varieties has lost a vowel, and, accordingly, presents the same vowel system as Spanish (/i/, /u/, /e/, /o/, /a/).

Morphological Typology

Purepecha has not undergone an important re-structuring of its typological profile. It is an agglutinative and synthetic language that comprises a very elaborated derivational verbal system. For example, for the passive, the verb presents a derivational verbal suffix na (1), and in order to express the equational constructions ( 2) the e suffix is used. In certain varieties, the suffix is i :

(1) Tʃkurhi kuɽi-ra-na-ʃ-ti xwata-ɽu. firewood burn-CAUS-PASSIV-AOR-ASS3 hill-LOC 'The firewood was burned on the hill.' (Jr)

(2)

Xwánu xoɽempiri-i-ʃ-ti. John teacher-PRED-AOR-ASS3 'John is a teacher.' (Jr) Nevertheless, Purepecha exhibits new tendencies, in which analyticperiphrastic constructions appear. Passive (3) and equational (5) periphrastic structures adapt Purepechan morphemes to Spanish patterns without the transfer of linguistic material, which suggests that contactinduced grammaticalization processes have taken place.

The passive periphrastic construction emerges from a patient-oriented resultative participle plus xa 'be there'; a verb which became an auxiliary. Evidence supporting the consideration of this construction as a remodeling of the structure (PAT) includes: a) Passive constructions involving passive participles appear in Indo-European languages, and are very rare in the Americas (Haspelmath 1994); b) the agent is introduced as an oblique complement by using the postposition ximpo (3) in the same way as the Spanish passive construction with ser, whereas this is generally impossible in the Purepecha passive derivational construction (1); c) The subject is always the patient, as in Spanish, whereas, in the derivational passive structure, the subject is the divalent-patient or the trivalent-recipient (Chamoreau in press); d) the younger generation use a passive periphrastic construction with the xinte 'be' copular verb (4), treated as the Spanish ser auxiliary, calquing the Spanish Aux.-Part. Order, whereas, in the passive periphrastic construction with xa (3), the Purepecha Part.-Aux. order is preserved:

(3)

Tʃkurhi kuɽi-kata xa-ɽa-ʃ-ti xutʃari firewood burn-PARTPP be there-FT-AOR-ASS3 POS1PL tata ximpo. father INST 'The firewood was burned by my father.' (Jr) (4)

Enka no u-a-ka xuramukwa-nkuni xinte-a-ti SUB NEG do-FUT-SUBJ law-COM be-FUT-ASS3 ʃuka-kata. dispute-PARTPP 'If he does not respect the law, he will be punished.' (Jr)

The analytic equational construction with xinte 'be' is an internallymotivated reanalysis, from a demonstrative to a 'be' verb used as a presentative (Chamoreau 2006). As a result of the influence of Spanish, many young people prefer to use the verb xinte (5) rather than use the derivational construction (2). Xinte appears essentially with nouns and pronouns. Many young people use xinte solely with adjectives (6) indicating a quality which refers to identity, and which is independent of the situation, as in 'ser' in Spanish. In ( 5) and ( 6), the Spanish SVAdj. order is a calque. This is a construction that is in opposition to the construction with xa (7) which expresses a relative quality dependent on the situation, as in 'estar' in Spanish. With xa, the order is generally the Purepecha SAdj.V order, although it is possible to find the Spanish SVAdj. Order.

(5)

Xwánu xinte-ʃ-ti xoɽempiri. John be-AOR-ASS3 teacher 'John is a teacher.' (Jr) (6)
Iʃu pakanta, kwhiripu miri-kwali-s-p-ti here Pacanda people forgot-MID-AOR-PAS-ASS3 ya ima-ni atʃati-ni ka myá-ntha-ʃa-p-ti already DEM-OBJ man-OBJ and think-IT-PROG-PAS-ASS3 eski ima xinte-p-ka riko. SUB DEM be-AOR/PAS-SUBJ rich 'Here in Pacanda, people had forgotten this man. They used to think that he was rich.' (Pc) ( 7)

Naranʃa téri xa-ɽa-ʃ-ti. orange sweet be there-FT-AOR-ASS3 'The orange is sweet.' (Jr)

Nominal structures

Changes that could have arisen through the influence of Spanish include the tendency to use the plural marker itʃa, and the object case marker ni, with inanimate entities (8). Traditionally, the plural and object case markers are only obligatory for animate and definite entities [START_REF] Villavicencio | P'orhépecha kaso sïrátahenkwa: desarrollo del sistema de casos del purépecha[END_REF].

(8) Ints-ku-ʃɨn-ti=kʃɨ tsɨtsɨki-itʃa-ni. give-3APP-PROG-ASS3=3PL flower-PL-OBJ 'They used to give her flowers.' (Jr)

The Spanish diminutive suffix has become productive in Purepecha, however, only the masculine ito is used, pronounced ito or itu. Gender does not exist in Purepecha. This suffix is used with nouns, adjectives (9a), and classifiers (9b). This latter exhibits an adaptation to the Purepecha nominal phrase.

(9) a. Witsintikwa phakha-ra-ʃ-ka=ni xantiakhu-itu. yesterday stay-MID-AOR-ASS1/2=1 alone-DIM 'I stayed alone yesterday.' (Jr) b. Ma itʃakwa-itu wítʃu-ni ká-ʃɨn-ka=ni.

one long-DIM dog-OBJ own-HAB-ASS1/2=1 'I have one little dog.' (Jr)

Verbal structures

There are only a few contact phenomena in the verbal structures. The most relevant of these is the transfer of the ser/estar semantic opposition (PATinfluence), being adapted as a xinte/xa dichotomy ( §3). As a result of the influence of Spanish, the constructions with the verb xinte 'be' gain a greater semblance to the Spanish construction with the verb 'ser': passive constructions (4), equational constructions (5), and attributive constructions (6). Many young speakers integrate an idiomatic expression, dejar de ser, that they have calqued from the Spanish (10):

(10) Xorentpherakwa xurakhu-sɨn-ti xinte-ni ísɨ. education let-HAB-ASS3 be-INF thus 'The education ceased to be like that.' (Pc)

In the same way, the constructions with xa 'be there' have adopted the values of the Spanish 'estar' structures: passive constructions (3), and attributive ones (7).

Other parts of speech

Purepecha shows a significant number of Spanish loans in the category 'other parts of speech'. Most loans are of the MAT type, but some cases of PAT-influence have been established within the numeral system and discourse markers.

The numeral system in Purepecha is vigesimal, and the remodeling to a decimal system is due to Spanish influence. The numbers from 1 to 6, and 10 and 20 are generally known and used, but younger speakers prefer to use Spanish numbers except for numbers below 5. Counting and adding are generally performed using Spanish numbers. There are no contact phenomena in quantifiers.

The indefinite pronoun siempre 'always' is highly integrated, whereas other indefinite pronouns appear only occasionally. Siempre is used, with the vowel adaptation siémpri, by all generations (11), and has gained ground relative to the Purepecha indefinite pronouns mameni and menkhu, which also express time ( 12 POS1PL father always POS1-RES be there-FT-HAB-ASS3 'Our father is always at home.' (Jr)

Purepecha has borrowed two Spanish coordinating connectors: o 'disjunction' (13) and pero 'contrast' ( 14). The Spanish connector y 'addition' has not been borrowed. In this case, the Purepecha connector ka 'and' is used (15). The connectors o and peru are concepts formerly unmarked in Purepecha. The native Purepecha marker ka 'addition' is used to combine clauses. Pero can additionally express a change of topic ( 16). On the phrasal level, o can be used to combine phrases (15). ( 13)

Tʃi tʃentʃeki urapi-ʃ-ki o tʃi kawayu POS2 donkey be white-AOR-INT or POS2 horse tuɽipi-ni. be black-INF 'Is your donkey white, or is your horse black?' (Jr) ( 14)

Xi wé-ka-ʃa-p-ka ni-ra-ni péro no 1 want-FT-PROG-PAS-ASS1/2 go-FT-INF but NEG ú-ʃ-ka ʃaná-ra-ni. be able-AOR-ASS1/2 walk-MID-INF 'I wanted to go, but I was not able to walk.' (Jr) (15) Ínts-a-sɨn-ti=ksɨ ima-nki aɽi-s-ka give-3PLOBJ-HAB-ASS3=3PL DEM-SUB tell-AOR-SUBJ ya tétʃakwa ka wiraterakwa ka already wine and alcohol and sáni tsíri o sáni ʃapumata. few corn or few roasted corn 'They used to give them what they asked for: wine and alcohol, and a little corn, or a little roasted corn.' (Tr) ( 16)

Atʃati pyá-ʃ-ti yámintu ampe nénki man buy-AOR-ASS3 all what SUB wé-ta-ɽi-a-ka ima péru want-CAUS-body-FUT-SUBJ DEM but ni-ntha-ʃ-ti=kʃɨ ya anima-itʃa. go-CENTRIF-AOR-ASS3=3PL already soul-PL 'The man has bought all he will need, but (on the other hand) the souls have left.' (Jr) Many subordinating conjunctions are borrowed from Spanish. The Spanish complementizer que, pronounced ke or ki, is never used alone. One hypothesis suggests that ke was borrowed from Spanish. Another possibility is that Purepecha also had a subordinating conjunction with the form ki, attested in the 16 th century. A convergence between the two elements has been favoured because they present the same form. This topic had not been studied yet. The subordinating conjunction ke is employed with other borrowed markers, functioning as complex conjunctions: porki in a causal clause (17), para ke in a purpose clause (18a), sikiera ke, which is a synthetic form of the Spanish 'si quiera' in a hypothetical clause (19a), and sino ke in a contrast clause (20). These elements are analyzed as subordinating conjunctions, because they respect the Purepecha constructions; the verb of the subordinating clause is marked by subjunctive mood.

Purepecha has various subordinating conjunctions, enki, eʃka and eʃki, which seem to be being progressively replaced in these constructions by ke. Nevertheless, many speakers, especially those of the middle-aged and older generations, prefer to use the Purepecha ximpoki 'because' instead of porki, and to use the borrowed markers para (18b) and sikiera (19b), in combination with the Purepecha conjunctions eʃka or eʃki.

( The situation of variation between the use of ke or iʃka/iʃki in subordinating constructions is also attested with the comparative structure (see §8).

Generally, para is introduced in a purpose clause with para ke or para iʃki (18a, 18b), however, it can also appear in a non-finite purpose construction (21).

(21)

Thu no xatsi-ʃ-ka para xaka-khu-ni.

2

NEG have-AOR-ASS1/2 for believe-FT-INF 'You don't have to believe him.' (Jr) Spanish temporal adverbializers that have been borrowed include: hasta 'until' ( 22), desde 'from' (23), apenas 'as soon as', pronounced apenaʃɨ (24), luego 'then' (20), and entonces 'then', generally pronounced tonses (25).

The adverbializer hasta additionally has a spatial deictic use ( 26). There is a native suffix of localization ɽu (26), which has an extended function (fixed and removed localization, ablative, translative, etc.). The use of hasta allows the specification of the type of localization.

(22)

Xima khama-ʃ-ti ya ásta wéxuɽini. then finish-AOR-ASS3 already until year 'He had finished it by the new year.' (Jr) ( 23)

Ántʃi-kuɽi-ʃa-ka=ni désde witsintikwa. work-MID-PROG-ASS1/2=1 for/since yesterday 'I have been working since yesterday.' (Jr) ( 24)

Petu kwhi-a-ti apenaxï thu nya-ra-ka. Peter sleep-FUT-ASS3 as soon as 2 arrive-FT-SUBJ 'Peter fell asleep as soon as you arrived.' (Jr) (25) Tonses no ampakiti=thu=tʃka ya Then NEG good=too=so already ni-ntha-ʃ-ti ya. go-CENTRIF-AOR-ASS3 already 'Then the devil has left too.' (Jr) ( 26)

Ni-a-ka=kʃɨ ásta xini yoɽekwa-ɽu. go-FUT-ASS1/2=1PL until there river-LOC 'We will go up to the river.' (Jr) Purepecha did not have prepositions before contact; we can assume that it was a language with only postpositions, and some suffixed case markers. So the prepositions para and por are borrowed in combination with their phrase-combining construction, i.e., they appear before the phrase or the morpheme (Chamoreau 2002b). The preposition para functions in a recipient clause (27a), and por expresses agentive (28a), causal (27a), and instrumental clauses (28a). The Purepecha postposition ximpo 'instrumental' can be used in functions similar to para (27b), or to por (28b, 29b, 30b). In all these contexts, the Purepecha marker may appear in a double construction (27c, 28c, 29c, 30c). The Spanish marker komo is used in Purepecha to introduce a manner clause.

(31)

Pos=sɨ komo ma atʃa=sɨ xa-ɽa-ʃ-ti. Thus=FOC like a man=FOC be there-FT-AOR-ASS3 'Thus, he was there like a man.' (Jr)

The Spanish phrasal adverb ya is used to mark temporal values with two different nuances: it can introduce a completive value, generally employed with the aspect aorist or the past aorist (32), or it can express a present value (33). The story in ( 32) is about a vulture that has transformed himself into a woman, and the woman into a vulture. The example expresses that the vulture turned into a woman; that it was no longer an animal. In the same narrative, in (33), there is a contrast between the first verb, in the past tense, which indicates the state of the woman before, and the second verb, in the interrogative clause, which indicates a question about the present state, which is the state of the vulture.

(32)

Ka ma waɽiti-i-ʃ-ti ya. and a woman-PRED-AOR-ASS3 already 'And it is already a woman.' (Jr) (33) Thu no xama-ʃ-p-ka lísto antiʃɨ=ri 2 NEG walk-AOR-PAS-ASS1/2 lively why=2 xa-ɽa-ʃ-ki ya. be there-FT-AOR-INT already 'You did not used to be lively, why are you now?' (Jr) Apart from marking temporal relations, this element ya functions like a discourse marker, with the addition connector ka 'and'. The latter begins a clause, while the former ends one (32).

Finally, many discourse markers are borrowed by Purepecha from the Spanish. The most frequent ones are the fillers: pues 'thus, then, well', pronounced pwes or pos (31), and bueno 'well, sure', pronounced wenu. It is also possible that as a result of the influence of Spanish, the use of the demonstrative inte 'this' is used as a filler like este in that language. This element appears in the same conditions as does inte in Spanish: it expresses a hesitation, a pause, etc. (34). It is a PAT-influence that is not connected to any direct Ximpoka=ni inte patsɨ-ntsɨ-ka=na. because=1 em be fade-head-SUBJ=EVID 'Because, em, I am bald, they said.' (Jr)

Constituent order

Constituent order seems to be influenced by areal contact prior to the 16 th century (see above, §1), with Spanish continuing the process, and increasing it via the introduction of prepositions (while Purepecha had traditionally used postpositions).

Syntax

The organization of passive and equational constructions has been influenced by Spanish (see above §3). Many subordinating conjunctions and adverbial markers are borrowed from Spanish, in combination with the grammatical constructions they appear in, in that language.

A syntactic domain which has undergone an important reorganization due to Spanish contact is the comparison of inequality. Purepecha had traditionally utilized a comparative construction of superiority of two types (Chamoreau 1995): the exceed verb of action ( 35), and the combination of the exceed verb of action and a coordinated polarity construction (36): (35) pedro hatztamahati juanoni ambaqueni (Gilberti [1558] Nowadays, there has been a reorganization as a result of a chain reaction triggered by Spanish interference. A cross-dialectal perspective shows that contact between the indigenous and Spanish constructions (the structure más…que) has brought about the emergence of nine constructions which may be classified in four different types (one type, the applicative construction, is not treated here, because it is marginal and corresponds to the derivative morphological characteristics of the language). I present here eight constructions organized in three types:

Type 1 is a borrowing or a PAT-influence of the Spanish comparative construction with borrowed degree and relator (37), with borrowed relator and the degree calque (38) or their Purepecha calques (39). ( 37)

Enrike mas ʃepe-s-ti ke Pedru. Henry more be lazy-AOR-ASS3 SUB Peter 'Henry is lazier than Peter.' (Cn) (38) I kamisa sáni=teru xuka-para-s-ti ke iʃu DEM shirt few=more put-shoulder-AOR-ASS3 SUB here anapu-e-s-ti. Iʃu sáni=teru yó-tha-ɽa-ʃɨn-ti ka no xini. here few=more long-leg-FT-HAB-ASS3 and NEG there 'Here is higher than there.' (Here is higher and there is not) (Jr) Type 3 is a hybrid type, employing the Spanish degree mas plus the relator ke, and a locative construction with the Spanish preposition 'de' (42), which represents an instance of code-mixing, because it only appears in a few expressions, and never alone (the Spanish preposition de 'of' appears in this context of comparative constructions and in some expressions, for example de veras 'sure'). This new hybrid locative construction does not occur either in Spanish or in traditional Purepecha. This construction can occur with the Purepecha degree calque sáni=teru (43):

(42)

Inte atʃa mas khéri-e-s-ti ke de ʃo DEM man more old-PRED-AOR-ASS3 SUB of here anapu yamintu. This hybrid construction may also occur with the Spanish preposition entre. In (44), we can observe the presence of the borrowed marker of degree más before the quality, and the comparative relator ke, which is followed by the Spanish preposition entre.

(44)

Iu más khé--ti ke entre xini. here more be big-AOR-ASS3 SUB between there 'Here is bigger than there.' (Sat) Finally, it is unclear whether Purepecha has ever had a comparative construction of inferiority. In order to express this domain, Purepecha employs two strategies: a) to use the borrowed Spanish comparative construction of superiority with the negation, employing either the Purepecha relator (45a) or Spanish relator (45b), and b) to borrow the Spanish construction with the Spanish degree menos (pronounced menuɨ in certain varieties), and the Purepecha calque relator eska (46), or the borrowed degree and relator (47).

Conclusion

The grammatical MAT-loans are numerous, and appear within their Spanish grammatical constructions. A relevant phenomenon is the typological profile of Purepecha, which shows new tendencies.

Purepecha is a synthetic-agglutinative language, and, nowadays, new analytic-periphrastic constructions appear, without modifying its elaborate morphological system, but revealing a structural rapprochement to the Spanish passive and equational constructions: two distinct structures (a morphological one and a periphrastic one) may simultaneously perform the same function.

Purepecha is exhibiting language-internal grammaticalization processes to replicate Spanish models.

There are PAT-influences that are not connected to any direct MATborrowing. Other PAT-influences are the comparative constructions, linked to MAT-borrowing in some varieties, and showing only pattern reduplication in others.

Abbreviations

  Ima siémpri mí-ti-ʃɨn-an-ti. DEM always know-face-HAB-PAS-ASS3 'He had always known it.' (Jr)(12) Xutʃari tati ménkhu xutʃi-o xa-ɽa-ʃɨn-ti.

(

  27) a. Ima kuɽa-tʃi-ʃ-ti=rini itʃuskuta para ama-mpa. DEM ask-1/2APP-AOR-ASS3=1OBJ tortilla for mother-POSP3 'He has asked me for tortillas for his mother.' (Jr) b. Ima kuɽa-tʃi-ʃ-ti=rini itʃuskuta ama-mpa ximpo. (Jr) c. Ima kuɽa-tʃi-ʃ-ti=rini itʃuskuta para ama-mpa ximpo. (Jr) (28) a. Mí-ti-ʃ-ti por ima. know-face-AOR-ASS3 by DEM 'He knows it through him.' (Jr) b. Mí-ti-ʃ-ti ima ximpo. (Jr) c. Mí-ti-ʃ-ti por ima ximpo. (Jr) (29) a. Tsɨtsɨki urapiti kunti-kuɽi-ʃa-ti por flower white bend-REF-PROG-ASS3 under/cause kwetsapikwa. weight 'The white flower is bending under the weight.' (Jr) b. Tsɨtsɨki urapiti kunti-kuɽi-ʃa-ti kwetsapikwa ximpo. (Jr) c. Tsɨtsɨki urapiti kunti-kuɽi-ʃa-ti por kwetsapikwa ximpo. (Jr) (30) a. Xu-ɽa-ʃ-ka-ni por kamioni. come-FT-AOR-ASS1/2-1 by bus 'I went by bus.' (Jr) b. Xu-ɽa-ʃ-ka-ni kamioni ximpo. (Jr) c. Xu-ɽa-ʃ-ka-n por kamioni ximpo. (Jr)

  is older than (of) all the others from here.' (Tr) (43) I tata sáni=teru=ɨ thana-ɨn-ti ke de DEM man few=more=FOC jugar-HAB-ASS3SUB of wapha-mpa son-POSP3 'This man plays more than his son.' (Cn)

(

  45) a. Maria sáni=taru no wiŋapi--ti eski thu. Maria few=more NEG be strong-AOR-ASS3 SUB 2 'Maria is weaker (less strong) than you are.' (Maria is not stronger than you are) (Ar) b. Maria sáni=taru no wiŋapi--ti ke thu. (Oc) (46)Selia menos yó-tha-la-ɨn-ti eska=ni. Celia less long-leg-FT-HAB-ASS3 SUB=1 'Celia is shorter (less tall) than I am.' (Cm) less than you want.' (Jr)

  Peter surpass-CAUS-TRANSF-PRES-ASS3 John-OBJ be good-INF 'Peter is better than John.'(Peter surpasses John in being good).

			1987: 109)
		Pedro xats-ta-ma-xa-ti	xwano-ni ampake-ni.
	(36)	pedro hatztamahati ambaqueni, ca noys juan
			(Gilberti 1987: 109)
		Pedro xats-ta-ma-xa-ti	ampake-ni ka
		Peter surpass-CAUS-TRANSF-PRES-ASS3 be good-INF and
		no=ʃɨ	xwano.
		NEG=FOC John
		'Peter is better than John.' (Peter surpasses with goodness and
		John does not).


Marina Oukacine

Rajae Rtimi

Nicole Goutal

Frédérique Larrarte

Vincent Loizeau

Sofiane Benhamadouche

Sébastien Proust

Large Eddy Simulation for flows through emerged or slightly sub-merged square obstacles

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

As a result of climate change, we believe that extreme floods will become more frequent and more intense. People and properties, such as housing and industrial facilities, must therefore be protected against these floods for which data are very scarce or even non-existent (European Union 2007). When moving from low to extreme flooding, the flood extent over the floodplain greatly varies. The nature of the obstacles encountered during the floods may change in the sense that they can be emerged for moderate flows or slightly submerged for high flows. Thanks to an experimental set-up, the uniform flow structure around a square array of emerged or slightly submerged square cylinders has been investigated and the measurements focused particularly on the vertical profile of the mean longitudinal velocity. The behaviour of the vertical profiles depends on the lateral and vertical confinements. The objectives of the present works are twofold; first we aim at validating a 3D numerical modelling in order to create a "numerical channel" able to reproduce the flow through the obstacles, second as a result of this validation, we numerically explore the influence of the geometrical parameters such as the lateral confinement on the flow structure.

EXPERIMENTAL SET-UP 2.1 Validation test-case description

The experiments were performed at the Hydraulic and Hydromorphologic laboratory at INRAE Lyon-Villeurbanne, France. The experiments were carried out in a 1 m wide and 17.25 m long open-channel flume with a rectangular cross-section (Fig. 1a). The bed slope S0 was equal to 1.05 mm/m, and the glass flume bottom was covered with dense artificial grass (0.005 m high rigid blades, see Fig. 1b). The water level is controlled by an adjustable vertical downstream weir. The vertical axis Oz is aligned with the vertical direction (normal to the flume bottom), its origin z0 is ABSTRACT: As a result of climate change, we believe that extreme floods will become more frequent and more intense. The flows through obstacles representing an urbanized floodplain is realised in a laboratory at Re = 4766 and 8580. The purpose of the present study is first to validate a numerical model using Large Eddy Simulation (LES) against experimental data regarding the average longitudinal velocity and the secondary vortices formation. Then, additional data can be obtained and quantified. Therefore the geometrical parameters can be changed and their influence analysed and compared to the literature. A good agreement was found between simulated and experimental vertical profiles of time averaged velocity for the flow through emerged or slightly submerged obstacles. The additional simulations highlight that the flow structure is mostly driven by the transverse aspect ratio using the distance between two adjacent obstacles. defined at the top of the rigid blades. The left-hand side wall, made of glass, is located at z = 0, and the right-hand side wall, made of Plexiglas, is at y = 1 m. Over the artificial grass, 833 (7x119) square cylinders were placed in a square array pattern (Fig. 1c). Each square cylinder has a square cross-section with a 0.064 m side length and a 0.0592 m height. The square cylinder height k is measured from the top of the grass blades (Fig. 1b).The distance l between two adjacent square cylinders is identical in the transverse and longitudinal directions and equals to 0.079 m. The distance between the side wall and the nearest square cylinder is 0.039 m. The first transverse row of square cylinders starts at 0.17 m downstream of the channel entrance (x = 0). Each transverse row is composed of 7 square cylinders, with 119 transverse rows along the channel (49 square cylinders/m²). Two immersion rates H/k equal to 93% and 148%, respectively, are studied, H being the flow depth [START_REF] Oukacine | Etude expérimentale et numérique des écoulements à surface libre en présence d'obstacles émergés à faiblement submergés[END_REF]. Time averaged velocities and velocity fluctuations were measured using an Acoustic Doppler Velocimetry (ADV) with a side looking probe, a Particle Image Velocimetry (PIV) system (2D-2C) and a Large Scale Particle Image Velocimetry (LSPIV). The uncertainty of ADV measurement is 0.5% of the value measured ±1 mm.s -1 (manufacturer's data).

Main results

The obstruction created by the obstacles results in wake zones behind the houses models (square cylinders), while a high-speed stream is located between two square cylinders. Flow is mainly one-dimensional in the longitudinal direction in the high speed-stream. The presence of obstacles implies that the characteristic velocity of the flow is not the bulk velocity uQ but the porosity velocity uΦ which takes into account the obstruction of the obstacles [START_REF] Oukacine | Etude expérimentale et numérique des écoulements à surface libre en présence d'obstacles émergés à faiblement submergés[END_REF]. For flows through emergent obstacles, the vertical profile of time-averaged streamwise velocity is characterised by a dip phenomenon [START_REF] Nezu | Cellular secondary currents in straight conduit[END_REF], i.e. a deceleration of the flow in the nearsurface layer due to helical secondary currents. This flow configuration can therefore be considered as a succession of flows on narrow channels, whose characteristic width is therefore the distance between square cylinders l thus the lateral aspect ratio Ary = l/H instead of B/H. The dip phenomenon, generated by secondary currents, is thus caused by the lateral confinement. In addition, the turbulent intensity is greater than 30% with the presence of vortex shedding located at the vertical square cylinder edges. In the case of emergent square cylinders (H ≤ k), the results show that flow depth does not influence the flow structure (mean flow and turbulence statistics). For slightly submerged cylinders, flow structure is unchanged below the top of the square cylinders. Around z = k, there is a mixing zone and above the fluid accelerates with a velocity distribution following a log-law, typical of wide channels. Last, a strong decrease in the turbulence intensity is observed from emergence to submergence conditions of the square cylinders. It is developed and distributed by EDF to solve fluid dynamics problems (CFD). It uses a collocated finite volume technique for computational cells of any shape. Pressure/velocity coupling is ensured via a SIMPLEC algorithm. Several turbulence models are available: from Reynolds Average Navier-Stokes models (RANS, eddy viscosity and Reynolds Stress models) to Large Eddy Simulation models (LES, Standard and dynamic Smagorinsky, Wale).

Modelling hypothesis

Three modeling hypotheses are made. The two first hypotheses would not a priori affect the predominant physical phenomenon [START_REF] Oukacine | Etude expérimentale et numérique des écoulements à surface libre en présence d'obstacles émergés à faiblement submergés[END_REF]). The third one is more important but as our interest is on the vertical flow profile, it should not affect the targeted physics that much.

The first one is the non-accounting of the channel slope S0 as it is incompatible with the biperiodic boundary condition (periodic boundary conditions will be explained in the next paragraph). The flow will not be imposed by the slope but thanks to a pressure gradient.

The second one is that the bottom roughness is not taken into account. In fact, the predominant physical phenomenon generating turbulence is not the roughness but the obstacles in the flow evaluated with the 1D momentum equation [START_REF] Oukacine | Etude expérimentale et numérique des écoulements à surface libre en présence d'obstacles émergés à faiblement submergés[END_REF]. The ratio between bottom roughness over the drag is equal to +7.5% for the 93% flow and +9.4% for the 148% flow. Here, the modelled channel will be a smooth-bottomed channel with no slip boundary conditions (𝑢 ̅, 𝑣̅ , 𝑤 ̅ = 0).

The third hypothesis is more significant: the free surface is not taken into account and a flat free surface is imposed. This will influence some physical phenomena, such as the interaction of surface vortex detachments with the free surface. Here, the goal is to highlight the vertical profile of the flow. The obtained results will determine whether the fixed surface influences the vertical profile of the flow or not. A symmetry plane is imposed; if, (u, v, w) stand for the velocity components, one has 𝜕𝑢 ̅/𝜕𝑧 = 𝜕𝑣̅ /𝜕𝑧 and 𝑤 ̅ = 0.

Initial and boundary conditions

The pattern used is made of two rows of two cylindrical arrays (Fig. 2). Periodic boundary conditions are applied in the longitudinal and transverse directions, respectively. The established regime found in the experiment justifies the condition of longitudinal periodicity (the number of rows seems to be enough to obtain a fully developed flow regime after some rows).

In addition, the fixed free surface condition will prevent flow to have interactions with a real free surface [START_REF] Ouro | Drivers for mass and momentum exchange between the main channel and river bank lateral cavities[END_REF]). This will mean that the seiching will not be present and that the vortex detachments interacting with the free surface will not exist [START_REF] Chetibi | Transverse surface waves in steady uniform and non-uniform flows through an array of emergent and slightly submerged square cylinders[END_REF].

Turbulence modelling

A Wall-Adapting Local Eddy-viscosity model (WALE, [START_REF] Nicoud | Subgrid-scale stress modelling base on the square of the velocity gradient tensor[END_REF]) is used. The meshes are of hexahedric shape. The LES capabilities of Code_Saturne have been on various academic and industrial cases including decaying isotropic turbulence, channel flows, side-byside cylinders, tube bundles and gusts over a plate; (see [START_REF] Benhamadouche | Wall-resolved Large Eddy Simulation of a flow through a square-edged orifice in a round pipe at Re=25,000[END_REF][START_REF] Benhamadouche | Wall-resolved Large Eddy Simulation of a flow through a square-edged orifice in a round pipe at Re=25,000[END_REF][START_REF] Oukacine | Etude expérimentale et numérique des écoulements à surface libre en présence d'obstacles émergés à faiblement submergés[END_REF] for example. The temporal discretization for the LES is second order Crank-Nicolson in time with linearized convection. The spatial discretization is a pure second order central difference scheme. By default, there are no external sweeps on the pressure-velocity coupling. The mesh used is a very refined near-wall mesh, with ∆y + = 1. Then, the mesh is unrefined according to a geometric progression of reason equal 1.1 (Fig. 2). Thus, a uniform mesh size is obtained far from the walls with a value of y+ between 5 and 10. These characteristics correspond to the recommended values for the LES simulations of [START_REF] Piomelli | Large-eddy simulations: theory and applications[END_REF].

Validation against experimental data

The comparison of the simulations results with PIV and ADV experimental data validate the vertical profile of longitudinal velocity (Fig. 3). The parabolic shape of the mean longitudinal velocity 𝑢 ̅, typical of narrow channels [START_REF] Nezu | Cellular secondary currents in straight conduit[END_REF], is recovered. The simulation overestimates the maximum velocity position by 25%. The overestimation is probably due to the friction at the bottom wall which is more important in the experiment. The major difference between the two velocity fields for the mean transversal velocity 𝑣̅ is located behind the P3 square cylinder (Fig. 4), the one from the experiment is both positive and negative while it is mainly negative in the simulation. This is due to the fact that the roof is fixed and the detachments vortices are different between experiment and numerical simulation. Indeed, behind the square cylinders (Fig. 5), the experiment shows the formation of a single vortex while the numerical simulation generates two symmetrical vortices with respect to the center of the square cylinder. This configuration is typical of entrained cavity flows. Depending on the longitudinal location of the measurement, the shape of the velocity is related to the shape of the vortex (Fig. 5). Indeed, if one is located in the middle of the vein or closer to a square cylinder upstream or downstream, the shape of the vortex being different, the velocity is different (Fig. 5). The comparison of the vertical velocity 𝑤 ̅ shows that at the center of the central vein the velocity is negative or nil (Fig. 4). However, the simulation underestimates the vertical velocity by 60%.

Finally, the flow through emergent obstacles, despite the fixed free surface model, the mean longitudinal velocity is well approached. This reinforces the fact that the surface has little influence on the latter. However, these assumptions influence the vortices generations. For the flow through submerged obstacles at H/k = 148%, the maximum of the mean longitudinal velocity profile 𝑢 ̅ is reached on the free surface for both experimental data and LES simulation (Fig. 6). At the elevation z/H = 44%, the LES mean longitudinal velocity 𝑢 ̅ is underestimated by 8%. The LES mean transverse velocity 𝑣̅ is very close to the experiment (Fig. 7) with vortices at the position z/k equal 0.6 and a negative velocity above the position z/k equal 1. This is due to the fact that the free surface is located above the roofs of square cylinders. On the other hand, at the position z/H = 42%, the experiment and the LES are out of phase and the numerical simulation overestimates the amplitude of the velocity by 25% (Fig. 7). Regarding the mean vertical velocity 𝑤 ̅, LES underestimated the area z/k between 0.6 and 1.5 and overestimated by 50% the velocity at the edges (Fig. 8).

The results showed that for both flows, the vertical profile of the mean longitudinal velocity 𝑢 ̅ is validated with the LES.

Influence of the geometrical repartition of obstacles for the flow through emergent obstacles

As LES has been fairly validated. It is now possible to explore others geometrical parameters that could not be experimentally conducted (Fig. 9). All the configurations below are numerical simulations using the same modelling assumptions as before with the same initial and boundaries conditions and the same mesh strategy and domain size. The obstacle density will be modified on the flow with emergent obstacles at 93%. 17 configurations have been tested with different square cylinders sizes and always with the same water height i.e. 0.055 m. Here, the inlet conditions remains unchanged. The flows were calculated using the formula of [START_REF] Guillén-Ludeña | Flow Resistance for a Varying Density of Obstacles on Smooth and Rough Beds[END_REF]. A quantitative approach to the velocity profile taken at the centre of the central vein is carried out. As a reminder, in the literature, it is the transverse aspect ratio Ary that defines whether the channel is narrow -under 5-or wide -upper than 5- [START_REF] Nezu | Cellular secondary currents in straight conduit[END_REF].

The objective is to assess whether the experimental value of Ary is still valid for discontinuous channels and regardless of the longitudinal aspect ratio Arx. The number 0 represents the experimental configuration (Fig. 9). In the limited range of configurations studied, the results showed that when Ary is under 6 regardless of longitudinal aspect ratio Arx, the dip phenomenon is still present. Here, in the case of discontinuous channel, it's still the transverse aspect ratio which governs the vertical profile of the mean longitudinal velocity.

CONCLUSIONS

Large Eddy Simulation based on solving Navier-Stokes equations with Code_Saturne, were carried out. First, they are validated from experimental measurements of vertical profiles of the mean longitudinal velocity 𝑢 ̅ for both emergent and slightly submerged square cylinders uniform flow. The strong hypothesis of a fixed free surface has little influence on the vertical distribution of mean longitudinal velocity, even though it leads to differences in vortex formation and position. The representation of the interactions of the free surface with the vortex detachments would require LES simulations with consideration of the free surface. The validation of the vertical longitudinal velocity distributions made it possible to use a "numerical channel" to explore other geometric configurations that could not be experimentally performed and to observe their influence on the vertical profile of the mean longitudinal velocity.

The different configurations tested showed that, regardless of the longitudinal aspect ratio Arx, the cross-sectional aspect ratio Ary plays a predominant role on the flow structure. So, the relationship found by [START_REF] Nezu | Cellular secondary currents in straight conduit[END_REF] remains valid even for discontinuous narrow channels. Work in progress would make it possible to study transitional situations.

Figure 1

 1 Figure 1. a) Schematic top view of the open-channel: inlet tank (1), vertical linear ramp with a 15% slope (2), working channel length (3), downstream weir (4), b) Sketch of the cross section: B = channel width, H = flow depth, z0 located at the top of the artificial grass blades, c) Picture from downstream of the square cylinders

Figure 2 .

 2 Figure 2. Computational domain and zoom of the mesh

Figure 3 .

 3 Figure 3. Comparisons for the flow through emerged obstacles (H/k = 93%) between PIV and ADV experimental measurements and LES simulations. Vertical mean longitudinal velocity 𝑢 ̅ made non dimensional using the porosity velocity 𝑢 𝛷 ̅̅̅̅.

Figure 4 .Figure 5 .

 45 Figure 4. Comparisons for the flow through emerged obstacles flow (H/k = 93%) between ADV experimental measurements and LES simulations mean velocity components 𝑣̅ , 𝑤 ̅ between the square cylinder 3 and 4 at x = 0.143 m (Fig. 2)

Figure 6 .

 6 Figure 6. The vertical mean longitudinal velocity 𝑢 ̅ made non dimensional using the porosity velocity 𝑢 𝛷 ̅̅̅̅ for the flow through submerged obstacles at H/k = 148 %. Comparisons between PIV and ADV experimental measurements and LES simulations at the green position between the square cylinder 3 and 4

Figure 7 .

 7 Figure 7. Comparisons for the flow through submerged obstacles flow (H/k = 148%) between ADV experimental measurements and LES simulations mean velocity components 𝑣̅ between the square cylinder 3 and 4 at x = 0.143 m (Fig. 2)

Figure 8 .

 8 Figure 8. Comparisons for the flow through submerged obstacles flow (H/k = 148%) between ADV experimental measurements and LES simulations mean velocity components 𝑤 ̅ between the square cylinder 3 and 4 at x = 0.143 m (Fig. 2)

Figure 9 .

 9 Figure 9. Classification of the configurations tested according to the aspect ratio Arx and Ary for different obstacles dimensions and spacing for the same flow depth H = 0.055 m, 0 is the experimental point

ACKNOWLEDGEMENT

The authors acknowledge the support of the FlowRes project by the French National Research Agency (ANR), under grant N•ANR-14-CE03-0010