L Gatilova

A Maestrini

J Treuttel

T Vacelet

Y Jin

A Cavanna

L Couraud

A Feret

G Gay

S Caroopen

Recent progress in the Development of French THz Schottky Diodes for Astrophysics, Planetology and Atmospheric Study

  L'archive ouverte pluridisciplinaire

I. INTRODUCTION

ILLIMETER and submillimeter heterodyne observations could help us to improve the understanding of the universe, the solar system and the planet's atmosphere. Among different available technologies to build THz and sub-THz devices for radio-astronomy, planar GaAs Schottky diodes play a crucial role. In particular, this technology enables the building of high frequency multipliers with sufficient output power and low noise mixers, both working at room temperature or at cryogenic temperature and capable of reaching the THz region [START_REF] Maestrini | Schottky diode based terahertz frequency multipliers and mixers[END_REF].

II. FRENCH THZ SCHOTTKY DIODE PROCESS

In 2006, LERMA -in close collaboration with C2N (formerly LPN) -started the development of GaAs-based planar Schottky nano-diode fabrication technology.

Approaching the THz frequencies, parasitic capacitances (dielectric substrate losses, pad-to-pad capacitance, and fingerto-pad capacitance), series resistance and velocity saturation, start to affect the performances of planar Schottky-diodebased mixer and multipliers, and made the fabrication process challenging. The dielectric losses could be partially decreased by reducing the substrate thickness to a few microns (membrane-based diodes). The use of air-bridge connection between anode and other parts of the circuits allows to reduce the finger-to-pad capacitance if the air-bridge is sufficiently vertical. The series resistance can be controlled by the distance between anode and ohmic contact and by increasing of doping level to 5x10 17 cm -3 . Moreover, in order to reduce the junction capacitance and to increase the cut-off frequency the anode area should be decreased down to the submicron size. All these parameters should be taken into account during the fabrication process.

The manufacturing of Schottky-based components is made in C2N's clean room that has all necessary equipment for complete Schottky diode fabrication, including the epitaxy of the active layer on GaAs substrate. In order to reach THz frequencies, we have developed a fabrication process, which is fully based on e-beam lithography, and allows a high precision on small structures (anode size less than 0.1μm2 ) and gives a great flexibility for monolithic microwave integrated circuit (MMIC) designs. An important effort has been made during the last years in order to improve our technology and manufacture the diodes with excellent characteristics and very good homogeneity across the wafer

The active diode layers and GaAs membrane are grown at C2N by Molecular Beam Epitaxy (MBE) technique on 500μm-thick semi-insulating 2-inch GaAs wafer. First, a 300-450 nm AlGaAs etch-stop layer is grown, followed by 2-5 μm-thick (depending on application) GaAs semi-insulating membrane. This has been followed by 50 nm AlGaAs etchstop layer and 700 nm heavily doped 5x10 18 cm-3 n ++ layer. The thickness and the doping level of the n epi-layer are adapted according to the chosen application (mixers or multipliers) and working frequency ranges.

The fist fabrication step consists in dry etching of n and n++ GaAs and 50-nm AlGaAs layers in Cl2-based inductively coupled plasma (ICP) in order to form the mesas. The using of ICP instead of wet etching allows a better control of the mesa size and verticality of mesa sidewalls. Then the ohmic contact is formed on the top of the mesas. The n epi-layer is etched down to n ++ layer in H3PO4:H2O2:H2O solution. The Ni/Ge/Au/Ni/Au metal films are successively evaporated and rapid thermal annealing is performed at Ar-H2 environment. Then anode is formed by evaporation of Ti/Pt/Au metal films on the top of the mesas and protected by a 50 nm of Si3N4 dielectric films deposited in plasma enhanced chemical vapor deposition (PECVD) reactor. The next step consists in the formation of the air-bridge connections. The challenge is to form the connection to the anode to be as vertical as possible (Fig 2b) in order to reduce the parasitic capacitance. The 2μmthick LOR resist is deposited and reflowed in order to form the support for the air-bridge. The Si3N4 passivation on anode is opened by SF6-based reactive ion etching (RIE) plasma and air-bridge fingers are formed by evaporation of a 600-nmthick gold metal film. After this step, the diodes are passivated again by 50 nm Si3N4 film in PECVD reactor. Then the circuits are separated by etching of the GaAs membrane (2-5 μm) down to the AlGaAs etch-stop layer in HBr-based ICP L. Gatilova 1&2 , A. Maestrini 1 , J. Treuttel 1 , T. Vacelet 1 , Y. Jin 2 , A. Cavanna 2 , L. Couraud 2 , A. Féret 1 , G. Gay 1 , S. Caroopen 1 , J. Valentin 1 , S. Mignoni 1 , J-M. Krieg 1 , C. Goldstein 3 plasma [START_REF] Bouchoule | Anisotropic and Smooth Inductively Coupled Plasma Etching of III-V Laser Waveguides Using HBr-O2 Chemistry[END_REF]. Then the wafer is protected by the resist, mounted topside-down onto the quartz support and chemically thinned down to the membrane. Finally the circuits are released in acetone and mounted in the micro-machined wave-guide blocks.

Our first success in 2012 was the realization of the discrete anti-parallel pairs of diodes with an anode size of 0.5 μm 2 (Fig. 1a). These diodes demonstrated the very good electrical characteristics (ideality factor n=1.15-1.19, serial resistance Rs = 10-15 Ohm) and were tested by Radiometer Physics GmbH (Germany) on a 664GHz sub-harmonic mixer. A double side band receiver equivalent noise temperature of 1600K was measured at room temperature with an IF LNA in the 0.5-8GHz band. Based on these very promising results we started the development of Schottky-diode-based MMIC integrating the diode cell and matching network on few microns thick GaAs membrane. In order to easily mount and maintain the MMIC circuits in metal wave-guide block, the 1-2μm-thick Au beamleads are formed by the same technique as for air-bridge fingers. Figure 2 shows an example of the beam-lead connection on our first MMIC 320GHz frequency doubler. In 2015, we have demonstrated state-of-the-art noise performance on our first MMIC 600GHz subharmonic mixer [START_REF] Treuttel | A 520-620-GHz Schottky receiver front-end for planetary science and remote sensing with 1070 K-1500 K DSB noise temperature at room temperature[END_REF]. At 295 K ambient temperature, an average of 1284 K DSB receiver noise temperature was measured over the 520-620 GHz frequency range. A record 1130 K minimum DSB receiver noise temperature at 557 GHz was measured. At 134 K ambient temperature, an average DSB receiver noise temperature of 685 K from 538 to 600 GHz was measured when correcting for the cryostat window loss. A minimum DSB receiver noise of 585 K was measured at an RF center frequency of 540 GHz.

In 2016-2017, we have built our first 1200GHz receiver for the SWI on ESA JUICE planetary probe. The record receiver sensitivities were obtained in the 1080-1280GHz band at room temperature and at cryogenic temperature [START_REF] Maestrini | The 1200GHz Receiver Frontend of the Submillimetre Wave Instrument of ESA JUpiter ICy moons Explorer[END_REF].

Fig. 1 .

 1 Fig.1. SEM image of antiparallel pair of discreet Schottky diode. a) Released diode on carbon membrane. b) Zoom on air-bridge connection.

Fig. 2 .

 2 Fig. 2. SEM image of 320 GHz MMIC doubler. a) Whole structure; b) Zoom on air-bridge and beam-lead connection.

Table1 1 :

 1 LERMA-C2N mixer diodes characteristics and RF

LERMA, Observatoire de Paris, PSL Research University, CNRS, UMR 8112, Sorbonne Université, 75014 Paris, France

Centre of Nanoscience and Nanotechnology (C2N) -CNRS, Univ. Paris-Sud, Univ. Paris-Saclay, 91120 Palaiseau, France

Centre national d'études spatiales (CNES), F-31401 Toulouse cedex 9, France

Authorized licensed use limited to: Universite Paris SUD-UMS 1786. Downloaded on August 16,2021 at 15:12:44 UTC from IEEE Xplore. Restrictions apply.

The authors would like to acknowledge all engineers and technicians of C2N clean room for theirs technical expertise and valuable advices. We also wish to thank Dr. Christian Ulysse for fruitful scientific discussions and especially for his significant participation in the development of metal film deposition technique. This work would not have been possible without technical and financial support of Centre national d'études spatiales (CNES).


Manoela C Brandão
email: manoela.costa.brandao@ifremer.fr

Thierry Comtet

Patrick Pouline

Caroline Cailliau

Aline Blanchet-Aurigny

Marc Sourisseau

Raffaele Siano

Laurent Memery

Frédérique Viard

Flávia Nunes

Flavia Nunes
email: flavia.nunes@ifremer.fr

Oceanographic structure and seasonal variation contribute to high heterogeneity in mesozooplankton over small spatial scales

Keywords: Mesozooplankton, mitochondrial COI, 18S rRNA, DNA metabarcoding, Highthroughput sequencing, Marine Protected Area, Ocean front

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

The coastal oceans can be highly variable, influenced not only by major oceanographic regimes, but also by processes related to bordering landmasses, such as river discharge, runoff, tidal forcing and currents influenced by the coastline and shallow water columns. Nearshore conditions can therefore be highly contrasted to adjacent offshore water masses, with the most striking examples being near ocean fronts. Ocean fronts occur where two distinct water masses come into contact, and are among the main oceanographic structures affecting the distribution of marine organisms as diverse as pelagic crustaceans, fish, marine mammals and birds [START_REF] Acha | Ecological Processes at Marine Fronts: Oases in the Ocean[END_REF]. They can arise from a diversity of processes and are defined by strong horizontal gradients of salinity and/or temperature. These hydrological structures create vertical fluxes, leading to aggregation processes, as well as increases in downward export or nutrient availability [START_REF] Acha | Ecological Processes at Marine Fronts: Oases in the Ocean[END_REF]. Ocean fronts have been shown to play an important role on plankton distribution, by aggregating, transporting, or separating specific assemblages [START_REF] Marra | Phytoplankton growth at the shelf-break front in the Middle Atlantic Bight[END_REF][START_REF] Flint | Plankton distribution associated with frontal zones in the vicinity of the Pribilof Islands. Deep-Sea Research Part II[END_REF][START_REF] Ohman | Mesozooplankton and particulate matter responses to a deep-water frontal system in the southern California Current System[END_REF]. In particular, the fronts formed in the transition between coastal bays and their oceanic adjacent regions affect the distribution of meroplankton (i.e. mainly composed of pelagic larvae of invertebrates) [START_REF] Shanks | Topographically generated fronts, very nearshore oceanography and the distribution of larval invertebrates and holoplankters[END_REF][START_REF] Ayata | Meroplankton distribution and its relationship to coastal mesoscale hydrological structure in the northern Bay of Biscay (NE Atlantic)[END_REF][START_REF] Brandão | Meroplankton community structure across oceanographic fronts along the South Brazil Shelf[END_REF].

Consequently, fronts may play a role in the dispersal of species with a bentho-pelagic life cycle, potentially altering their broad-scale connectivity and distribution along the coasts [START_REF] Acha | Ecological Processes at Marine Fronts: Oases in the Ocean[END_REF]. Furthermore, because they affect ecosystem functions such as primary productivity, biogeochemical cycling and biomass production [START_REF] Woodson | Ocean fronts drive marine fishery production and biogeochemical cycling[END_REF], ocean fronts also affect ecosystem services [START_REF] Martinetto | Linking the scientific knowledge on marine frontal systems with ecosystem services[END_REF], particularly fisheries. As such, the influence of ocean fronts on coastal communities merits adequate investigations.

The Iroise Sea, where the northeastern Atlantic transitions into the English Channel, constitutes an interesting environment for examining the effects of ocean fronts on pelagic communities. This part of the coast of western Brittany (France) is characterized by a megatidal regime (5 -10 m tidal amplitudes), which generates strong tidal currents. Tidal friction produces enough turbulence to constantly mix the entire water column in nearshore areas, but as depth increases, tidal mixing is not sufficient to erode the seasonal thermocline [START_REF] Brumer | Impacts of surface gravity waves on a tidal front: A coupled model perspective[END_REF].

The result is a tidally influenced thermal front called the Ushant Front that is characterized by a strong temperature gradient that separates warm stratified offshore waters from cool vertically mixed nearshore waters (Le [START_REF] Boyer | Observations of the Ushant tidal front in September 2007[END_REF][START_REF] Chevallier | Observations of the Ushant front displacements with MSG/SEVIRI derived sea surface temperature data[END_REF]Cadier et al., 2017a). Where nearshore and offshore water masses meet, a frontal zone is generated with specific characteristics between both water masses, such as thermal stratification coupled with high chlorophyll-a near the thermocline, which results from either subduction of productive coastal upper layers or nutrient enrichment due to mixing of the two water masses (or both). The Ushant Front is the dominant feature of the summer oceanographic structure of the Iroise Sea, which usually occurs from April/May to October every year [START_REF] Chevallier | Observations of the Ushant front displacements with MSG/SEVIRI derived sea surface temperature data[END_REF]Cadier et al., 2017a). This front is known to increase primary production [START_REF] Videau | Primary production and physiological state of phytoplankton at the Ushant tidal front (west coast of Brittany, France)[END_REF] but also to influence the size and abundance of phytoplankton [START_REF] Pingree | Summer phytoplankton blooms and red tides along tidal fronts in the approaches to the English Channel[END_REF][START_REF] Landeira | Biophysical interactions control the size and abundance of large phytoplankton chains at the ushant tidal front[END_REF], with longer diatom chains during the frontal establishment [START_REF] Landeira | Biophysical interactions control the size and abundance of large phytoplankton chains at the ushant tidal front[END_REF]. This coastal front also acts as an ecological boundary for free-living bacteria, with photosynthetic bacteria being most abundant offshore of the front, oligotrophic bacteria being more abundant in water masses with low phytoplankton and high inorganic nutrients, and opportunistic copiotrophic bacteria being most abundant in the most productive period of the year, associated with the front [START_REF] Lemonnier | Linking Spatial and Temporal Dynamic of Bacterioplankton Communities With Ecological Strategies Across a Coastal Frontal Area[END_REF]. In addition, the mesozooplankton community showed its highest diversity at the front as a result of the cooccurrence of species from stratified and mixed waters [START_REF] Schultes | Influence of physical forcing on mesozooplankton communities at the Ushant tidal front[END_REF].

The Ushant Front occurs within the boundaries of the Iroise Marine Natural Park (Parc Naturel Marin d'Iroise, PNMI), the oldest marine protected area (MPA) in France. Due to its influence on primary productivity and planktonic communities the front may affect the stocks of planktivorous fish, in particular sardines and anchovies, which are important fisheries in the Iroise Sea. To better understand these potential effects, the PNMI has established a monitoring program that has been in place for 10 years.

DNA metabarcoding, which combines high-throughput sequencing technologies with DNA barcoding, is revolutionizing how biodiversity is assessed in the marine environment [START_REF] Baird | Biomonitoring 2.0: A new paradigm in ecosystem assessment made possible by next-generation DNA sequencing[END_REF][START_REF] Cristescu | From barcoding single individuals to metabarcoding biological communities: Towards an integrative approach to the study of global biodiversity[END_REF], by allowing DNA taken from environmental (e.g. water, sediment) or bulk (e.g. plankton) samples to be sequenced concurrently, followed by taxonomic assignment by comparison to a reference sequence database, such as the Barcode of Life Data Systems for COI [START_REF] Ratnasingham | The Barcode of Life Data System[END_REF]. Thus, species diversity can be recovered across many broad taxonomic groups [START_REF] Valentini | Next-generation monitoring of aquatic biodiversity using environmental {DNA} metabarcoding[END_REF]. In order to capture a representative sample of community biodiversity, multiple loci are often used in metabarcoding due to their complementarity, as there is a trade-off between the taxonomic resolution and the taxonomic range recovered [START_REF] Carroll | Multilocus DNA metabarcoding of zooplankton communities and scat reveal trophic interactions of a generalist predator[END_REF][START_REF] Couton | Metabarcoding on planktonic larval stages: An efficient approach for detecting and investigating life cycle dynamics of benthic aliens[END_REF]. Metabarcoding has been broadly applied for benthic monitoring of marine ecosystems [START_REF] Fonseca | Second-generation environmental sequencing unmasks marine metazoan biodiversity[END_REF][START_REF] Lejzerowicz | High-throughput sequencing and morphology perform equally well for benthic monitoring of marine ecosystems[END_REF][START_REF] Cowart | Exploring Environmental DNA (eDNA) to Assess Biodiversity of Hard Substratum Faunal Communities on the Lucky Strike Vent Field (Mid-Atlantic Ridge) and Investigate Recolonization Dynamics After an Induced Disturbance[END_REF], and a growing number of studies are now using DNA metabarcoding to examine zooplankton community dynamics [START_REF] Chain | Metabarcoding reveals strong spatial structure and temporal turnover of zooplankton communities among marine and freshwater ports[END_REF][START_REF] Stefanni | Multimarker metabarcoding approach to study mesozooplankton at basin scale[END_REF][START_REF] Carroll | Multilocus DNA metabarcoding of zooplankton communities and scat reveal trophic interactions of a generalist predator[END_REF][START_REF] Couton | Metabarcoding on planktonic larval stages: An efficient approach for detecting and investigating life cycle dynamics of benthic aliens[END_REF][START_REF] Questel | Metabarcoding of zooplankton diversity within the Chukchi Borderland, Arctic Ocean: improved resolution from multi-gene markers and region-specific DNA databases[END_REF]. Although metabarcoding is considered semi-quantitative due to methodological biases [START_REF] Clarke | Effect of marker choice and thermal cycling protocol on zooplankton DNA metabarcoding studies[END_REF][START_REF] Carroll | Multilocus DNA metabarcoding of zooplankton communities and scat reveal trophic interactions of a generalist predator[END_REF], other studies have recently revealed significant positive correlations between total abundance counts from morphological taxonomic identification and metabarcoding sequence numbers [START_REF] Bucklin | Timeseries metabarcoding analysis of zooplankton diversity of the NW Atlantic continental shelf[END_REF][START_REF] Schroeder | DNA metabarcoding and morphological analysis -Assessment of zooplankton biodiversity in transitional waters[END_REF], thus indicating that relative abundances of reads can be considered as a proxy of relative abundances of taxa. Furthermore, metabarcoding applied to a time-series of meroplankton showed variations in read abundances that corresponded well with expectations based on the reproductive season of the identified species [START_REF] Couton | Metabarcoding on planktonic larval stages: An efficient approach for detecting and investigating life cycle dynamics of benthic aliens[END_REF]. In addition, despite the potential biases associated with metabarcoding, the method does present various advantages, such as the greater power for taxonomic identification for some groups, including undescribed or cryptic taxa, reducing time-consuming counts under the microscope, and the ability to recover information for a broad range of organisms [START_REF] Lindeque | Next generation sequencing reveals the hidden diversity of zooplankton assemblages[END_REF][START_REF] Clarke | Effect of marker choice and thermal cycling protocol on zooplankton DNA metabarcoding studies[END_REF][START_REF] Deagle | Genetic monitoring of open ocean biodiversity: An evaluation of DNA metabarcoding for processing continuous plankton recorder samples[END_REF].

In this study, we investigated the composition of the mesozooplankton in the Iroise Sea and the potential role of an ocean front in shaping this community over the course of the year. We were particularly interested in the two contrasting groups of the mesozooplankton: meroplankton (partial life-cycle in the water column) and holoplankton (full life-cycle in the water column). Our specific goals were (i) to investigate the spatial and temporal distribution of mero-and holoplankton in the Iroise Sea using DNA metabarcoding of the mitochondrial COI and the nuclear ribosomal 18S genes, and (ii) to examine the environmental variables, including the ocean front characteristics, that best explain differences observed in the mero-and holoplankton community composition. Our central hypothesis is that the establishment of the Ushant Front in summer has an impact on the structure of the mesozooplankton community in the Iroise Sea, increasing its diversity.

Materials and Methods

Sample collection

Mesozooplankton sampling took place in the Iroise Marine Natural Park (Parc Naturel Marin d'Iroise, PNMI), a marine protected area (MPA) that covers 3,550 km 2 of the Iroise Sea.

Sampling in the MPA was achieved on board the Valbelle (PM 509) and Augustine (PM 510) PNMI vessels, and was part of a regular monitoring program, the PNMIR, which started in 2010.

The PNMIR consists in sampling along two parallel cross-shelf transects, in front of the bays of Brest (seven stations) and Douarnenez (six stations). For the present study, zooplankton was sampled in six stations, three in each transect, in spring (23-05-2019), summer (11-07-2019) and fall (22-10-2019 to 24-10-2019) (Fig. 1a). Previous work has shown that the Ushant front usually occurs in summer and fall (June -September). In order to examine the potential effect of frontal conditions, sampling dates were chosen to capture conditions before, during and after the establishment of the Ushant Front. Vertical tows were performed from 5 m above the bottom to the surface with a WP2 plankton net with a 200-μm mesh size (UNESCO, 1968), equipped with a flowmeter (KC Denmark). Plankton was then sieved (200 µm) in order to remove seawater, and preserved onboard in a guanidinium thiocyanate buffer, not exceeding the volume of 100 ml.

To describe the abiotic conditions associated with each plankton sample, vertical profiles of temperature, salinity, fluorescence and turbidity were performed using a CTD probe (Seabird SBE19) coupled to a fluorimeter (NKE Mpx). Data from additional stations (four in the transect of Bay of Brest and three in the transect of Bay of Douarnenez; Fig. 1b-d) followed in the PNMIR monitoring program, taken on the same day of sampling, were included to better characterize the water column. An index of the thermal stratification (ΔT) was calculated as the difference between the surface and the bottom temperatures. A value higher than 1.5°C was considered as characterizing a stratified water column [START_REF] Schultes | Influence of physical forcing on mesozooplankton communities at the Ushant tidal front[END_REF].

DNA extraction, PCR amplification and sequencing

DNA was preserved in a guanidine thiocyanate buffer which effectively lysed the plankton samples at room temperature over the course of one week, thereby eliminating the need for filtering samples post-collection. Two replicate DNA extractions were performed using 20 mL of each plankton sample following homogenization by inversion, with a 2:1 volume of phenol:chloroform:isoamyl alcohol and 1:1 of an extraction buffer, followed by precipitation with 2:1 volume of isopropanol, 2 washes with 70% ethanol, resuspension in Milli-Q water and treatment with RNase A (10 mg/ml; Sigma-Aldrich, St. Louis, MO, USA) [START_REF] Fukami | Geographic differences in species boundaries among members of the Montastraea annularis complex based on molecular and morphological markers[END_REF].

The primers mlCOIintF (5'-GGWACWGGWTGAACWGTWTAYCCYCC-3') [START_REF] Leray | A new versatile primer set targeting a short fragment of the mitochondrial COI region for metabarcoding metazoan diversity: Application for characterizing coral reef fish gut contents[END_REF] and jgHCO2198 (5'-TAIACYTCIGGRTGICCRAARAAYCA-3') [START_REF] Geller | Redesign of PCR primers for mitochondrial cytochrome c oxidase subunit I for marine invertebrates and application in all-taxa biotic surveys[END_REF] were used to amplify a 313-bp portion of the highly variable mitochondrial Cytochrome c Oxidase subunit I (COI) gene. In addition, the primers SSU_F04 (5'-GCTTGTCTCAAAGATTAAGCC-3') [START_REF] Fonseca | Second-generation environmental sequencing unmasks marine metazoan biodiversity[END_REF] and SSU_R22mod (5'-CCTGCTGCCTTCCTTRGA-3') [START_REF] Sinniger | Worldwide analysis of sedimentary DNA reveals major gaps in taxonomic knowledge of deep-sea benthos[END_REF] were used to amplify a ca. 450-bp portion of the V1-V2 regions of the nuclear small subunit rDNA (18S rDNA). Primers including Illumina sequencing adaptors are detailed in Table S1.

For each marker, four PCR reactions (20 μl final volume) were run for each of the two DNA extractions, for a total of eight PCRs per biological sample, containing 1μl of total DNA template, 1μl of each primer, 0.5μl of BSA (New England Biolabs), 6.5μl of ultrapure water, and 10μl of Q5 High-Fidelity 2X Master Mix (New England Biolabs). For COI, due to inosine content in the reverse primer, the Q5U Hot Start High-Fidelity DNA Polymerase (New England Biolabs) was used instead. Cycling conditions for COI started with a 2-min denaturation step followed by 16 initial cycles of 98°C for 10s, 30s at 62°C (-1°C per cycle), 72°C for 60s, followed by 25 cycles at 46°C annealing temperature, and a final extension of 72°C for 2 min (modified from [START_REF] Leray | A new versatile primer set targeting a short fragment of the mitochondrial COI region for metabarcoding metazoan diversity: Application for characterizing coral reef fish gut contents[END_REF]. For 18S, cycling included a 2-min denaturation step followed by 30 cycles of 98°C for 10s, 30s at 57°C, 72°C for 30s, and a final extension of 72°C for 2 min (modified from [START_REF] Fonseca | Second-generation environmental sequencing unmasks marine metazoan biodiversity[END_REF]. The positive amplifications were identified on a 1.5% agarose gel stained with GelRed (Biotium). PCR products from the eight replicates per biological sample were pooled at equal volumes. Then a second PCR was done to add the Illumina index. These PCR products were quantified using an Epoch spectrophotometer (BioTek Instruments) and pooled at equimolar amounts. Paired-end reads (2 × 250 bp) were generated on a MiSeq (Illumina) at the Get-PlaGe Genomics platform (Toulouse, France).

Read processing and taxonomic assignment

Resulting raw sequence reads were processed with the FROGS v.2.0 pipeline [START_REF] Escudié | FROGS: Find, Rapidly, OTUs with Galaxy Solution[END_REF], implemented on a Galaxy interface [START_REF] Goecks | Galaxy: a comprehensive approach for supporting accessible, reproducible, and transparent computational research in the life sciences[END_REF]. First, paired-end reads were merged into contigs with the FLASH algorithm [START_REF] Magoč | FLASH: Fast length adjustment of short reads to improve genome assemblies[END_REF] before filtering by length (minimum 250 bp for COI, and 350 bp for 18S). Chimera and singleton were filtered using the VSEARCH tool [START_REF] Rognes | VSEARCH: A versatile open source tool for metagenomics[END_REF] in each sample, and the remaining sequences underwent SWARM v3.0 clustering, using the default parameters [START_REF] Mahé | Swarm: Robust and fast clustering method for amplicon-based studies[END_REF]. SWARM uses a clustering algorithm with a threshold corresponding to the maximum number of differences between two sequences in an OTU [START_REF] Mahé | Swarm: Robust and fast clustering method for amplicon-based studies[END_REF].

Each representative OTU sequence was aligned and assigned to a taxon using BLAST, with the following reference databases: BOLD_COI (https://www.boldsystems.org/) and Silva 18S rRNA v132 (https://www.arb-silva.de/) for COI and 18S, respectively. Potential false-positive OTUs were removed by filtering OTUs representing less than 0.005% of the OTU reads [START_REF] Bokulich | Quality-filtering vastly improves diversity estimates from Illumina amplicon sequencing[END_REF].

In addition, we assigned trophic regime traits for the copepods, due to their high relative abundance and important role in the pelagic community. Traits respective to trophic regime (omnivore-herbivore, omnivore-detritivore, omnivore, carnivore), and feeding strategy (filter, cruise, active ambush and mixed) were determined based on two available reference datasets [START_REF] Benedetti | Identifying copepod functional groups from species functional traits[END_REF][START_REF] Brun | A trait database for marine copepods[END_REF].

Data analyses

Vertical profiles of environmental data (temperature, salinity and fluorescence) were generated using CTD cast data in Ocean Data View (Schlitzer, 2016). In addition, we used weekly averaged satellite images of sea surface temperatures (SST) for the sampling dates. Images were obtained from NASA MODIS Aqua Global Level 3 (NASA OBPG, 2020).

In order to account for differences in sequencing depth among samples, rarefaction to an equivalent number of reads (minimum of 59,000 and 56,000 reads for COI and 18S, respectively) was applied to all samples. Filtered rarefied data were used for Nonmetric Multidimensional Scaling (nMDS) ordination and hierarchical clustering, according to the community composition of mero-and holoplankton, which were sorted at the family level (Table S2). A resemblance matrix was generated using Euclidean distances based on Hellinger-transformed rarefied read abundances. Permutational multivariate analysis of variance (PERMANOVA) was conducted to test the statistical significance of groups formed a priori (factors shelf position and season), as well as of their interaction [START_REF] Anderson | A new method for non-parametric multivariate analysis of variance[END_REF].

In order to assess the relationship between the distribution of the main mesozooplankton groups and the environmental variables, a Redundancy Analysis (RDA) was conducted. In order to avoid collinearity of explanatory variables, we applied a variance inflation factor (VIF) and removed collinear variables. A cut-off VIF value of 10 [START_REF] Zuur | Mixed Effects Models and Extensions in Ecology with R[END_REF] was applied to get the final set of covariates (distance from the coast, temperature, salinity, fluorescence, and thermal stratification), which excluded depth and turbidity. Mean values of temperature, salinity and fluorescence of each vertical CTD profiles were used in the RDA analysis. Read abundances were transformed using the Hellinger transformation to reduce the wide disparity in magnitude of the number of reads between taxa [START_REF] Legendre | Ecologically meaningful transformations for ordination of species data[END_REF]. Taxa that represented less than 5% of the reads were not included in this analysis.

In addition, we calculated the Shannon diversity index, considering OTUs as proxies of species, as used previously for estimating plankton diversity (e.g. [START_REF] Ibarbalz | Global Trends in Marine Plankton Diversity across Kingdoms of Life[END_REF].

The analyses were performed with the R v3.5.2 environment (R foundation [START_REF] Core | R: A Language and Environment for Statistical Computing[END_REF]. The normalization, RDA, nMDS, clustering, PERMANOVA and additional tests were conducted with the packages vegan [START_REF] Oksanen | Community ecology package[END_REF] and HH [START_REF] Heiberger | Package ' HH[END_REF].

Results

Hydrological structure

Variations in temperature profiles between sampling dates were observed in the Iroise Sea (Fig. 1b-d; Fig. S1). Surface temperature reached 18°C in both transects during summer (Fig. 1c; Fig. S1b), while it did not exceed 15°C during spring and fall (Fig. 1b,d; Fig. S1a,c). The water column was well-mixed during spring and fall (Fig. 1b,d), while it was strongly stratified during summer in the offshore stations, in both transects, as shown by the stratification index (ΔT) (Fig. 1c). This showed that the westernmost stations (B7 and D6) were located in the frontal zone, where water masses come into contact and mix (Fig. 1b). To a lesser extent, the nearshore stations, especially the one located at the entrance of the bay of Douarnenez (D2), were also stratified (Fig. 1c).

Regarding fluorescence, values ranged between 0.5 and 15 µg l -1 , with highest values observed during spring and summer (Fig. S2). Peaks were observed below 5 m during spring, and at mid-depth (15-20 m) during summer for the Brest transect, especially at station B7 (Fig. S2a,b). Salinity increased offshore, especially during spring (Fig. S3). However, the range of values was very narrow (between 34.5 and 35.5) regardless of the sampling time or location.

Taxonomic composition

After bioinformatic filtering, the high-throughput sequencing effort yielded a total of 1,143,663 reads for the COI, and 1,039,947 for the 18S datasets. Additional information on number of reads before processing, as well as mean number of reads per sample can be found in Table S3.

From the 380 and 296 metazoan OTUs (for COI and 18S, respectively), 95% belonged to six phyla: Arthropoda (241 and 169 OTUs), Mollusca (47 and 33 OTUs), Cnidaria (31 and 40 OTUs), Annelida (19 and 12 OTUs), Chordata (12 and 14 OTUs), and Echinodermata (15 and 9 OTUs) (Table 1), with Arthropoda, especially copepods, representing nearly 60% of those. The remaining 5% belonged to seven phyla that contained no more than 14 OTUs each (COI and 18S combined) (Table 1).

Regarding the relative abundance (proportion of reads) over all samples combined, the mesozooplankton community was dominated by copepods (61.2%), hydrozoans (9.7%), appendicularians (8.5%), branchiopods (mainly cladocerans, 5.9%), chaetognaths (5.4%), ctenophores (3.4%), polychaetes (2.5%), and malacostracans (euphausiids, amphipods and decapods, 1.8%) (Table 1). The results obtained with both molecular markers were generally consistent. However, the spatial distribution of some groups, such as Chaetognatha in spring (Fig. 2a,d) or Malacostraca in summer (Fig. 2b,e), was quite different when estimated with COI or 18S.

In addition, Porifera and Ostracoda were only detected with COI, while Cnidaria and Appendicularia had lower relative abundances with COI (Fig. 2a-f).

Community structure varied over the course of the year, for instance, with polychaetes and chaetognaths being more representative in spring (Fig. 2a,d), and malacostracans, branchiopods and ctenophores in summer (Fig. 2b,e). During fall, the community composition was mainly homogeneous along the stations, largely dominated by copepods and appendicularians (Fig. 2i,l).

The Shannon diversity index of the mesozooplankton community was slightly higher with COI as compared with 18S (Fig. 2a-f). Overall, a cross-shelf pattern was observed for diversity, with higher values closer to the coast and lower values in the most offshore stations (Fig. 2a-f). This trend did not vary over time.

Holoplankton dominated the mesozooplankton community in the Iroise Sea, whatever the transect and sampling time (Fig. 2g-l). Overall, meroplankton depicted an increase towards the coast, and were more abundant during summer.

Taking a closer look at the meroplankton community, the effect of sampling time was the most striking feature observed (Fig. 3a-c). This was exemplified by the near absence of reads assigned to Decapoda in spring and their large relative abundance in summer in both transects.

This feature was statistically confirmed by the PERMANOVA that showed a significant effect of sampling time on the composition of meroplankton (Table 2), and was also observed in the nMDS and clustering analyses (Fig. 4a-b for COI; Fig. S4a-b for 18S). Conversely, no significant effect of the shelf position was observed on the taxonomic composition of meroplankton, meaning that the composition is stable across the shelf, at these high taxonomic levels (Table 2). Regarding the taxonomic composition, polychaete larvae were remarkably more abundant in spring (Fig. 3a). In turn, cnidarians (here exclusively hydroids), were mostly dominant in fall (Fig. 3c). Echinoderm larvae were also found in greater numbers during fall (Fig. 3c), while decapod larvae were very abundant during summer, and mainly in the most nearshore stations (Fig. 3b). Overall, the Shannon index for meroplankton showed an increase towards the coast (Fig. 3a-c).

Meroplankton composition is shown at the family level for the most represented phylum (Echinodermata), classes (Polychaeta and Bivalvia), and order (Decapoda) in Fig. 5. Overall, the Shannon diversity index was higher towards the shore for most groups, with a few exceptions, in accordance with the general trend observed for the whole meroplankton community (Fig. 3a-c). In addition, Shannon indices were generally higher during spring and summer, and lower during fall.

Decapods were however one exception, presenting the highest diversity values during summer.

Generally, the meroplankton community showed a highly heterogeneous distribution over relatively short spatial distances (stations were less than 30 km apart), as well as over time. Substantial changes were also observed over seasons. For instance, amid echinoderms, larvae of echinoids and holothurians were dominant during spring and summer, while larvae of ophiuroids were mainly dominant during summer and fall (Fig. 5a-c). Polychaete larvae were dominated by the families Oweniidae and Pectinariidae (Fig. 5d-f). Among bivalves, Mytilidae were dominant during all three seasons, with contribution of Pectinidae during spring, and of Hiatellidae during summer and fall (Fig. 5g-i). For decapods, caridean shrimps and brachyuran crabs were present during all seasons, while anomuran crabs were only present during spring and summer, being notably dominant during the warmest season (Fig. 5j-l).

In contrast to meroplankton, the Shannon diversity of holoplankton was relatively homogeneous among months, but showed a decrease towards the nearshore stations (Fig. 3d-f).

The community was largely dominated by copepods, then by chaetognaths, appendicularians, brachiopods and ctenophores. Pelagic polychaetes were also present in the community, mainly during spring (Fig. 3d), while copepods were less represented in the offshore stations in spring and summer (Fig. 3d,e). Shelf position was a significant factor for the holopelagic community with both markers (Fig. 4c-d; Table 2; Fig. S4c-d). Season was also a significant factor for the holoplankton community, but only with the 18S marker (Table 2; Fig. S4c-d), probably due to more marked differences between months in comparison with the COI dataset. For instance, 18S revealed higher relative abundance of appendicularians in fall and of polychaetes in spring (Fig. 2d-f).

Regarding the holoplankton, 183 OTUs were assigned to copepods with COI, which belonged to 16 families (Fig. 6a-c). Shannon diversity values were relatively constant, showing however a decreasing trend towards the coast. Calanoids were largely dominant in the area during the sampling seasons, followed by cyclopoids. The calanoids Acartiidae, Temoridae and Paracalanidae were the most abundant overall (Fig. 6a-c). During fall, a higher number of families were present in the area, with the notable contribution of Centropagidae, Corycaeidae and Oncaeidae, in addition to the regularly dominant calanoids (Fig. 6c).

Regarding copepod feeding traits, most were filter feeders with an omnivore-herbivore trophic regime (Fig. 6d-i). Some spatial patterns were observed, with an increased proportion of copepods with a mixed feeding strategy towards the offshore stations (Fig. 6g,i). In addition, omnivore-detritivore copepods increased offshore during fall (Fig. 6f).

Mesozooplankton distribution in relation to the oceanographic structure

Regarding the influence of environmental variables on the distribution of the meroplankton, holoplankton and copepod feeding traits, the first and second axes of the Redundancy Analysis (RDA) ordination accounted together for 58.0%, 63.8, and 53.6% of the constrained variance, respectively (Fig. 7; Table S4). All ordinations showed the segregation of sampling times, with samples collected in summer being more distinct than those collected in spring and fall (Fig. 7). This seems to be mainly driven by the unique thermohaline condition of summer in the Iroise Sea, with a warmer and stratified water column, especially in the outer shelf stations (yellow squares) (Fig. 7). Distance from the coast was an important factor, thus describing the cross-shelf gradient, as clearly depicted along the ordinations (Fig. 7). Among meroplankton, polychaete and mollusc larvae were mainly related to nearshore and intermediate shelf environmental conditions, as opposed to cnidarians, which were found offshore (Fig. 7a). Amid holoplankton, copepods showed an association with the nearshore stations (Fig. 7b). Regarding the ordination for holoplanktonic groups, axis 2 mainly described the thermohaline gradient, with highest temperature and thermal stratification (ΔT) opposed to salinity (Fig. 7b). Among the taxa, brachiopods and ctenophores seemed to be the most associated with the summer conditions (Fig. 7b). For meroplankton, malacostracans (decapod larvae) were mostly associated with nearshore summer stations (yellow circles) (Fig. 7a). Filter feeders and omnivore-herbivore copepods were associated with summer warmer and stratified conditions (Fig. 7c).

Discussion

Here we investigated spatio-temporal variation in the composition of the mesozooplankton community in a marine protected area (MPA) in the northeast Atlantic Ocean, based on a multilocus DNA metabarcoding approach.

Meroplankton contributes to mesozooplankton community structure across seasons

The mesozooplankton community composition based on DNA metabarcoding data showed significant differences throughout the year, consistently with both markers. This is coherent with temporal variation described for temperate oceans, in response to oceanographic conditions [START_REF] Thomas | Regulation of zooplankton biomass and production in a temperate, coastal ecosystem. 1. Copepods[END_REF][START_REF] Beaugrand | Marine biodiversity, ecosystem functioning, and carbon cycles[END_REF]. The CTD profiles revealed a clear springto-summer transition in the Iroise Sea, represented by the stratification of the water column, and the establishment of the Ushant Front in July, with the most offshore stations (B7 and D6) being located in the frontal zone. Although our dataset did not include monthly sampling, inspection of satellite SST images showed that the front persisted in August and September 2019 (data not shown), while it was no longer present in October.

Mesozooplankton community structure was particularly strong in the meroplankton component over the course of the year, with abundant polychaete larvae during spring and decapod larvae during summer, for instance. In agreement with the present findings, and, importantly, using the same sampling gear (i.e. 200-µm WP2 net), a 20-year time-series from the Western English Channel (station L4), also reported a peak of polychaete larvae in late spring, of decapod larvae in June/July, and of echinoderm larvae in August and September [START_REF] Highfield | Seasonal dynamics of meroplankton assemblages at station L4[END_REF]. This time series also found that seasonal variation accounted for the main changes in the composition of the meroplankton, in addition to inter-annual variability. We hypothesize that the marked temporal variation found for meroplankton in the Iroise Sea was due to two main factors, the spawning/reproductive periods of species and the availability of food for the larvae.

Known spawning times for the most abundant bentho-pelagic species in the Iroise Sea coincided with peaks in meroplankton proportions in spring and summer. For instance, the polychaete Lagis koreni (Pectinariidae) is known to have its main spawning period from April to June [START_REF] Nicolaidou | Life history and productivity of Pectinaria koreni Malmgren (polychaeta)[END_REF] in agreement with our detection of a peak in polychaete larvae in spring.

Another study in the NE Atlantic, including the area off the bay of Douarnenez, also found larvae of L. koreni in May and June [START_REF] Ayata | Meroplankton distribution and its relationship to coastal mesoscale hydrological structure in the northern Bay of Biscay (NE Atlantic)[END_REF]. In addition, Ophiothrix fragilis and Ophiocomina nigra, two co-occurring ophiuroids very abundant in the area [START_REF] Blanchet-Aurigny | Multi-decadal changes in two co-occurring ophiuroid populations[END_REF][START_REF] Guillam | Vertical distribution of brittle star larvae in two contrasting coastal embayments: implications for larval transport[END_REF], were detected in all sampling periods, particularly in fall. Both have extended breeding seasons, with spawning taking place at approximately monthly intervals from April to October [START_REF] Smith | Memoirs: The Reproductive System and Associated Organs of the Brittle-Star Ophiothrix Fragilis[END_REF], in agreement with our observations. Changes in phytoplankton community structure may reflect differential bloom timings and intensities, with high contributions of diatoms over dinoflagellates in spring and summer, observed in previous reports in this region [START_REF] Birrien | Nutrients and primary production in a shallow stratified ecosystem in the Iroise Sea[END_REF][START_REF] Ragueneau | Phytoplankton dynamics in relation to the biogeochemical cycle of silicon in a coastal ecosystem of Western Europe[END_REF]Cadier et al., 2017a).

In the Iroise Sea, spring blooms are associated with higher proportions of diatoms, followed by moderate drops in diatom abundances in summer, with dinoflagellates being more preponderant in fall (Cadier et al., 2017a;[START_REF] Benedetti | The seasonal and inter-annual fluctuations of plankton abundance and community structure in a North Atlantic Marine Protected Area[END_REF]. Diatom blooms are triggered by the seasonal stratification in April-May, which creates favorable conditions in nutrients and irradiance allowing large opportunistic diatoms to grow (Cadier et al., 2017a). Phytoplankton continue to show high concentrations throughout summer due to the replenishment of nutrients in the coastal waters through the establishment of the Ushant Front (Cadier et al., 2017a). The front may therefore favor larval survival by increasing resources available in the zone of the front as compared to nearshore waters (Cadier et al., 2017a[START_REF] Cadier | Assessing spatial and temporal variability of phytoplankton communities' composition in the Iroise Sea ecosystem (Brittany, France): A 3D modeling approach. Part 1: Biophysical control over plankton functional types succession and distribution[END_REF].

Like meroplankton, copepods also showed strong temporal variations. Regarding family compositions, Acartiidae were dominant in spring, while Temoridae and Paracalanidae were present during all seasons. During fall, a higher number of copepod families were present. When evaluating the temporal variability of mesozooplankton in the area, [START_REF] Benedetti | The seasonal and inter-annual fluctuations of plankton abundance and community structure in a North Atlantic Marine Protected Area[END_REF] also found higher contributions of Acartiidae in spring and a higher number of unidentified Calanoida in fall. With respect to the feeding traits, we observed the dominance of omnivore-herbivore filterfeeders overall, with an increase of omnivore-detritivores and carnivores in fall. In the North Atlantic, peaks of copepods that graze on phytoplankton have been seen in spring, while copepods that feed on microzooplankton and detritus were dominant in other seasons [START_REF] Friedland | Seasonal phytoplankton blooms in the North Atlantic linked to the overwintering strategies of copepods[END_REF]. Overall, omnivorous filter-feeding taxa (i.e. Temoridae and Paracalanidae copepods, appendicularians and cladocerans) represented the dominant trophic trait over the mesozooplankton community throughout the water column. To a lesser degree, carnivory was also an important feeding behavior, with Corycaeidae copepods peaking during fall, and hydrozoans and chaetognaths constituting the second and third most abundant groups in the area.

High spatial heterogeneity in the mesozooplankton community from the nearshore to offshore

Stratification of the water column and temperature were key factors in determining mesozooplankton community structure together with distance from the coast, reflecting the nearshore-offshore gradient, as these explain most of the variation of the first RDA components.

In a previous study, using a nearshore-offshore transect in September 2009, [START_REF] Schultes | Influence of physical forcing on mesozooplankton communities at the Ushant tidal front[END_REF] found that the East-West gradient was the main pattern of zooplankton abundance variations in the Iroise Sea. In our study, a noticeable differentiation along the cross-shelf gradient was observed, mainly in terms of community composition for holoplankton and Shannon diversity index for meroplankton. The inner stations had the highest level of diversity for meroplankton. This likely reflects the influence of larval export from the bays, which hosts abundant and highly diverse benthic communities [START_REF] Chauvaud | Long-term variation of the Bay of Brest ecosystem: Benthic-pelagic coupling revisited[END_REF][START_REF] Gallon | Regional and latitudinal patterns of soft-bottom macrobenthic invertebrates along French coasts: Results from the RESOMAR database[END_REF]. In addition, groups that are known for their coastal affiliations (e.g. malacostracans and echinoderms) were associated with nearshore and intermediate shelf environmental conditions. Furthermore, we found that the mesozooplankton community was highly heterogeneous at a small spatial scale, especially along the cross-shelf gradient. Changes in zooplankton community composition between relatively nearby sites have been observed elsewhere, mainly attributed to plankton patchiness and the presence of ocean fronts [START_REF] Seda | Zooplankton community structure along a trophic gradient in a canyon-shaped dam reservoir[END_REF][START_REF] Trudnowska | Plankton patchiness in the Polar Front region of the west Spitsbergen Shelf[END_REF]. Plankton distribution and its patchiness are regulated by both biological and physical processes that govern its abundance and community composition [START_REF] Mackas | Plankton patchiness: biology in the physical vernacular[END_REF][START_REF] Acha | Ecological Processes at Marine Fronts: Oases in the Ocean[END_REF]. In addition, the outflows from each of the bays may also play a role in the community observed in the adjacent sampled area. The mixing intensity from the bays to the front leads to localized and variable small oceanographic processes, contributing to the spatial variability even within the coastal zone for the meroplankton community.

Mesozooplankton in the Iroise Sea provides a wide range of food resources for the higher trophic levels. For example, crustaceans (small copepods, and decapod and cirriped larvae) are a significant part of the diet of the sardine species Sardina pilchardus, a locally important commercial species [START_REF] Garrido | Diet and feeding intensity of sardine Sardina pilchardus: Correlation with satellite-derived chlorophyll data[END_REF]. Crustaceans are also an important food resource for the exclusively planktivorous basking shark (Cetorhinus maximus), which annual sightings in the Iroise Sea are associated with the Ushant Front [START_REF] Sims | Chapter 3 Sieving a Living. A Review of the Biology, Ecology and Conservation Status of the Plankton-Feeding Basking Shark Cetorhinus Maximus[END_REF], and for seabirds [START_REF] Springer | Hot oceanography: Planktivorous seabirds reveal ecosystem responses to warming of the Bering Sea[END_REF]. In addition, recent evidence showed that gelatinous zooplankton (ctenophores, hydromedusae, chaetognaths and salps), which were also very abundant in our samples, form an important part of fish diet with higher levels of protein, carbon content and other nutrients than previously thought [START_REF] Henschke | Rethinking the Role of Salps in the Ocean[END_REF][START_REF] Diaz Briz | Gelatinous zooplankton (ctenophores, salps and medusae): an important food resource of fishes in the temperate SW Atlantic Ocean[END_REF].

Safeguarding the biodiversity of coastal waters and managing the sustainable exploitation of marine resources are the main objectives within the establishment of the Iroise Marine Natural Park. The plankton monitoring program (PNMIR) aims particularly to evaluate the interannual variations in the phyto-and zooplankton communities and their link with fisheries of commercially important species in the area, such as the European sardine S. pilchardus [START_REF] Benedetti | The seasonal and inter-annual fluctuations of plankton abundance and community structure in a North Atlantic Marine Protected Area[END_REF].

Regarding the influence of the Ushant Front in the pelagic communities, a longer monitoring timeseries, with more frequent sampling would aid to follow the full cycle of the front. One further limitation of our observations is the absence of sampling in fully oligotrophic waters, offshore of the frontal zone. Sampling offshore would have allowed us to determine whether communities in the frontal zone represented a combination of nearshore and offshore taxa, or whether taxa specific to the frontal zone were present, as observed for phytoplankton [START_REF] Landeira | Biophysical interactions control the size and abundance of large phytoplankton chains at the ushant tidal front[END_REF]. Offshore sampling was logistically difficult to implement with the resources available to the MPA, but future sampling and monitoring efforts that include sites beyond the frontal zone may improve our understanding of the dynamics of planktonic communities and their effects on trophic webs and biogeochemical cycles in the area. In addition, we recommend incorporating multi-marker DNA metabarcoding as a standard tool for biodiversity assessment and environmental monitoring timeseries, as multiple compartments of the planktonic community sampled concurrently can be examined in parallel.

Conclusions

Our study is the first to implement DNA metabarcoding to document the spatial and temporal variations in the community composition and diversity of mesozooplankton in the Iroise Sea. Metabarcoding of mixed tissue samples allowed us to detect a diverse array of marine zooplankton and examine changes in community structure across several different phyla. Although the mesozooplankton community was overwhelmingly dominated by holoplankton in terms of relative abundance of reads, meroplankton showed a relatively high contribution of taxa present in the area, expressed by the number of OTUs. It is worth pointing out that some meroplanktonic groups may be underestimated due to the size of the mesh (200 μm), notably bivalve larvae.

Our findings indicate that spring and summer are the periods with higher relative abundances and diversity for most meroplankton groups in the Iroise Sea, associated with the spawning period of benthic species and with favorable environmental conditions for the development of larvae, probably due to the presence of the Ushant Front. During fall, despite the presence of some meroplanktonic groups, holoplankton taxa dominate the mesozooplankton community in terms of relative abundance. Most meroplankters have likely settled by this time period, or less larvae are released, and that the holoplankton taxa present feed mainly on sinking and suspended particles (detritivores) and/or microzooplankton (carnivorous).

Our results for copepod feeding traits are in general agreement with observations for bacterial communities associated with the Ushant Front. Copiotrophic bacteria that recycle detrital organic matter were also dominant in communities following the period of the phytoplankton blooms [START_REF] Lemonnier | Linking Spatial and Temporal Dynamic of Bacterioplankton Communities With Ecological Strategies Across a Coastal Frontal Area[END_REF]. Both copepod and bacterial communities therefore appear to respond to increases in available organic matter post-bloom.

The significant small-scale spatial variation observed also reflect the strong nearshore-offshore gradient. In addition, the importance of the stratification of the water column reflects the influence of the Ushant Front in structuring the mesozooplankton community.In the future, the present findings should be integrated with the characterization of other target communities, such as phytoplankton, bacterioplankton, prokaryotes and higher trophic levels, in order to present a full picture of the influence of the Ushant Front in the pelagic component of the Iroise Sea. Copepods traits based on available datasets [START_REF] Benedetti | Identifying copepod functional groups from species functional traits[END_REF][START_REF] Brun | A trait database for marine copepods[END_REF].

Tables and Figures

Figure 1 .

 1 Figure 1. Location of the study area and vertical profiles of temperature. (a) Position of the sampling stations in the Iroise Sea, along the transects off the bays of Brest (B2-B7) and Douarnenez (D2-D6). The red dashed line represents the boundaries of the Iroise Marine Natural Park. Vertical profiles of temperature, and stratification index (ΔT; indicated with color dots at the

Figure 2 .

 2 Figure 2. Proportion of reads of the mesozooplankton taxa, and reads associated to meroand holoplankton. Proportion (percentage of reads) of mesozooplankton taxa with COI (a-c) and 18S (d-f) genes, and of mero-and holoplankton with COI (g-i) and 18S (j-l), in the Iroise Sea during spring, summer and fall 2019, along the two study transects. Black dots represent the Shannon diversity index. Taxa that represented less than 0.02% of the reads are not shown.

Figure 3 .

 3 Figure 3. Proportion of main taxa for mero-and holoplankton. Proportion (percentage of reads) of the main taxa of mero-and ichthyoplankton (a-c) and holoplankton (d-f) in the Iroise Sea during spring, summer and fall 2019 with the COI gene. Black dots represent the Shannon diversity index.

Figure 4 .

 4 Figure 4. NMDS and clustering of the samples for mero-and holoplankton taxa. Nonmetric multidimensional scaling (nMDS) ordination and clustering of samples collected in the Iroise Sea based on the rarefied abundance (number of reads) of OTUs assigned to mero-(a,b) and holoplankton (c,d) taxa with the COI gene. Samples are classified according to shelf position and season of sampling.

Figure 5 .

 5 Figure 5. Community composition, at the family level, for Echinodermata, Polychaeta, Bivalvia and Decapoda, focusing on meroplankton. Proportion (percentage of reads) per family for Echinodermata (a-c), Polychaeta (d-f), Bivalvia (g-i) and Decapoda (j-l) in the Iroise Sea during spring, summer and fall 2019 with the COI gene. Black dots represent the Shannon diversity index.For echinoderms, Ec = Echinoidea, Ho = Holothuroidea, and Op = Ophiuroidea. For decapods, An = Anomura, Br = Brachyura, Ca = Caridea, and Ge = Gebiidea.

Figure 6 .

 6 Figure 6. Taxonomic composition and feeding traits of copepods. Proportion (percentage of reads) of copepod families (a-c), and copepods feeding traits (d-i) in the Iroise Sea during spring, summer and fall 2019 as obtained from taxonomic assignment with the COI gene. Black dots represent the Shannon diversity index. Copepods are colored according to their Orders: Ca = Calanoida (shades of blue), Cy = Cyclopoida (shades of pink), Ha = Harpacticoida (yellow), Mo = Monstrilloida (purple), and Si = Siphonostomatoida (orange). Copepods traits based on available

Figure 7 .

 7 Figure 7. Redundancy Analysis (RDA) ordination for meroplankton, holoplankton and copepods feeding traits in relation to environmental variables. Triplot of the RDA ordination with explanatory variables (arrows), taxa (abbreviations in blue) and samples (symbols), based on OTUs retrieved from the COI dataset and assigned to meroplankton (a), holoplankton (b), and copepods feeding traits (c). Samples are classified according to shelf position and season of sampling.

Table 1 . Number of reads and OTUs by Phylum and Class.

 1 Number of reads and OTUs assigned to Phylum and Class for COI and 18S markers, ordered by higher to lower number of reads.

	OTUs	Reads

Acknowledgements

We thank Yannis Turpin, Rémy Destabeau, Arthur Hebert, Pierre Joffredo, Anne-Louise Blier, and Nathalie Dridi-Moreul for their help in sampling. We thank Louis Marié for providing the SST maps. We also thank Gabin Droual and Martin Marzloff for suggestions on data analyses and interpretation. This work was supported by the ISblue project, Interdisciplinary Graduate School for the Blue Planet (ANR-17-EURE-0015), co-funded by a grant from the French government under the program "Investissements d'Avenir", and by a grant from the Regional Council of Brittany (SAD programme). It was also supported by a grant from Ifremer (Politique de Site: LADIDA, to F. Nunes and T. Comtet). Sampling was conducted with support from the Iroise Marine Natural Park (Parc Naturel Marin d'Iroise), which is part of the Office Français de la Biodiversité (OFB). This is publication ISEM XX-XXX.

Data Availability Statement

The data will be made available within a DOI once the acceptance of the manuscript.


Gianluca Lavalle

Sophie Mergui

Nicolas Grenier

Georg F Dietze

Superconfined falling liquid films: linear versus nonlinear dynamics

Keywords:

The effect of a counter-current gas flow on the linear stability of an inclined falling liquid film switches from destabilizing to stabilizing, as the flow confinement is increased. We confront this linear effect with the response of nonlinear surface waves resulting from long-wave interfacial instability. For the strongest confinement studied, the gas flow damps both the linear growth rate and the amplitude of nonlinear travelling waves, and this holds for waves of the most-amplified frequency and for low-frequency solitary waves. In the latter case, waves are shaped into elongated humps with a flat top that resist secondary instabilities.

For intermediate confinement, the linear and nonlinear responses are opposed and can be non-monotonic. The linear growth rate of the most-amplified waves first decreases and then increases as the gas velocity is increased, whereas their nonlinear amplitude is first amplified and then damped. Conversely, solitary waves are amplified linearly but damped nonlinearly.

For the weakest confinement, solitary waves are prone to two secondary instability modes that are not observed in unconfined falling films. The first involves waves of diminishing amplitude slipstreaming toward their growing leading neighbours. The second causes wave splitting events that lead to a train of smaller, shorter waves.

Introduction

We consider a gravity-driven two-dimensional liquid film falling down a plane tilted at an angle w.r.t. the horizontal, in contact with a counter-current gas flow that is strongly confined by an upper wall placed at = (figure 1). Both fluids are Newtonian with constant fluid properties and the flow is laminar. Confined falling liquid films occur in rectification columns for cryogenic air separation, which contain structured packings that subdivide the column cross-section into millimetric channels (Valluri et al. 2005). Even stronger confinement is realized in compact reflux condensers (Vlachos et al. 2001), falling † Email address for correspondence: dietze@fast.u-psud.fr Abstract must not spill onto p.2 film microreactors (Zhang et al. 2009), and micro-gap coolers (Kabov et al. 2011). We are interested in nonlinear waves that form on the surface of the falling liquid film due to the long-wave Kapitza instability (Kapitza 1948), and, in particular, how these are affected by the gas velocity in a strongly-confined setting. Such waves are known to trigger flooding events, either by local obstruction of the channel, flow reversal, or wave reversal (Vlachos et al. 2001;Trifonov 2010a;Tseluiko & Kalliadasis 2011).

For weak confinements, flooding seems to be favoured by decreasing the gap height and/or increasing the gas flow rate. Experiments (Kofman et al. 2017) and numerical simulations (Trifonov 2010a,b) alike have shown that the amplitude of nonlinear waves increases with increasing counter-current gas flow and that this growth diverges in the vicinity of the flooding point (Drosos et al. 2006). Moreover, actual flooding experiments have shown that the critical gas flow rate decreases with diminishing gap height (Sudo 1996). Linear stability investigations, which demonstrate an increase in the maximal linear growth rate with increasing gas velocity, tend to confirm this nonlinear picture (Alekseenko et al. 2009;Vellingiri et al. 2015;Schmidt et al. 2016;Trifonov 2017).

On the other hand, recent investigations suggest that strong confinements may, in fact, lower the risk of flooding. Lavalle et al. (2019) have shown that the Kapitza instability can be entirely suppressed by sufficiently confining the gas, as suggested by Tilley et al. (1994) and confirmed by Kushnir et al. (2021), and that this is facilitated by low tilt angles. Further, the authors observed that the linear stabilization, which they confirmed experimentally, is amplified by increasing the counter-current gas flow rate. Recent nonlinear direct numerical simulations (DNS) of inclined falling liquid films (Trifonov 2020) have identified a nonmonotonic variation of the interfacial velocity, mean film thickness, and inter-phase friction coefficient with increasing counter-current gas velocity, although the trend of the wave amplitude remained monotonic and increasing. We aim to confront linear stability predictions with the response of nonlinear surface waves to an increasingly strong counter-current gas flow. In particular, we wish to know whether nonlinear travelling waves can be damped under the effect of the gas flow, in line with the linear observations, and, if so, whether they may resist secondary instability. Such a situation would amount to a reduced flooding risk. By secondary instability we mean the loss of stability of travelling-wave solutions (TWS) produced by the primary Kapitza instability (Liu & Gollub 1993;Lavalle et al. 2020), and our analysis is restricted to two-dimensional such instability modes. Our manuscript is structured as follows. The mathematical description and numerical methods are introduced in §2, followed by section 3, which reports results of our linear and nonlinear computations. Subsection 3.1 is dedicated to surface waves of the linearly mostamplified frequency, whereas subsection 3.2 concerns low-frequency solitary waves (here, we will also introduce our DNS data). Conclusions are drawn in section 4.

Mathematical description

The flow in figure 1 is governed by the Navier-Stokes and continuity equations, written in Einstein notation using the directional indices =1,2 and =1,2 ( 1 = , 1 = , 2 = , and 2 = ), and the phase indicator , which identifies liquid ( = ) and gas ( = ):

+ = - + Re -1 + 2 Fr -2 { 1 sin( ) -2 cos( )} , (2.1a) = 0, (2.1b)
where lengths have been scaled with the channel height L= ★ (stars denote dimensional quantities throughout), velocities with the phase-specific signed superficial velocities U = ★ 0 / ★ , time with T =L/U , and the phase-specific pressure with U 2 . Further, is the Kronecker symbol, =1, and =U /U . The gravitational acceleration enters through the Froude number Fr=U / L, and the Reynolds numbers Re =U L = ★ 0 are based on the phase-specific signed nominal flow rates ★ 0 of the flat-film primary flow, ★ 0 and Re being negative for a counter-current gas flow. The boundary conditions are:

| =0 = | =0 = =1 = =1 = 0, (2.1c)
and the kinematic and dynamic coupling conditions at the film surface =ℎ( , ):

= -1 , = -1 = ℎ + ℎ, (2.1d) + = -2 Π + -1 Π + We , (2.1e) = -1 Π , (2.1f )
where = 1 2 + denotes the strain rate tensor, Π = / and Π = / are the dynamic viscosity and density ratios, and the surface tension enters through the Weber number We= -1 U -2 L -1 . The orthonormal surface coordinate system is constructed by

=[-ℎ, 1] (1 + 2 ℎ) -1/2 and =[1, ℎ] (1 + 2 ℎ) -1/2 ,
       ℎ Φ Ψ        =        ℎ 0 Φ 0 ( ) Ψ 0 ( ) 0 ( , )        +         ĥ ( ) ( ) ˆ ( )         exp { ( -)} , (2.2)
where Φ and Ψ designate the stream functions in the liquid and gas, the subscript 0 denotes the flat-interface base flow, ∈ C is the complex wave number of the perturbation, and ∈ R its angular frequency. We focus on long-wave instability modes, which we track

{ + + ℎ = -We ℎ + Fr -2 1 -Π {sin( ) -cos( ) ℎ} + Re -1 + Re -1 ( ℎ) 2 + ℎ + ℎ + ,
(2.3a) We perform linear stability calculations by solving the dispersion equation DR( , )=0, obtained by linearizing (2.3) around ℎ 0 , 0 , 0 , for = + at a given ∈ R:

+ ℎ = 0, - ℎ = 0, ( 2
ℎ, , = ℎ 0 , 0 , 0 + ĥ, ˆ , ˆ exp { ( -)} , (2.4a)
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DR = 2 - + - + 2 (2.4b) + 2 Fr -2 cos( ) -Π cos( ) -3 4 We + Re -1 -Re -1 -Re -1 ℎ -2 3 Re -1 + 2 2 Re -1 -Re -1 .
We also compute nonlinear travelling-wave solutions (TWS), which remain unaltered in a reference frame moving at the wave speed , through numerical continuation based on (2.

Results

We set the tilt angle to =10 Kapitza number for this combination is Ka= -1/3 -1/3 -4/3 =509.5. The channel height

★ is varied as ★ =1.2, 1.7, 1.8, 1.9, 2.1, and 2.4 mm, which corresponds to values of =2, 2.8, 3, 3.1, 3.4, and 3.9 for the relative confinement:

= ★ / ℎ ★ 0 =1 = 1/ ℎ 0 | =1 , (3.1)
where ℎ 0 | =1 is the primary flow film thickness for an aerostatic gas pressure gradient, i.e. = /sin( )=1. We wish to confront the linear and nonlinear implications of increasing the counter-current gas flow rate at fixed Re . In particular, we wish to know whether nonlinear waves can be damped via increasing Re . Panel 2c plots the upper and lower relative film height deflections ℎ max / h-1 and ℎ min / h-1 for nonlinear TWS at = max , where h=Λ -1 ∫ Λ 0 ℎ is the film height averaged over one wavelength, with h ≠ ℎ 0 in the case of nonlinear waves. For =3, 3.1, and 3.4, TWS display a non-monotonic trend that is opposed to the linear one. That is, ℎ max / h -1 in panel 2c, which we will refer to as the wave amplitude, first increases and then decreases with increasing Re , whereas -max / -max =1 in panel 2a first decreases and then increases. Conversely, for =2 and 2.8, the nonlinear and linear trends both imply stabilization, and, for =3.9, they both imply destabilization, at least up to the amplitude maximum in panel 2c. Except for the two weakest confinements ( =2, 2.8, 3, 3.1), TWS are bounded by a nonlinear wave suppression, where ℎ max =ℎ min , resulting from period-halving (PH) bifurcations (marked by symbols), which sets in before the linear AI and S thresholds in panel 2a. Panel 3a shows wave profiles leading up to such a PH bifurcation ( =3). The sole precursory capillary ripple is seen to grow until splitting the wave into two identical halves. Conversely, for =3.9 (panel 3b), the capillary ripple disappears when increasing Re toward the AI limit.

Most-amplified waves

We conclude from figure 2 that linear stability predictions can be misleading. In particular,

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Journal of Fluid Mechanics the amplitude of nonlinear waves may grow with increasing counter-current gas velocity, even though the linear growth rate decreases. Further, TWS become unstable to periodic secondary instability modes (dot-dashed lines in panel 2c) beyond a threshold Re , which we have determined via transient periodic computations started from TWS. These periodic modes do not lead to dangerous events, but TWS are also prone to a subharmonic instability in the case of a spatially-evolving film (Movie1.avi). Originally identified in unconfined films (Liu & Gollub 1993), this instability triggers wave coalescence events (Chang et al. 1996a) that can lead to intermittent flooding in long channels (Dietze & Ruyer-Quil 2013).

Solitary waves

We focus now on low-frequency solitary waves at a fixed wavelength Λ=4.5 Λmax , where

Λmax denotes the linearly most-amplified wavelength for a passive outer phase, all other parameters remaining as in figure 2. These waves lie on the ascending branch of the linear dispersion curves in panels 2b and 2d, and thus the linear effect of increasing the gas flow is monotonous, either destabilizing ( =3, 3.1, 3.4, 3.9) or stabilizing ( =2, 2.8). Panel 4a represents the nonlinear response of solitary TWS, evidencing a monotonous gas-induced attenuation of the wave amplitude for =2, 2.8, 3, and 3.1. For =3 and 3.1, this nonlinear effect is opposed to the linear amplification, and both effects are inverted w.r.t. the initial response of the most-amplified waves (panels 2a, 2c). Solution branches of solitary TWS in panel 4a are bounded either by the linear thresholds of absolute instability (AI, =3, 3.1, and 3.4) and full stabilisation (S, =2 and 2.8) from panel 2a, or by a nonlinear limit point (LP, =3.9) that occurs slightly before (about 2% in terms of Re ) the AI bound.

For the strongest confinement, =2 (open squares in panel 4a), linear and nonlinear effects are aligned and stabilizing. In that case, the gas shapes the wave hump into an elongated flat-top form (panel 4d). In panel 4e, we compare this solution (solid line) with TWS in the limits Π =0 (red dot-dot-dashed) and Π =0 (blue dashed), which respectively deactivate the gas pressure and the gas-side viscous stresses in (2.1e) and (2.1f). From this comparison, we can conclude that the gas pressure gradient and not the gaseous viscous stresses are the cause for wave flattening. The flat-top TWS (also shown in figure 1), which we have reproduced with a DNS at slightly greater Re =15.7 (open circles in panel 4e), is stable in periodic transient computations, and undergoes only weak modulations in a spatially-evolving film (Movie2.avi).

For the weakest confinement, =3.9, solitary TWS are more susceptible to secondary instability modes. We discuss this based on the wave profiles in panel 4b, which correspond et al. 1996b), where larger-amplitude waves catch up with and accumulate the smaller ones travelling in front. The slipstreaming occurs in concert up-and downstream of a leading wave, and thus the latter is increasingly exposed to the counter-current gas flow, leading eventually to its destruction through a wave breaking event, before coalescence can occur.

When increasing the counter-current gas velocity further, TWS become periodically

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Conclusion

In this work, we have demonstrated that linear stability predictions of strongly-confined falling liquid films can mislead in estimating the effect of a counter-current gas flow on the film's waviness. Both for waves of the most amplified frequency and for low-frequency solitary waves, we have identified situations where the linear and nonlinear responses are opposed, i.e. linear waves are damped while nonlinear ones are amplified, or vice-versa. In some cases, linear waves are bounded by absolute instability, whereas nonlinear waves are fully suppressed via a period-halving bifurcation. Nonetheless, at very strong confinement, both the linear and nonlinear responses imply stabilization and travelling-wave solutions (TWS) resist secondary instability. This suggests that the risk of wave-induced flooding can be lowered by strongly confining the flow. At weaker confinement, we have found two new secondary instability modes not observed in unconfined films. The first tends to coarsen the wave train, via smaller waves accelerating in the slipstream of their leading neighbours.

The second causes wave splitting events that refine the wave train into a sequence of less dangerous shorter and smaller daughter waves.

Our two-dimensional analysis cannot account for the spanwise destabilization of TWS, which entails the formation of three-dimensional waves in the downstream portion of a spatially-evolving falling liquid film (Chang 1994;Liu et al. 1995;Scheid et al. 2006;Kofman et al. 2014;Dietze et al. 2014;Kharlamov et al. 2015). Nonetheless, we expect our conclusion on the stabilizing effect of strong confinement to extend to that situation. Firstly, the inertia-driven three-dimensional secondary instability mode (Kofman et al. 2014) is known to weaken at the small tilt angles considered here. In experiments, this translates to quasi-two-dimensional wave fronts with only weak spanwise modulations, which are maintained up to large gas velocities (Kofman et al. 2017). Secondly, the spanwise instability mode is dictated by the wall-normal acceleration of liquid within the initially two-dimensional wave hump. Thus, the gas-effect on the amplitude of two-and three-dimensional wave humps is expected to be concurrent. This is supported by the weakly-confined experiments of Kofman et al. (2017), where the counter-current gas flow amplified both instability modes.

In our strongly-confined setting, we expect the opposite, i.e. a damping of both modes.

The channel heights considered here (1.2 mm (Kabov et al. 2007(Kabov et al. , 2011) ) have shown that it is possible to produce the strong crosswise confinement levels studied here ( ★ =2 mm) at weak spanwise confinement ( ★ =40 mm).

Figure 1 :

 1 Figure 1: Problem sketch: gravity-driven falling liquid film (lower blue streamlines) in contact with a counter-current gas flow (upper red streamlines) flowing through a channel of dimensional gap height ★ inclined at an angle w.r.t. the horizontal. Streamlines (separated by constant stream function increments) are shown in the wall-fixed reference frame, and Λ is the wavelength.

  These investigations have motivated us to take a closer look at strongly-confined inclined falling liquid films, in contrast toDietze & Ruyer-Quil (2013) andLavalle et al. (2020), who studied the vertical configuration, where the gas-induced linear stabilization is relatively weak. This is because the inertia-induced destabilizing mechanism of the Kapitza instability is weakened less and less by the stabilizing effect of normal gravity as the tilt angle is increased, and thus the relative weight of the gas effect diminishes(Lavalle et al. 2019).

  through numerical continuation using Auto07P (Lavalle et al. 2019), having checked with a Chebyshev collocation code (Barmak et al. 2016) that short wave modes remain stable throughout the studied parameter range. Second, we perform a DNS with the finite-volume solver Basilisk (Popinet 2015), based on the volume of fluid (VOF) and the continuum surface force (CSF) methods, following Dietze (2019). Here, we impose periodic conditions on a domain spanning the wavelength Λ. Our low-dimensional model is based on the weighted residual integral boundary layer (WRIBL) approach (Ruyer-Quil & Manneville 1998; Kalliadasis et al. 2012), which describes the flow via evolution equations for the flow rate and film height ℎ. We employ the two-phase formulation of Dietze & Ruyer-Quil (2013) written in Einstein notation ( = , and = , ):

  .3b) where and denote the liquid and gas flow rates (per unit width) and the coefficients , , , , , , , and are known functions of the film height ℎ (Dietze & Ruyer-Quil 2013).

  3), using Auto07P (Doedel 2008). Our code allows to track TWS at the linearly most-amplified angular frequency = max , via the following constraints (Dietze et al. 2020): DR( max , ) = 0, | = max = 0. (2.5) Finally, we check the stability of nonlinear TWS via transient computations based on (2.3), using either periodic or inlet/outlet boundary conditions (Lavalle et al. 2020).

Figure 2

 2 Figure2demonstrates the effect of increasing the counter-current gas flow rate on the linearly most-amplified waves ( = max ) at fixed Re =15 for different values. Along each curve in panels 2a and 2c, the channel height ★ remains fixed while ℎ 0 increases (between 10% for the strongest and 20% for the weakest confinement), and so (3.1) specifies a representative confinement for each case, corresponding to the rightmost point of each curve (where =1). Curves in panel 2a track the maximum linear spatial growth rate -max in terms of Re , dashed lines corresponding to OS and solid lines to WRIBL calculations.At the largest (filled squares, =3.9), the growth rate increases monotonically with Re , implying a gas-induced destabilization, up to the onset of absolute instability (AI), where max diverges(Vellingiri et al. 2015). Conversely, at very small values (open squares and pentagons, =2, 2.8), the effect of the gas is monotonically stabilizing, up to the point of fully suppressing (S) the long-wave Kapitza instability(Lavalle et al. 2019; Kushnir et al. 2021). In the intermediate range (crosses, asterisks, and diamonds, =3, 3.1, and 3.4), the behaviour is non-monotonic, stabilization occurring at low and destabilization at large values of Re . Panels 2b ( =3.1) and 2d ( =2) represent dispersion curves for the non-monotonic and fully-stabilizing cases. Overall, there is quantitative agreement for Re <150 between linear OS and WRIBL predictions in panels 2a, 2b, and 2d, whereas qualitative agreement is retained when approaching the AI limits.

Figure 2 :

 2 Figure 2: Most-amplified waves: =10 • , Re =15, Ka=509.5. Linear (panels a, b, d) versus nonlinear (panel c) predictions. Filled squares: =3.9, diamonds: =3.4, asterisks: =3.1, crosses: =3; pentagons: =2.8; open squares: =2. (a) Maximal linear growth rate -max versus Re , related to the aerostatic limit -max =1 , where = /sin( ). Solid: WRIBL, dashed: OS; (b,d) dispersion curves -( ) for two cases from panel a. Red curves trace -max ( max ) up to absolute instability (AI) or full stabilization (S). (b) =3.1; from right to left: =1, Re =-60, -100, -145, -170, and -184; (d) =2; from right to left: =1, Re =-4, -7, and -10; (c) amplitude of nonlinear TWS (WRIBL) at = max . PH denotes period-halving bifurcations and dot-dashed green lines identify periodically unstable TWS.

Figure 3 :

 3 Figure 3: Wave profiles of TWS from panel 2c. (a) =3 (cross in panel 2c). Approaching the PH bifurcation: Re =-37 (thick solid) to Re =-88 (green); (b) =3.9 (filled square in panel 2c). Suppression of the capillary ripple while approaching the AI limit: Re =-79 (thick solid) to Re =-348 (green).

Figure 4 :

 4 Figure 4: Solitary waves: =10 • , Re =15, Ka=509.5, Λ=4.5 Λmax . (a) Amplitude of nonlinear TWS (WRIBL). Right to left: =2, 2 (Π =0), 2 (Π =0), 2.8, 3, 3.1, 3.4, and 3.9. Dot-dashed green lines highlight periodically unstable solutions; (b) wave profiles corresponding to open circles ( =3.9) in panel a. Bottom to top: Re =-10, -100, -145, and -149; (c) transient periodic computation started from thick-solid TWS in panel b. Black: local film height, green: wave height; (d) flat-top wave corresponding to black filled circle in panel 4a: =2, Re =-7. Streamlines in the wave-fixed reference frame; (e) different limits of the =2 solution in panel d (filled circles in panel a). Solid black: full inter-phase coupling; dashed blue: Π =0 in (2.1e) and (2.1f); dot-dot-dashed red: Π =0 in (2.1e); open circles: DNS at = /sin( )= TWS =84.8, Re =15.7.

Figure 5 :

 5 Figure 5: Slip streaming (panels a, b) and wave splitting (panels c, d) in solitary wave trains. Spatio-temporal computations with our WRIBL model (2.3) on an open domain of length =31.4 Λ TWS , applying coherent inlet forcing at = TWS : =10 • , =3.9, Re =15, Ka=509.5. Space-time plots of the film height ℎ (panels a, c), and wave profile snapshots (panels b, d). Parallel green dashed lines indicate initial TWS celerity. (a,b) Re =-145, TWS =0.20; (c,d) Re =-149, TWS =0.19. Red symbols identify primary/secondary wave maxima.

★ 2 .

 2 4 mm) lie in between the range of classical (Vlachos et al. 2001) falling-film experiments ( ★ 5 mm) and micro-channel (Zhang et al. 2009; Hu & Cubaud 2018) falling-film experiments ( ★ 1 mm). Also, strongly-confined experiments have generally not considered small tilt angles. Our numerical computations suggest that this uncharted part of the regime map deserves experimental attention. Should experiments confirm our findings, it would mean that surface waves can be maintained in very compact liquid/gas exchangers without the risk of flooding. Current microreactor designs consist of arrays of narrow grooves, where the film surface is pinned laterally (Al-Rawashdeh et al. 2008), and this effectively suppresses surface waves (Pollak et al. 2011), solving the flooding problem, but at the cost of waiving the substantial wave-induced intensification of heat/mass transfer (Yoshimura et al. 1996). Our results suggest relaxing the lateral confinement in such devices to allow for the development of surface waves. Experiments in horizontal wavy liquid-film/gas flows through mini-gaps

  from which we obtain the film surface curvature =-∇ • . We perform two types of calculations based on the first principles (2.1) to validate our low-dimensional model. First, we solve the OS linear stability problem (Tilley et al. 1994), assuming spatially growing normal modes (Barmak et al. 2016):

Acknowledgements

We appreciate helpful discussions with J. P. Hulin. This work was supported by the ANR wavyFILM project, grant ANR-15-CE06-0016-01 of the French Agence Nationale de la Recherche.

Declaration of interests

The authors report no conflict of interest.

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Supplementary data

The manuscript includes four supplementary movies.