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Introduction: Louth Crater is a 36 km diameter located at 70 °N, 103.2 °E (Fig. 1) less than 1000 km from the Martian North Polar Cap. At the center of Louth crater a perennial water ice cap ~10 km in diameter, ~250 m in width (Fig. 1) that undergoes phase changes (condensation / sublimation cycles) during the Martian year [1 - 4]. Some periodic structure at the surface of its perennial water ice cap have been observed [2]. The presence of smaller ice undulations superimposed on this periodic structure, comparable to the sublimation waves on the Martian North Polar Cap [5] could be formed during sublimation and condensation period of the water ice. The characterization of this ice waves could make it possible to specify environmental conditions favorable to their formation. The first part of the study consists of identifying these ice waves using orbital topography and imaging data, and then associating these results with data from the Martian Database [6-7] and with the scaling laws inherent to the formation of sublimation and condensation waves. Fig. 1: Louth crater in summer. CTX product J02_045439_2504_XN_70N256W Ls = 133.2° Geomorphological analysis: Methods: Digital Elevation Model (DEM) at ~100 m/pixel and MOLA elevation data at ~128 m/pixel have been coupled with imagery data from HRSC ~10 m/pixel, CTX at ~6 m/pixel and HiRISE images for more precise areas for up to 25 cm/pixel. Data were georeferenced in ESRI’s ArcMap GIS software to produce geomorphological map and analyzed to evaluate ice waves shape and spatial organization. Observations: Louth presents two units (Fig. 2). (a) Lower unit with dark stucco texture and stratifications (Fig. 3a). (b) Fresh ice overlies this older, stratified structure (Fig 3.a). This fresh ice is distributed in a non-uniform manner as shown by the kilometrics waves of about 560 m wavelength on which are superimposed decametrics waves of about 55 m wavelength which are both perpendicular to the prevailing wind (Fig 3.b). The crests of both wave populations show similar NW-SE. The main wind direction was assessed from barkhane field on the sand mound. Fig. 2: Louth’s geomorphological map in summer. CTX product J02_045439_2504_XN_70N256W Ls = 133.2°. Fig. 3: Boxes from Fig. 2. (a) East side of the Louth crater ice cap. Green lines represents stratifications, HiRISE product EPS_045439_2505, Ls = 133.2°. (b) decametric waves on the ice waves. Black dashes represent leeside foot of each kilometric waves. Blue lines emphasize decametric waves, same HiRISE product from (a). Transport hypothesis: Preliminary experiments studied the threshold velocity necessary to initiate a transport of ice grains in Martian Simulation Wind Tunnel [8]. These experiments were carried out for grains from a few hundred micrometers to 2 mm in diameter under atmospheric pressures of 40 to 1000 mbar. To transport ice particles under near-Martian condition is hard because the threshold velocity is ten times higher than Earth. The wind speeds estimated from the Martian Database [6-7] in Louth crater are much lower than those needed to transport ice grains at Martian pressure. We support the hypothesis of diffusion by sublimation/condensation rather than the transport of icy particles by the wind. Mass transfer hypothesis: In a recent theoretical model [5] scaling laws explain the formation of sublimation waves and have been validated on terrestrial bedforms and on the Martian North Polar Cap. These waves are periodic and oriented in accordance with a turbulent boundary layer flow that diffuse the sublimated vapor. These laws, which are superimposed on the two ice waves studied, make these waves suitable geomorphological markers for climatic predictions. This model has been adapted to study similar waves created by condensation [9] and results indicate that condensation waves would be larger with one order gap than sublimation waves. Discussion: From the wind tunnel experimentation of ice particles transport in Martian-Like environment [8], wind necessary to initiate transport of ice particles is unlikely in Louth. Friction velocities of 3 m.s-1 would be required, compared to 0.6 m.s-1 deduced from scaling laws, to transport the most mobilizable 0.3 mm ice particles [8]. Wind speed in Louth is too weak for initiating particles transport. From the scaling laws, we extract values of friction velocity and flow velocity at a given altitude that can be compared with those extracted from the Martian Data Base over two Martian periods: a period of sublimation (during the summer in the northern hemisphere) at the origin of the formation of decametric waves and a period of condensation at the end of the summer, beginning of the autumn favorable for the kilometric waves formation. Scaling laws are in agreement with the predicted ratio velocity between sublimation and condensation period from the Martian Data Base values. From the Martian Data Base, independent velocity values are larger. This can be explained by the gridding of the database which takes place on a global scale larger than the crater. Conclusion: The observations indicate kilometric bedforms on the ice cap of Louth Crater, on which decametric bedforms appear with an order of magnitude gap. Comparison with numerical results suggests that the kilometric bedforms are formed by condensation and the smaller ones by sublimation. These condensation and sublimation waves are suitable markers to constrain mesoscale climate modelling in small, complex regions such as this type of crater, where topographic and/or seasonal effects can affect climate data. These waves can also be used as geomarkers on other planetary bodies where climatic conditions are not well constrained. Acknowledgments: We acknowledge PNP (Plan National de Planétologie) for founding the project “sublimation and condensation waves”. We used Planetary Data System (PDS) for observational data. References: [1] Conway et al. (2012) Icarus. [2] Brown et al. (2008) Icarus. [3] Hofstader & Murray (1990) Icarus. [4] Appéré et al. (2011) Journal of Geophysical Research. [5] Bordiec M. et al. (2020) Earth-Science Reviews, 211, 103350.[6] Forget et al. (1999). [7] Millour et al. (2018). [8] Herny et al. (2020). 7th Mars Polar Science Conf. Abstract #2099. [9] Carpy S. et al. (2022). EGU, Abstract #5998.

Sublimation combined with wind: Volatiles (N2, CH4, CO2, H20, NH3) are very common in the solar system (Fig 1). The average pressure and temperature conditions at the surface of many bodies suggest that volatile ices are stable and we thus expect that solid bedforms may form on these surfaces by either sublimation and/or condensation. These mass transfers between ice and overlying atmospheres are already known as landforms-shaping processes at different scales. These processes are very effective on the Martian North Polar Cap [2], whose spirals of the MNPC are known to be the result of sublimation on one side and condensation on the other [3-4], and as Pluto, where the Bladed Terrain Deposits are associated with sublimation of N2 and condensation of CH4 [5]. FIGURE 1 – Superimposed phase diagrams of the predominantly represented species (N2, CH4, CO2, NH3, H2O) in the Solar System in (p,T), using the Clausius-Clapeyron relationship. Scientific goal: To understand the process of material redistribution by the wind on icy planetary surfaces subject to phase changes, we propose a theoretical model coupling of flow dynamics and mass transfer and perform a linear stability analysis [6]. As done for loose bedforms, we use solid transverse bedforms as geomarkers to identify sublimation zones and to deduce erosion rate. We aim to physically and morphologically characterise these periodic waves perpendicular to the main flow over icy substrates and we are looking for analogues to assess the validity of our model before interpreting the observations on other bodies. On Earth, field analogues could be found in extreme cold and icy environment. Similar laboratory experiments are also suggested to complete the dataset. Sublimation waves analogues: We have identified two possible analogues for sublimation patterns from the literature: in the Blue Ice areas (Fig 2a) of the Antarctic ice sheets [1] and in ice caves such as the Eisriesenwelt cave (Fig 2b) in Austria [7]. We also use new measurements made in a laboratory experiment on the sublimation of CO2 ice in an atmospheric wind tunnel (Fig 2c). FIGURE 2 – Sublimation waves analogues [6]: (left: a) Blue Ice areas (middle: b) the Eisriesenwelt ice cave (right: c) CO2 ice in an atmospheric wind tunnel. In all these environments, linear and transverse bedforms appear. However, there are quite different in scales and involve different compositions of the icy substrate and the atmosphere. Despite those differences, the winds that flow on these surfaces are always turbulent and of infinite height and the environmental conditions are favorable to sublimation of ice: the surface temperatures are lower than the triple point and the partial pressure of the species is far from pressure at saturation. These sublimation waves have been classified as net ablation areas from surface energy balance. Theoretical model for redistribution processes: We consider a simple 2D case of a wavy surface of wavelength l and small amplitude with an overlying turbulent atmospheric boundary layer, of height H much larger that the wavelength. The mass transfer rate varies along the profile and has a maximum somewhere in the troughs, shifted from the crests by a phase lag. This effect allows the growth of a range of wavelengths and their migration, depending on the location of the maximum. The flow is perturbed by the topography and modify the mass transfer in turn, which may lead to the instability of such bedforms. From the stability analysis [6] we obtain 3 scaling laws: (1) the first law can predict either the friction velocity or the wind speed from a measure of the wavelength and if the viscosity is known, (2) the second law show that the migration velocity is found to scale linearly with the average value of the sublimation rates and thus depends on the kinetics of the phase transition, (3) the third law links the characteristic time of formation with the viscous length and the sublimation rate. FIGURE 3 – Model (black line), measurements (symbols) and prediction (MNPC) for sublimation waves [6]. Sublimation bedforms as geomorphic markers: The model prediction, black line (Fig 3), is superimposed on the natural terrestrial and the experimental model. This allows us to predict either the friction velocity or the wind speed from a measurement of the wavelength for the Martian Northern Polar Cap. The values predicted are in good agreement with those obtained by the martian climate database at the same place where these sublimation waves have been detected, and those both for the frictional velocities and the wind speeds. Conclusion: We propose a formation model for the sublimation waves by coupling mass waste with the hydrodynamic instability of the overlaying turbulent flow, in the case where the flow heigh is larger than the wavelength. The subjacent objective was to determine if terrestrial analogues exist or some experimental facilities could be used. We show it is possible to link the dimension of the sublimation waves to their environment and produce three scaling laws that links the geomorphological characteristics of these bedforms (wavelengths, migration, formation time) and the flow (velocity, viscosity, flow height). The adequacy between the observations/experiments and our model allows us to validate these environments as terrestrial/experimental analogues of sublimation waves. New experiments could thus be designed in controlled atmospheric wind tunnel like Aarhus wind tunnel, Denmark to explore controlling parameters. Acknowledgments: Plan National de Planétologie. References: [1] Bintanja R. (1999) Reviews of Geophysics, 37(3) :337–359 [2] Herny C. et al. (2014) EPSL, 4013, 56-66. [3] Howard A. D. (2000)Icarus, 144(2) :267–288. [4] Smith I. et al (2010) Nature, 465(7297). [5] Moore et al (2017) Icarus, 287 :320–333, 2017. [6] Bordiec M. et al. (2020) Earth & Sci. Reviews. Sci., 103350. [7] Obleitner and Spötl, (2011) Cryosphere, 5(1) :245–25.

Aeolian processes are at the origin of a large number of bedforms, which are topographic patterns that are spatially organised in a periodic manner and that can be observed both on Earth and on other planetary bodies. Two main categories of bedforms can be distinguished: (i) "loose" bedforms, generated on a bed of mobilisable grains by erosion, transport and deposition and (ii) "solid" bedforms, not induced by grain transport but by mass transfers such as ice sublimation or condensation under turbulent winds. Although the mechanisms involved in the growth of some solid bedforms have been studied (penitents, sublimation ripples, …), the subject remains largely less treated to date than loose bedforms, partly because of the lack of terrestrial environments favourable to sublimation. Comparison with other planetary environments has opened up new horizons for understanding these objects and the aeolian environments in which they develop.Among these bedforms, sublimation waves are transverse linear waveforms: regular and parallel ridges oriented perpendicular to the main direction of the turbulent flow interacting with the ice surface. The height of the flow is greater than their wavelength. The emergence of the bedforms is due to a hydrodynamic instability mechanism of the band-pass type which allows their growth. Our theoretical linear stability study shows that this instability appears in the laminar-turbulent transition regime, based on the near-wall Reynolds number, only if the modulation of the viscous sublayer by an effective longitudinal pressure gradient is taken into account in the turbulence model enabling to reproduce the feedback of the topography on the flow.These sublimation waves have been observed in different environments [Bordiec et al, 2020], by sublimation and diffusion of (a) water ice in air, in Antarctica or Ice caves, (b) water ice in CO2 atmosphere, on some areas of the northern polar cap of Mars, (c) and experimentally with CO2 ice in air. They are also observed on a Martian H2O glacier near the northern polar cap of Mars [Collet et al, in prep.], however, in the latter case, these sublimation waves are observed on larger icy waves. How can this difference in scale between two wavelengths be explained? What is their size selection process? To answer these questions, we investigate in our theoretical study the dependence on environmental conditions through (i) the fluid properties (wind speed, fluid viscosity) (ii) the direction of the transfer (sublimation or condensation) and (iii) the height of the flow in front of the wavelength (infinite or finite).

This paper adresses the numerical modelling of the solidification of a binary alloy which obeys a liquidus-solidus phase diagram. In order to capture the moving melting front, we introduce a Lagrange projection scheme based a random sampling projection. Using a finite volume formulation, we define accurate numerical fluxes for the temperature and concentration fields which guarantee the sharp treatment of the boundary conditions at the moving front, especially the jump of the concentration according to the liquidus-solidus diagram. We provide some numerical illustrations which assess the good behaviour of the method: maximum principle, stability under CLF condition, numerical convergence toward self-similar solutions, ability to handle two melting fronts.

Introduction: The transport of ice by wind plays a major role in the surface mass balance of polar caps [1, 2]. Ice can be redistributed by wind due to (1) transport of ice particles and/or (2) transport of water vapour associated with sublimation/condensation. On Mars, although the low atmospheric density is less favourable for the transport of particles than on Earth, both dust and sand have been observed to be transported by wind [3,4]. Despite ice aeolian landforms have been observed at the surface of the North Polar Cap of Mars [2, 5, 6], ice particle transport has not been directly observed on the Martian surface. Similarly, no laboratory studies of snow/ice particle transport under Martian-like conditions have been attempted thus far due to the complexity of the material. In this study we performed experiments of ice particle transport in a wind-flow under low temperatures and low pressures. From the experiments, threshold shear velocity of water ice particle transport is retrieved for different pressures and sizes in order to evaluate the plausibility of ice particle wind-driven transportation at the surface of Mars. The North Polar Cap of Mars: The Martian atmosphere is thin (7 mbar), cold (220 K) and dry (< 80 μm-pr) [7]. These conditions favoured ice sublimation/condensation processes. Spectral analyses [8, 9] suggested the optical ice grain sizes to vary between 10 μm to about 2000 μm for the seasonal frost and surface of the perennial North polar cap. But, the mechanisms of ice deposition are not well established. It can potentially come from vapour condensation directly onto the surface [9] or from snow fall [10]. This will affect the shape and size of ice particles and degree of ice sintering, which all influence the shear velocity threshold. The North polar cap experiences a permanent katabatic wind regime [11] with a typical friction shear velocity u* about 0.2 m.s-1. The complex interaction between the cryosphere and the wind leads to the formation of aeolian features at different scales [2, 5, 6]. Wind tunnel experiments: We performed experiments using the environmental wind tunnel AWTSII at Aarhus University. It is a cylindrical vacuum chamber, housing a recirculating wind tunnel about 8 m long, 2 m wide and 1 m high [12]. The facility can achieve a turbulent boundary layer flow at both low temperature and low pressure. The ice samples were produced by using the Setup for production of Icy Planetary Analogues [13]. The ice samples were sieved (125 - 250 μm, 250 - 500 μm, 500 - 2000 μm) as a monolayer on a plate covered with volcanic regolith (125 μm). The fan speed was increased by steps (shear velocity u* = 0 to 2 m.s-1) and the wind flow characterized by laser Doppler anemometry. The removal of ice particles was monitored by webcam. We performed the experiments for the different particle shapes and sizes for 4 different air pressures; 40, 100, 500 and 1000 mbar. The air temperature was maintained low (~-25°C) close to the sample plate to prevent the ice melting, sublimating and sintering. Threshold shear velocity calculation: The threshold shear velocity was determined from analysis of acquired images. When bright ice particles are removed from the dark volcanic regolith plate, the reflectance of the surface decreases. Black and white reference targets are placed close to the sample plate in the field of view of the webcam. The reflectance evolution of a region of interest (ROI) on the sample plate is calculated as follow: reflectance = (ROI – black target)/(white target – black target) The reflectance serves as a proxy for ice mass removal. For each image the reflectance is linked to the corresponding shear velocity. In most of the cases performed, the reflectance is constant until a certain wind speed and then decreases. To determine the threshold shear velocity uth, we set the threshold reflectance at 10% decrease from the first image at u* = 0 m.s-1. Results and conclusion: We have performed for the 1st time experiments of ice particles transportation at low pressure in a planetary wind tunnel. The averaged threshold shear velocity obtained at 1000 mbar, uth = 0.4 m.s-1, is consistent with theoretical and experimental calculation of ice/snow at terrestrial condition [14, 15], from 0.3 m.s-1 to 0.6 m.s-1 for range of ice particles sizes selected, supporting our set-up reliability. The shear velocity increases significantly as the pressure decreases. The influence of the ice grain sizes is not clear and more experiments are required. The results should then be scaled to Martian gravity in order to compare the results to wind speed simulations and conclude about the likeliness of transport of ice particles by wind at the surface of Mars. References: [1] Das I. et al. (2013) Nature Geoscience, 6, 367-371. [2] Howard A. D. (2000) Icarus, 144, 267-288. [3] Cantor B. A. et al. (2010) Icarus, 208, 61-81. [4] Bridges B. A. et al. (2012) Geology, 40, 31-34. [5] Smith I. B. and Holt J. (2010) Nature, 465, 450-453. [6] Herny C. et al. (2014) EPSL, 403, 56-66. [7] Pankine A. A. et al. (2010) Icarus, 210, 5871. [8] Langevin Y. et al. (2005) Science, 307, 1584-6. [9] Appéré T. et al. (2011) JGR : Planets, 116, E05001. [10] Spiga A. et al. (2017) Nature Geoscience, 10, 652-657. [11] Spiga A. et al. (2011) PSS, 59, 915-922. [12] Holstein-Rathlou C. et al. (2014) Am. Met. Society, 31, 447-457. [13] Pommerol A. et al. (2019) Space Sci. Rev., 215. [14] Shao Y. and Lu H. (2000) JGR, 105, 437-443. [15] Clifton A. et al. (2006) JoG, 52, 585-596. [16] Herny C. et al. (2016) 6th MPSC, Abstract #6075. [17] Bordiec M. et al. (2018) ICAR X. Acknowledgements: This work has been fund by Europlanet (Europlanet 2020 RI has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 654208). This work has been supported by the University of Bern. This work has been carried out within the framework of the NCCR PlanetS supported by the Swiss National Science Foundation.

International audience; Sublimation waves are periodic, linear and transverse bedforms that grow by sublimation of icy substrates under turbulent winds. They occur in different environments of the Earth and other planets, where the climate is favorable to sublimation. Their morphological and kinematic characteristics (wavelength, migration velocity, characteristic time of formation) depend on the environmental conditions in which they develop (atmosphere viscosity, wind speed, sublimation rate). To highlight these relations, we designed a theoretical model for their formation, based on models previously designed for dissolution bedforms. From a linear stability analysis of the model, we derived a dispersion relation and three scaling laws. These are validated by comparison with measurements available for two natural terrestrial examples (Blue Ice Areas of the Antarctic ice sheets and ice caves) and with new measurements in a laboratory experiment. They are applied to linear bedforms, of hitherto unknown origin, that we identified on the Martian North Polar Cap. We thus demonstrate that sublimation waves are convenient geomorphic markers to constrain surface compositions, atmospheric properties, climates, and winds on terrestrial ice sheets and other icy planetary surfaces.