Scaling laws for ablation waves formed by ice sublimation and rock dissolution: applications to the Earth, Mars and Pluto

Ablation waves involve solid substrate such as ice or soluble rocks. Ablation by sublimation or dissolution under turbulent winds or liquid flows may lead to the development of transverse linear bedforms (ablation waves) on volatile or soluble susbtrates. In glaciology, geomorphology, karstology and planetology, these ablation waves may provide relevant morphological markers to constrain the flows that control their formation. For that purpose, we describe a unified model, that couples mass transfers and turbulent flow dynamics and takes into account the relationship between the viscosity of the fluid and the diffusivity of the ablated material, for both sublimation and dissolution waves. From the stability analysis of the model, we derive three scaling laws that relate the wavelength, the migration velocity and the growth time of the waves to the physical characteristics (pressure, temperature, friction velocity, viscous length, ablation rate) of their environment through coefficients obtained numerically. The laws are validated on terrestrial examples and laboratory experiments of sublimation and dissolution waves. Then, these laws are plotted in specific charts for dissolution waves in liquid water, for sublimation waves in N2-rich atmospheres (e.g., Earth, Titan, Pluto) and in CO2-rich atmospheres (e.g., Mars, Venus). They are applied to rock dissolution on the walls of a limestone cave (Saint-Marcel d’Ardèche, France), to H2O ice sublimation on the North Polar Cap (Mars) and to CH4 ice sublimation in Sputnik Planitia (Pluto), to demonstrate how they can be used (1) either to derive physical conditions on planetary surfaces from observed geometric characteristics of ablation waves (2) or, conversely, to predict geometric characteristics of ablation waves from measured or inferred physical conditions on planetary surfaces. The migration of sublimation waves on regions of the Martian North Polar Cap and sublimation waves candidates on Pluto are discussed

Emergence of tip singularities in dissolution patterns

Chemical erosion, one of the two major erosion processes along with mechanical erosion, occurs when a soluble rock like salt, gypsum or limestone is dissolved in contact with a water flow. The coupling between the geometry of the rocks, the mass-transfer and the flow leads to the formation of remarkable patterns, like scallop patterns in caves. We emphasize the common presence of very sharp shapes and spikes, despite the diversity of hydrodynamic conditions and the nature of the soluble materials. We explain the generic emergence of such spikes in dissolution processes by a geometrical approach. Singularities at the interface emerge as a consequence of the erosion directed in the normal direction, when the surface displays curvature variations, like those associated to a dissolution pattern. First, we demonstrate the presence of singular structures in natural interfaces shaped by dissolution. Then, we propose simple surface evolution models of increasing complexity demonstrating the emergence of spikes and allowing us to explain at long term by coarsening the formation of cellular structures. Finally, we perform a dissolution pattern experiment driven by solutal convection and we report the emergence of a cellular pattern following well the model predictions. Although the precise prediction of dissolution shapes necessitates to perform a complete hydrodynamic study, we show that the characteristic spikes which are reported ultimately for dissolution shapes are explained generically by geometrical arguments due to the surface evolution. These findings can be applied to other ablation patterns, reported for example in melting ice.Comment: 13 pages, 8 figure

MODELLING BINARY ALLOY SOLIDIFICATION BY A RANDOM PROJECTION METHOD

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

A RESCALED V2-F MODEL: FIRST APPLICATION TO SEPARATED AND IMPINGING FLOWS

International audienceThe ability of the rescaled version of the υ^2-f model, designed to improve the predictions in channel flows, to reproduce pressure driven separation and impinging flows is investigated. First, it is shown that the recalibration of the coefficients does not suppress the gain obtained previously in channel flows concerning the prediction of the mean velocity and υ^2 profiles, and the evolution of the friction coefficient with the Reynolds number. The original and rescaled υ^2-f models are then applied to a plane asymmetric diffuser and an impinging jet, which are known for being well reproduced by the original model. The rescaled model globally gives very similar results in these flows. However, room for improvement exists in predicting the reattachment region in the diffuser and the Nusselt number distribution in the impinging jet

Contribution à la modélisation instationnaire de la turbulence (modélisations urans et hybride rans/les)

Cette thèse concerne la modélisation instationnaire de la turbulence. La présence de structures à grande échelle dans des écoulements statistiquement stationnaires invalide certaines hypothèses. L introduction du terme pour les équations URANS ne suffit pas, une nouvelle décomposition et un opérateur associé sont nécessaires. L applicabilité des méthodes de fermeture usuelles doit alors être vérifiée. Par exemple, la périodicité du jet synthétique entraîne un non-équilibre créant un non-alignement permanent des tensions de déformation et d anisotropie que le modèle RSM reproduit mais pas le modèle k- . La modélisation hybride RANS/LES non-zonale, dérivée d une proposition initiale de Schiestel, repose donc sur des équations de transport pour les tensions de Reynolds ( ij)SGS, et pour la dissipation, où l opérateur de décomposition joue le rôle d un filtre dont la fréquence de coupure peut être maîtrisée. La qualité des résultats obtenus sur une couche de mélange temporelle atteste de la capacité de ce modèle à capter les grandes structures de l écoulement.The aim of this work is to account for the unsteadiness effects on the turbulence in single point closure. The existence of large scale structures in statistically steady flows leads to reconsider some hypothesis. Much more than adding the time derivatives , the URANS equations needs to consider a new decomposition and an assiociated operator. Therefore, the applicability of usual closure methods has to be examined. For exemple, the periodicity of a synthetic jet leads to a non-equilibrium, which induces a permanent misalignment of anisotropy tensor and strain tensors. RSM are able to reproduce this misalignment, whereas k- . model can't. A seamless hybrid RANS/LES method, based on the version of Schiestel's model, relies on transport equations for the subgrid stress ( ij)SGS and dissipation. The decomposition operator is then assimilated as a filter with an adapatative cutoff frequency. The predictions obtained on a temporal mixing layer shows the ability of this model to capture the very large structure of the flow.POITIERS-BU Sciences (861942102) / SudocNANCY/VANDOEUVRE-INPL (545472102) / SudocSudocFranceF

Scaling arguments to experimentally model deep oceans trapped between icy layers on Ganymede

National audienceThe potential habitability in icy giant moons such as Ganymede, Callisto (moons of Jupiter),and Titan (moon of Saturn) has been recently studied, where some basic conditions of life may be abundant. Namely, the conditions include the presence of liquid water, a stable source of energy and supply of nutrients. A systematic understanding of the physical processes taking place on these giant moons may be a key to addressing the fundamental question of habitability of these moons. A common feature of such giant moons relates to the presence of a liquid water layer sandwiched in between two layers of ice: a surface layer and a deep layer with a different polymorphism triggered by the high pressure conditions. The study of the exchange processes that occur in the deep layers of giant icy moons and water-rich worlds is a highly non-trivial one. The origin of the natural phenomena cannot be easily reproduced in laboratory experiments particularly because the high pressures acting on the inner ice layers of the moons are virtually impossible to reproduce in table top laboratory experiments.However, based on the fundamental rule of thermodynamic phases stated by Gibbs, we attempt herein to replace in the table top experiments the pressure differences existing on the moons by another pair of (thermodynamically) conjugated variables: an external shear and a stress. To support this, we present preliminary scaling arguments and design a table-top experimental setup able to capture the main physics taking place within the giant moons. The similarity is mainly based on the similaritybetween the convective and thermo-diffusive time scales. Additionally, we pay attention that the flows at laboratory scale remain laminar at all times which is the case of the convective flows existing on the moons. As an appropriate phase change material that models the ice we chose a paraffin wax. The thermophysical and rheological properties of the paraffin wax have been investigated which allows us to estimate the suitable dimensions of the table top experimental setup that may capture most physicstaking place on the giant moons

Role of the global water ocean on the evolution of Titan’s primitive atmosphere

International audienceDuring the accretion of Titan, impact heating may have been sufficient to allow the global melting of water ice and the release of volatile compounds, mainly constituted of CO 2 , CH 4 and NH 3. The duration and efficiency of exchange between the primitive massive atmosphere and the global impact-induced water ocean likely play a key role in the chemical evolution of the early Titan's atmosphere. To investigate the atmospheric composition of early Titan for a wide range of global (atmosphere + ocean) composition in volatils, we first developed a gas-liquid equilibrium model of the NH 3-CO 2-H 2 O system, where the non-ideal behavior of both gas and liquid phases, and the speciation of volatiles dissolved in the aqueous phase are taken into account. We show that the relative abundance of CO 2 and NH 3 determine the composition of Titan's atmosphere. For CO 2 /NH 3 ≤ 1 , CO 2 is massively dissolved in the ocean. On the contrary, for CO 2 /NH 3 > 1, CO 2 is the main constituent of Titan's primitive atmosphere while the NH 3 atmospheric content is dramatically decreased. We then investigate the conditions for the formation of CH 4-rich clathrates hydrates at Titan's surface that could be the main reservoir of methane for the present-day atmosphere. In absence of reliable experimental data in the CH 4-CO 2-NH 3-H 2 O system, the dissolution of methane in water is included using a simplified Henry's law approach. We find that if the concentration of CH 4 in Titan's building block was higher than ∼0.1 mol.kg −1 and CO 2 /NH 3 < 3, a large fraction of methane may be stored in the primordial crust, which would form at temperature below ∼10 • C

Effect of a superficial porous brittle layer on the thermal equilibrium of Europa’s Ice shell

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Sediment transport by boiling seeping water: exploring effects of grainsize and atmospheric conditions

International audienceMany active and recently active surface processes on Mars have been controversially linked to the action of liquid water, yet the sediment transport capacity of water under martian environmental conditions is poorly understood. An understanding of the sediment transport capacity allows the amount of water required for any given landform to be back-calculated from its observed size/volume at the martian surface. Here we present a series of experiments where we explore the effects of grainsize, atmospheric pressure, humidity and temperature on the sediment transport capacity of seeping liquid water under martian conditions

Jumping grains on Mars, or sediment transport by boiling: experiments and models

International audienceIn our previous laboratory work we reported a new sediment transport mechanism relevant for Mars: sediment saltation through boiling. We found seeping water was able to transport sediment downslope under martian conditions even though no sediment transport was observed under terrestrial conditions. This finding has important implications for inferring water reservoirs of recently active surface processes and hence for Mars' hydrosphere and habitability. However, in order to robustly transfer this finding to Mars we need to understand the physics behind this process. We can use this knowledge to define the limits of the process in terms of surface properties and/or environmental conditions found on Mars. In our previous work we inferred the physical mechanisms behind the saltation, yet we had little empirical data to test this inference. In this series of experiments we focused on the grain-scale processes involved in saltation via boiling with the objective of validating our physical model. Our experiments were performed in the large Mars chamber at the Open University. Our setup consists of two parallel confining walls 40 mm apart and 3.2 mm high adhered to an inclined roughened plane 0.4 m wide by 0.9 m long. Sediment was placed between the walls and levelled off. The water source was located at the top of the slope between the walls. We varied both initial slope angle (5 • , 15 • , 25 •) and grainsize (120, 250 and 500 µm). Each experiment was performed at least in triplicate. Once the water is released, it percolates downslope through the sediment between the walls and the grains are observed to saltate at the saturated-dry interface. We used a high-speed camera in order to capture videos of the grain scale processes. We analyse these data with an open source particle tracking code called tractrac developed by Joris Heyman (https://perso.univ-rennes1.fr/joris.heyman/trac.html). We extract particle trajectories and from those an estimate of the initial ejection velocity for tens to hundreds of particles for the videos we collected. We then compare our experimental trajectories and ejections speeds with those predicted by our physical model. In this contribution we will report on this comparison