Field analogues and laboratory experiments to constrain sublimation waves on planetary icy surfaces
Authors: Carpy Sabrina , Bordiec Maï , Bourgeois Olivier , Herny Clémence , Massé Marion , Pochat Stéphane 
Published: September 2022

&lt;p&gt;&lt;strong&gt;&lt;span lang=&quot;EN-US&quot;&gt;Sublimation combined with wind: &lt;/span&gt;&lt;/strong&gt;&lt;span lang=&quot;EN-US&quot;&gt;Volatiles (N&lt;sub&gt;2&lt;/sub&gt;, CH&lt;sub&gt;4&lt;/sub&gt;, CO&lt;sub&gt;2&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;0, NH&lt;sub&gt;3&lt;/sub&gt;) 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&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; sublimation of N&lt;sub&gt;2&lt;/sub&gt; and condensation of CH&lt;sub&gt;4&lt;/sub&gt; [5].&lt;/span&gt;&lt;/p&gt;
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&lt;p&gt;&lt;span lang=&quot;EN-US&quot;&gt;FIGURE 1 &amp;#8211; 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.&lt;/span&gt;&lt;/p&gt;
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&lt;p&gt;&lt;strong&gt;Scientific goal: &lt;/strong&gt;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.&lt;/p&gt;
&lt;p&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;strong&gt;Sublimation waves analogues: &lt;/strong&gt;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).&lt;/span&gt;&lt;/p&gt;
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&lt;p&gt;FIGURE 2 &amp;#8211; Sublimation waves analogues [6]: (left: a) Blue Ice areas &amp;#160;(middle: b) the Eisriesenwelt ice cave (right: c) CO2 ice in an atmospheric wind tunnel.&lt;/p&gt;
&lt;p&gt;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.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Theoretical model for redistribution processes: &lt;/strong&gt;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.&lt;strong&gt; &lt;/strong&gt;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.&lt;/p&gt;
&lt;p&gt;&lt;span lang=&quot;EN-GB&quot;&gt;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 t&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;he 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. &lt;/span&gt;&lt;/p&gt;
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&lt;p&gt;FIGURE 3 &amp;#8211; Model (black line), measurements (symbols) and prediction (MNPC) for sublimation waves [6].&lt;/p&gt;
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&lt;p&gt;&lt;strong&gt;Sublimation bedforms as geomorphic markers: &lt;/strong&gt;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.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Conclusion:&lt;/strong&gt; 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.&lt;/p&gt;
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&lt;p&gt;&lt;strong&gt;Acknowledgments: &lt;/strong&gt;Plan National de Plan&amp;#233;tologie.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;References:&lt;/strong&gt; [1]&amp;#160;Bintanja R. (1999) Reviews of Geophysics, 37(3) :337&amp;#8211;359 [2] Herny C. et al. (2014) EPSL, 4013, 56-66. [3] Howard A. D. (2000)Icarus, 144(2) :267&amp;#8211;288. [4] Smith I. et al (2010) Nature, 465(7297). [5] Moore et al (2017) Icarus, 287 :320&amp;#8211;333, 2017. [6] Bordiec M. et al. (2020) Earth &amp; Sci. Reviews. Sci., 103350. [7] Obleitner and Sp&amp;#246;tl, (2011) Cryosphere, 5(1) :245&amp;#8211;25.&lt;/p&gt;
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