Daniela Mansutti

Modeling the evolution of the melt front under gravity in the presence of a horizontal thermal gradient is a challenging issue, hitherto tackled exclusively with the concepts and tools of computational continuum thermomechanics, too phenomenologically driven to have satisfactory predictive capabilities. Here, we show that this complex phenomenon is amenable to treatment by the methods and tools of Non-Equilibrium Molecular Dynamics (NEMD). To do so, we addressed all the difficulties caused by the necessity of applying suitable boundary conditions and minimizing surface effects so that the bulk behavior of the system in non-equilibrium conditions can be detected. Sufficient adiabatic separation of the time scales permits us to use macroscopically relatively short—but microscopically long enough—time averages to get the macroscopic bulk behavior of the system accurately. To get an adequate signal-to-noise ratio, we had to use an unphysically large value of the gravity. However, we know from NEMD simulations in transport studies that the phenomena produced are stable over many orders of magnitude. In conclusion, our work proves that molecular simulation can be a good tool to study this family of non-equilibrium phenomena, although further work is needed to achieve quantitative predictive capabilities.

This work concerns the rock glacier flow model introduced, in its basic form, by Kannan and Rajagopal in [1]  and extended with inclusion of temperature effects by Kannan, Rajagopal, Mansutti and Urbini in [2]. This one is based on the general conservation laws (momentum, mass and energy) and takes into account the effect of shear rate, pressure and rocks and sand grains volume fraction onto viscosity, also by implementing the effects of local pressure melting point variation. Here we present the results of a sensitivity analysis of the parameters developed by shooting the location of the internal sliding occurence, induced by the presence of rocks and sand grains trapped within the interstices of the glacier, and the value of the shear velocity.  The case of the Murtel-Corvatsch glacier in Switzerland is considered for the availability of the detailed description based on measured data published by Arenson, Hoelzle and Springman in [3].The numerical results obtained improve those ones presented in [1] and show clearly the contribution of each numerical and functional parameter of the model. They also exhibit a very good agreement with observations which makes this modelling approach very promising for general application.[1] Kannan, K., Rajagopal, K.R.: A model for the flow of rock glaciers. Int. J. Non-lin. Mech., 48, pp. 59– 64 (2013) [2] Kannan, K., Mansutti, D., Rajagopal, K.R. and Urbini, S.: Mathematical modeling of rock glacier flow with temperature effects, in Mathematical Approach to Climate Change and its Impacts (P. Cannarsa, D. Mansutti and A. Provenzale, eds.), pp. 137-148, Springer-INDAM series, vol.38 (2020) [3] Arenson, L., Hoeltzle, M. and Springman, S.: Borehole Deformation Measurements and Internal Structure of Some Rock Glaciers in Switzerland. Permafrost and Periglacial Processes, 13, pp. 117-135 (2002).Acknowledgements: D. Mansutti acknowledges Piano Nazionale Ricerca Antartide (PNRA) for financial support of this topic within the project ENIGMA (project PNRA$16-00121$).