Thermo-mechanical modeling of pancakelike domes on Venus

In this paper, we present a mathematical model aimed at describing both the effusive and relaxing phase of pancakelike lava domes on the Venus surface. Our model moves from the recent paper by Quick et al. \citep{quick2016} but generalizes it under several respects. Indeed, we consider a temperature field, playing a fundamental role in the flow evolution, whose dynamics is governed by the heat equation. In particular, we suggest that the main mechanism that drives cooling is radiation at the dome surface. We obtain a generalized form of the equation describing the dome shape, where the dependence of viscosity on temperature is taken into account. Still following Quick et Al. \citep{quick2016}, we distinguish an isothermal relaxing phase preceded by a non-isothermal (cooling) effusive phase, but the fluid mechanical model, developed in an axisymmetric thin-layer approximation, takes into account both shear thinning and thermal effects. In both cases (relaxing and effusive phase) we show the existence of self-similar solutions. In particular, this allows to obtain a likely scenario of the volumetric flow rate which originated this kind of domes. Indeed, the model predicts a time varying discharge which is maximum at the beginning of the formation process and decreases until vanishing when the effusive phase is over. The model, in addition to fitting well the dome shape, suggests a possible forming scenario which may help the largely debated questions about the emplacement and lava composition of these domes. %(see, e.g., \cite{fink1993,Head1991,Stofan2000,sakimoto1995spreading,Bridges1995,Bridges1997}).