Horizontal Convection in Icy Satellite Oceans with Melting and Freezing

Thermal buoyancy is a primary driver of icy-satellite ocean dynamics, caused by mantle heating at the seafloor and cooling at the ice–ocean interface. A significant driver of mantle heating is dissipation by cyclic tidal deformation. When this buoyancy forcing is spatially uniform, laboratory and numerical experiments have shown that it can create overturning circulation, melting and freezing of the overlying ice, and alternating east–west jets of rapid circulation. Tidal dissipation, however, naturally varies in space, causing differential heating of the ocean bottom. These temperature variations will drive horizontal convection, a large-scale overturning circulation with a zonal structure. Here, we investigate the mechanics of this horizontal convection, its interaction with Rayleigh-Bénard (vertical) convection, and dynamic feedback with ice-shell thickness, melting, and freezing. 

We perform non-rotating simulations of convection in a 2D Cartesian geometry with a mobile ice–ocean interface using the pseudo-spectral code, Dedalus. A sinusoidal temperature profile is imposed on the bottom of the ocean as well as a vertical (average) temperature difference. The relative amplitude of horizontal to Rayleigh-Bénard convection is varied by changing the ratio of the vertical to horizontal temperature differences, as well as the aspect ratio of the domain. The phase change between pure water and ice is captured using the phase field method. We perform sensitivity tests to determine the optimum phase field parameters that best approximate stagnation-point flow solutions in the vicinity of the ice–ocean interface. These optimum parameters vary as a function of vertical Rayleigh number. We then investigate the competition between Rayleigh-Bénard and horizontal convection without phase change, before including melting and freezing to study the dynamic feedback of ice topology on this competition. Finally, we seek to place our simulations in the context of icy-satellite oceans by determining scaling relationships between the horizontal Rayleigh and Nusselt numbers.