Scaling Laws for Mixed‐Heated Stagnant‐Lid Convection and Application to Europa

Abstract

AbstractBecause rocks and ices viscosities strongly depend on temperature, planetary mantles and ice shells are often thought to be animated by stagnant‐lid convection. Their dynamics is further impacted by the release of internal heat, either through radioactive isotopes decay or tidal dissipation. Here, we quantify the impact of internal heating on stagnant‐lid convection. We perform numerical simulations of convection combining strongly temperature‐dependent viscosity and mixed (basal and internal) heating in 3D‐Cartesian and spherical geometries, and use these simulations to build scaling laws relating surface heat flux, Φsurf, interior temperature, Tm, and stagnant lid thickness, dlid, to the Rayleigh number, heating rate, H, and top‐to‐bottom viscosity ratio, Δη. These relationships show that Tm increases with H but decreases with Δη, while Φsurf increases with H and Δη. Importantly, they also describe heterogeneously heated systems well, provided that the maximum dissipation occurs in hottest regions. For H larger than a value Hcrit, the bottom heat flux turns negative and the system cools down both at its top and bottom. Two additional interesting results are that (a) while the rigid lid stiffens (its mobility decreases) with increasing H, it also thins; and (b) Hcrit increases with increasing Δη. We then use our scaling laws to assess the impact of tidal heating on Europa's ice shell properties and evolution. Our calculations suggest a shell thickness in the range 20–80 km, depending on viscosity and dissipated power, and show that internal heating has a stronger influence than the presence of impurities in the sub‐surface ocean.