(2014), Stagnant lid convection in bottom-heated thin 3-D spherical shells: Influence of curvature and implications for dwarf planets and icy moons, J. Geophys. Res. Planets, 119, 1895-1913, doi:10.1002 Abstract Because the viscosity of ice is strongly temperature dependent, convection in the ice layers of icy moons and dwarf planets likely operates in the stagnant lid regime, in which a rigid lid forms at the top of the fluid and reduces the heat transfer. A detailed modeling of the thermal history and radial structure of icy moons and dwarf planets thus requires an accurate description of stagnant lid convection. We performed numerical experiments of stagnant lid convection in 3-D spherical geometries for various ice shell curvatures f (measured as the ratio between the inner and outer radii), effective Rayleigh number Ra m , and viscosity contrast Δ . From our results, we derived scaling laws for the average temperature of the well-mixed interior, m , and the heat flux transported through the shell. The nondimensional temperature difference across the bottom thermal boundary layer is well described by (1 − m ) = 1.23 f 1.5 , where is a parameter that controls the magnitude of the viscosity contrast. The nondimensional heat flux at the bottom of the shell, F bot , scales as F bot = 1.46Ra 0.27 m 1.21 f 1.78 . Our models also show that the development of the stagnant lid regime depends on f . For given values of Ra m and Δ , the stagnant lid is less developed as the shell's curvature increases (i.e., as f decreases), leading to improved heat transfer. Therefore, as the outer ice shells of icy moons and dwarf planets grow, the effects of a stagnant lid are less pronounced.

[1] We conducted experiments of isoviscous thermal convection in homogeneous, volumetrically heated spherical shells with various combinations of curvature, rate of internal heating, and Rayleigh number. We define a characteristic temperature adapted to volumetrically heated shells, for which the appropriate Rayleigh number, measuring the vigor of convection, ishkk , where f is the ratio between the inner and outer radii of the shell. Our experiments show that the scenario proposed by Parmentier and Sotin (2000) to describe convection in volumetrically heated 3D-Cartesian boxes fully applies in spherical geometry, regardless of the shell curvature. The dynamics of the thermal boundary layer are controlled by both newly generated instabilities and surviving cold plumes initiated by previous instabilities. The characteristic time for the growth of instabilities in the thermal boundary layer scales as Ra VH À1/2, regardless of the shell curvature. We derive parameterizations for the average temperature of the shell and for the temperature jump across the thermal boundary layer, and find that these quantities are again independent of the shell curvature and vary as Ra VH À0.238 and Ra VH À1/4 , respectively. These findings appear to be valid down to relatively low values of the Rayleigh-Roberts number, around 10 5 .

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