Rotating convective turbulence in moderate to high Prandtl number fluids

Abstract

Rotating convective turbulence is ubiquitously found across geophysical settings, such as surface and subsurface oceans, planetary atmospheres, molten metal planetary cores, magma chambers, magma oceans, and basal magma oceans. Depending on the thermal and material properties of the system, buoyant convection can be driven thermally or compositionally, where a Prandtl number ( Pr = ν / κ i ) defines the characteristic diffusion properties of the system, with κ i = κ T representing thermal diffusion and κ i = κ C representing chemical diffusion. These numbers vary widely for geophysical systems; for example, the liquid iron undergoing thermal-compositional convection in Earth's core is defined by P r T ≈ 0.1 and P r C ≈ 100 , while a thermally-driven liquid silicate magma ocean is defined by P r T ≈ 100 . Currently, most numerical and laboratory data for rotating convective turbulent flows exists at Pr = O ( 1 ) ; high Pr rotating convection relevant to compositionally-driven core flow and other systems is less commonly studied. Here, we address this deficit by carrying out a broad suite of rotating convection experiments made over a range of Pr values, employing water and three different silicone oils as our working fluids ( Pr = 6, 41, 206, and 993). Using measurements of flow velocities (Reynolds, Re) and heat transfer efficiency (Nusselt, Nu), a baroclinic torque balance is found to describe the turbulence regardless of Prandtl number so long as Re is sufficiently large ( Re ≳ 10 ). Estimated turbulent scales are found to remain close to onset scales in all experiments, a result that may extrapolate to planetary settings. Lastly, we use our data to build Pr-dependent predictive nondimensional and dimensional scaling relations for rotating convective velocities that can be applied across a broad range of geophysical fluid dynamical settings.