Numerical and experimental investigation on the effect of topography on the hydrodynamics of planetary fluid envelops.

The majority of investigations into planetary core and subsurface ocean dynamics have traditionally assumed a perfectly smooth interface. However, geodynamical models and seismic observations on Earth suggest the presence of topography. This study addresses the role of topography in the simplified but fundamental case of differential rotation between the topography and the fluid within a cylinder. We conducted numerical and experimental analyses, exploring various ranges of Rossby numbers (from 10-1 to 10-4 ) and different wavelengths and heights of topography, always greater than the Ekman boundary layer. Numerical simulations were performed using the spectral elements code Nek5000, while experiments were conducted with water on a rotating table employing particle imagery velocimetry (PIV). Our observations reveal that the topography emits inertial waves into the fluid, and their patterns are correlated with the derivatives of the topography's height, rather than directly with its height. The controlling parameters influence the frequencies and amplitudes of the inertial waves, leading to the derivation of scaling laws in Rossby number, wavelength, and topography height. From these scaling laws, we propose a model for the dynamics of the fluid, including energy transfers.