Investigating the drag force due to inertial waves generated by topography

Internal fluid layers can contribute to energy dissipation within planets, thereby influencing the planet’s rotational parameters. Traditionally, dissipation and angular momentum transfer in such fluid layers have been analysed assuming smooth surfaces. Here, we account for the effects of topographical irregularities, particularly the wave drag caused by inertial waves.

In rapidly rotating fluids, topography can excite inertial waves that propagate deep into the fluid interior. These waves contribute to the fluid drag exerted at the topography. We present a theoretical model for the drag caused by topographically excited inertial waves, validated through a two-step approach.

In the first step, we validate our model for the simplest case: steady flow over a monochromatic topography in a periodic Cartesian box. Numerical simulations are conducted using the computational fluid dynamics solver Nek5000, showing that the drag scales with the square of the topography height (h^2) for low-slope topographies. For steeper slopes exceeding unity, the drag becomes wavelength-dependent.

In the second step, we examine a more complex case involving the differential rotation of the fluid and the monochromatic topography in a cylinder. We demonstrate experimentally and numerically that the torque from inertial wave drag can be predicted from our previous results, with the resulting torque exhibiting the same scaling properties as the drag in the periodic box.

This two-step approach provides the foundation for understanding angular momentum transfer in planetary interiors. It sets the stage for calculating the resulting torque over a full spherical shell.