Scattering of Internal Waves by (Cyclo)geostrophic Turbulence

The Surface Water and Ocean Topography mission is the next generation of satellite altimetry, with the capability to measure sea surface height (SSH) with unprecedented resolution. To anticipate the interpretation of this new data, we seek to characterize the scattering effects and energy exchanges between internal tides and geostrophic turbulence. Internal tides share some of the same spatial and velocity scales as eddies. This makes them susceptible to be influenced by the eddies, making their signature on SSH hard to predict. We use idealized, shallow-water spectral numerical simulations to study the interaction between low mode internal waves and turbulent flow in (cyclo)geostrophic balance. We explore the parameter space spanned by the Rossby number and the ratio of the incoming wavelength to the characteristic wavelengths inside the turbulence, among others. We consider two types of turbulent flows, both localised in the center of the domain. The first is an isotropic field with a well-defined energy peak wavelength, which allows for a fine-tuning of the turbulence characteristics. The second is the eddy field resulting from an unstable baroclinic jet, which more closely resembles the turbulent fields observed in the ocean. We perform harmonic analysis on the SSH to characterize variations in the amplitude and frequency of the internal wave. We then split the domain into several sections and calculate the energy spectrum in each. Consistent with previous theoretical work, we see the strongest scattering for turbulence at the same wavelength as the internal tide, and for the energy to be redistributed to wavenumbers of the same magnitude during its propagation. The numerical simulations allow us to reach near-submesoscale Rossby numbers.