Numerical investigation of the turbulent gravity wave break-up near a critical level

In stratified fluids, turbulent patches can arise due to breaking internal gravity waves (GWs). One important breaking mechanism is associated with the presence of a critical level, which occurs when the phase speed of the GW matches the background flow velocity in the direction of propagation. Linear theory predicts a diverging amplitude and energy density as the wave approaches the critical level, ultimately leading to wave breaking and the eventual onset of turbulence. However, the precise physics of the turbulent state after the wave breaking and during GW dissipation have received limited attention in the past and remains less understood. This lack in research renders a challenge for the physical representation of GW breaking in contemporary weather and climate models.

To address this issue, we perform idealized direct numerical simulations (DNS) of a GW approaching its critical level and analyze the resulting turbulent flow. We present our simulation framework and investigation results regarding different background flow configurations and obtain the scaling of the turbulent kinetic energy (TKE) dissipation with the wavelength and the background buoyancy frequency. Furthermore, Reynolds number similarity as well as the generation of secondary GWs is observed. Numerical results regarding TKE dissipation are also compared to atmospheric observations. This comparison suggests that the DNS are able to represent the physics we want to address despite their idealized nature. Additionally, the observation of secondary emissions by the turbulent layer indicates that turbulent wave breaking enables tunneling of energy across the critical level, which is a phenomenon not permitted in linear theory.