Evolution of weak, homogeneous turbulence subject to rotation and stratification: Comparable wave and nonpropagating components.

Abstract

Following on from previous work [J. F. Scott and C. Cambon, J. Fluid Mech. 979, A17 (2024)10.1017/jfm.2023.1046], this article concerns weak (small Rossby or Froude number), homogeneous turbulence subject to rotation and stable stratification. The flow is expressed as a combination of particular solutions (modes) of the linearized governing equations without viscosity or diffusion. Modes are of two types: oscillatory ones which represent inertial-gravity waves and time-independent ones that express a nonpropagating (NP) component of the flow. It was shown in the previous work that, at leading order, the NP component evolves independently of the wave component and a specifically adapted direct numerical simulation (DNS) approach was introduced to describe the NP component, the same approach which is employed here. Using wave-turbulence analysis and assuming the NP amplitude is small compared with the wave amplitude, evolution equations for the wave spectra were derived and numerically exploited. Here, those equations are extended to the case when the NP and wave components are of comparable magnitude. The NP spectra then appear in the wave-turbulence equations, which means those equations are no longer closed. As a result, a combination of adapted DNS for the NP component and the wave-turbulence equations is used and numerical solutions of the latter are given. Terms in the wave-turbulence equations arising from the NP component couple pairs of wave modes, adding to the three-wave interactions of the previous work when the latter exist. This is found to considerably increase the wave dissipation. Indeed, it provides the only mechanism for significant dissipation in the cases for which three-wave interactions are absent. The additional dissipation is especially important for wave modes having wave vectors perpendicular to the vertical or rotation axis, but is also effective for other directions.