# Internal gravity waves in the energy and flux budget turbulence-closure theory for shear-free stably stratified flows

## TL;DR

This paper extends the energy and flux budget turbulence-closure theory to include internal gravity waves in shear-free stably stratified flows, revealing how wave intensity influences turbulence production, damping, and anisotropy.

## Contribution

It introduces a coupled model accounting for wave-turbulence interactions, highlighting nonlinear effects and wave intensity dependence in stratified turbulence.

## Key findings

- More intensive waves generate stronger turbulence and are more strongly damped.
- Less intensive waves produce turbulence with higher anisotropy, up to 90% potential energy.
- The model explains properties of high-altitude tropospheric turbulence.

## Abstract

We have advanced the energy and flux budget (EFB) turbulence closure theory that takes into account a two-way coupling between internal gravity waves (IGW) and the shear-free stably stratified turbulence. This theory is based on the budget equation for the total (kinetic plus potential) energy of IGW, the budget equations for the kinetic and potential energies of fluid turbulence, and turbulent fluxes of potential temperature for waves and fluid flow. The waves emitted at a certain level, propagate upward, and the losses of wave energy cause the production of turbulence energy. We demonstrate that due to the nonlinear effects more intensive waves produce more strong turbulence, and this, in turns, results in strong damping of IGW. As a result, the penetration length of more intensive waves is shorter than that of less intensive IGW. The anisotropy of the turbulence produced by less intensive IGW is stronger than that caused by more intensive waves. The low amplitude IGW produce turbulence consisting up to 90 \% of turbulent potential energy. This resembles the properties of the observed high altitude tropospheric strongly anisotropic (nearly two-dimensional) turbulence.