Energy- and flux-budget turbulence closure model for stably stratified flows. Part II: the role of internal gravity waves

TL;DR

This paper extends a turbulence closure model for stably stratified flows by incorporating the effects of internal gravity waves, revealing their significant influence on flux Richardson number, turbulence anisotropy, and energy distribution.

Contribution

The paper introduces an extended turbulence closure model that accounts for internal gravity waves, improving predictions of fluxes and turbulence characteristics in stratified flows.

Findings

Flux Richardson number varies with wave energy, exceeding 1 or becoming negative.

Internal gravity waves reduce turbulence anisotropy and increase turbulent potential energy.

Model predictions align with experimental and simulation data.

Abstract

We advance our prior energy- and flux-budget turbulence closure model (Zilitinkevich et al., 2007, 2008) for the stably stratified atmospheric flows and extend it accounting for additional vertical flux of momentum and additional productions of turbulent kinetic energy, turbulent potential energy (TPE) and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). Main effects of IGW are following: the maximal value of the flux Richardson number (universal constant 0.2-0.25 in the no-IGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. In the heterogeneous stratification, when IGW propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes counter-gradient. IGW also reduce anisotropy of turbulence and increase the share of TPE in the turbulent total energy. Depending on the direction (downward or upward), IGW either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and large-eddy simulations.