The Nonlinear Forcing of Large-Scale Internal Gravity Waves by Stratified Shear Instability

Abstract

The forcing of large-scale internal gravity waves by shear-unstable stratified free shear layers is investigated. The gravity wave forcing mechanism considered arises from the nonlinear interaction of unstable modes of differing horizontal wavenumber as they reach finite amplitude in the shear layer. The analysis assumes an initially plane-parallel shear flow and no preferred horizontal scales in the perturbations that initiate instability. Therefore, the large-scale gravity wave forcing mechanism considered arises only from the dynamical action of eddies in the shear layer. One of the primary goals of this study is to estimate the vertical flux of horizontal momentum of propagating gravity waves forced by this mechanism. A numerical model is used to simulate the Kelvin‐Helmholtz instability of the shear layer, and the induced large-scale gravity wave radiation. Owing to the large horizontal scale of the radiated waves, numerical simulations are practical only in two spatial dimensions. Therefore, to make a physically meaningful estimate of the vertical momentum flux, a diagnostic procedure is developed to identify the gravity wave radiation that arises from the early nonlinear evolution of the shear layer. This early evolution is well modeled by the simulations, because it occurs prior to the time at which three-dimensional motions would develop in a three-dimensional unstable shear layer. The results of this study are applied to the real atmosphere to address the question: does stratified shear instability, occurring in localized patches on the upper flank of the tropospheric westerly jet, significantly contribute to midlatitude mesospheric gravity wave drag in summer? The single-event estimates of vertical momentum flux derived here are combined with observed statistics of stratified shear instability occurring in the lower stratosphere. This gives an estimate of the average mesospheric vertical momentum flux in summer arising from the nonlinear gravity wave forcing mechanism considered here. The estimate indicates that gravity waves forced by stratified shear instability may account for a significant fraction of mesospheric gravity wave drag in summer.