Shear Excitation of Gravity Waves. Part II: Upscale Scattering from Kelvin-Helmholtz Waves

Abstract

Upscale scattering of Kelvin-Helmholtz waves to gravity shear waves involves the nonlinear interaction of two Kelvin-Helmholtz waves with wavenumbers k and k? to produce a wave with wavenumber k?k?. Calculations show that the process produces long-wavelength radiating gravity waves in atmospheric conditions that favor the Kelvin-Helmholtz instabilities. Both line and continuum evaluations are presented in the context of the unstable tropospheric jet. It is shown that even when the unstable shear in the jet is confined to a shallow sublayer, producing markedly small-scale Kelvin-Helmholtz instabilities, upscale scattering to the large-scale waves is an efficient process.