On shear-generated gravity waves that reach the mesophere. Part I : Wave generation

A long unresolved issue in nonorographic gravity wave generation is whether there is significant emission from Kelvin-Helmholtz (KH) shear instability in the lower stratosphere, for instance, just above tropopause jets. Such emission has often been suggested as significant for the angular momentum budget and hence for the wave-driven circulation of the middle atmosphere, most crucially in the summer mesosphere. An idealized model thought experiment is studied in which it is assumed that the KH shear instability rapidly mixes a thin layer, producing a "pancake" of three-dimensional clear-air turbulence, and emitting low-frequency inertia-gravity waves whose aspect ratio matches that of the turbulent layer and whose horizontal wavelength is large enough to avoid back-reflection and hence reach the summer mesosphere. The wave emission is modeled as a linear initial-value problem in which the rapid mixing of mass and momentum achieved by the turbulence is treated as instantaneous, and hence as determining the initial conditions. Care is taken to cast the problem into a form that permits well-conditioned numerical evaluation of the analytical solution, in both rotating and nonrotating cases, which behave very differently. Comparison with fully nonlinear numerical simulations in two dimensions of the same initial-value problem indicates that the linear theory is much better than might be expected on order-of-magnitude grounds. A companion paper (Part II) investigates the transmission of the emitted waves to the mesosphere subject to refraction and radiative damping.