Shear Excitation of Gravity Waves. Part I: Modes of a Two-Scale Atmosphere

Abstract

The stabilities of two model tropospheric jets are compared. The first jet is a simple, smooth, idealized profile governed by a single scale length of tropospheric dimensions. The second jet takes the first model flow and superimposes on it a localized deformation of much smaller scale. In this second model, the shears deriving from the small-scale structure provide the subcritical Richardson numbers that support instability. The two-scale model produces a much wider range of wave instabilities. Its Kelvin-Helmholtz waves span a wavenumber domain that is nearly two orders of magnitude wider than the domain of the one-scale model, while the gravity shear waves fill out into the small wavenumber areas of the stability diagrams. However, the growth rates of the instabilities displace significantly toward smaller scales in the two-scale model. It is suggested that the two-scale model is probably geophysically more realistic, and removes the necessity for deep layers of subcritical Richardson numbers, making it more in agreement with radiosonde observations than are smooth one-scale models.