Excitation of internal waves in a stably-stratified atmosphere with considerable wind-shear

Abstract

The rate of generation of internal waves by a thin turbulent boundary layer was calculated in a previous paper for a stably-stratified atmosphere with no significant wind-shear outside the boundary layer by considering the excitation of normal modes of wave propagation. By using the concept of wave-packets propagating upwards from the boundary layer, the effects of wind-shear can be included. Conditions for the validity of the approximation are given. In general, the spectral distribution of wave-energy at a particular height takes large values in two bands of horizontal wave-number, one band deriving from wave-packets undergoing internal reflexion near that height and the other from wave-packets of very small local frequency that accumulate there. The ‘reflexion’ wave-numbers are dominant if the wind increases with height and the ‘accumulation’ wave-numbers if the wind initially decreases with height. The spectral energy distributions and intensities of the wave-motion are discussed in more detail for an atmosphere of uniform stability and unidirectional wind-shear. The accumulation process may lead to instability or overturning of the waves, and estimates are made of the probable scale and intensity of the ‘clear-air’ turbulence produced. An interesting point is that the rate of energy loss from the boundary layer by radiation of internal waves turns out to be comparable with the rate of production in the outer nine-tenths of the layer, both for atmospheric boundary layers and for the surface layer of the ocean. It seems likely that radiation limits the layer thickness to some extent.