Packet-Scale Motions Forced by Nonlinearities in a Wave System

Abstract

Second-order theory is formulated for a wave packet propagating in a stratified fluid, and the packet-scale flows in the system are examined. These large-scale flows originate from interactions between first-order field components with wavenumbers k and k + ?, which force second-order motions with wavenumber ? (large scale) as well as the more familiar harmonics. The perturbation method used produces second-order field equations in which by-products of the linearized wave packet fields appear as source terms. The large-scale part of this forced flow is extracted through a k space projection operation. This flow field is then obtained, first formally for a rather general system and then explicitly for a packet propagating in a simple model of the surface layer inversion. Flow within the body of the packet takes the form of a quasi-horizontal velocity field with a marked vertical shear structure. This flow is examined for consistency with steady-state assumptions and for stability with respect to local Kelvin-Helmholtz, wave formation. It appears that such flows can be unstable at physically realizable amplitudes, and this is suggested as a possible source of the turbulent laminae observed in atmospheric inversions.