Nonlinear Formation of the Three-Dimensional Spectrum of Mesoscale Wind Velocity and Temperature Fluctuations in a Stably Stratified Atmosphere

Abstract

The theory of formation of the space–time spectrum of the mesoscale fluctuations in the horizontal wind velocity and vertical displacements (or relative temperature fluctuations) in a stably stratified atmosphere is developed. The nonlinear mechanism of the formation of the finescale layered inhomogeneities in the internal wave fields associated with the nonresonant wave–wave and wave–vortical mode interactions is described. The 3D spatial spectra of the layered inhomogeneities are obtained from the approximate solutions of Lagrangian motion equations for internal waves and subsequent transition to the Eulerian coordinate system. Because of such transition, the advection of internal waves by the wind induced by the waves and vortical modes is taken into account. The contributions from the large-scale wind disturbances and finescale layered inhomogeneities to the horizontal wavenumber spectrum of the velocity fluctuations are found. Using an analytic form obtained for the 3D spectrum, the comparison is made between the modeled one-dimensional (1D) wavenumber spectra (vertical and horizontal) of the fluctuations with the observed spectra in the upper troposphere and lower stratosphere. The observed 1D (horizontal and vertical) wavenumber spectra of the horizontal velocity fluctuations with a −3 power-law decay are explained.