On the High-Wavenumber Form of the Eulerian Internal Wave Spectrum in the Atmosphere

Abstract

The theoretical model of the atmospheric internal wave spectrum developed here takes into account the influence of strong wave interactions caused by nonlinearity of Eulerian motion equations on the high-wavenumber form of the spectrum. The analytic relationship is found that describes the distortion of the form of the internal wave spectrum due to the transfer from the Lagrangian to the Eulerian frame of variables. Such distortion is associated with the advective nonlinearity, inherent to the Eulerian system only, and results in generating of a high-wavenumber tail in the Eulerian spectrum of the wave-induced displacements and velocities. The asymptotic forms at high wavenumbers are obtained for both the 3D and 1D wavenumber spectra of the vertical displacements and horizontal velocities. It is important that these forms do not depend on the detailed form of the spectrum of the Lagrangian displacements caused by random internal wave sources in the atmosphere. The obtained spectrum of the Eulerian horizontal velocity allows the form, anisotropy, and characteristic scales of the observed spectra of the horizontal wind speed fluctuations in the middle atmosphere to be explained.