The spectrum of high-frequency internal waves in the atmospheric waveguide

The vertical structure and power spectrum of the field of internal waves generated in the atmospheric waveguide by random vertical displacements were considered in this paper. The two-layered model of the atmosphere being used as a simple model of the waveguide takes into account the discrete spectrum of internal waves (both guided and vertically propagating), It is shown that these waves can produce the thin turbulent layers at certain heights, which are independent of random parameters of the source of internal waves. In the Eulerian frame of variables the wavenumber spectrum of internal waves, both three-dimensional and one-dimensional, tends asymptotically to a universal form at large wavenumbers. It is shown that the universal ''tail'' of the spectrum is formed by a strong mode's interaction caused by the advective nonlinearity and that the amplitude of the tail does not depend on the height above the ground. The characteristic vertical and horizontal wavenumbers of the three-dimensional Eulerian spectrum are found to be inversely proportional to the variances of the vertical and horizontal particle displacements correspondently. The three-dimensional spectrum is essentially anisotropic up to the wavenumbers that reach their critical values, defined by a condition of convective or shear instability. These critical vertical and horizontal wavenumbers are estimated. It is shown that the spectral amplitude of the wave-induced wind shear increases when wavenumber transits from the range of the vertically propagating waves to the range of the guided waves, so the discrete spectrum of internal waves plays an important role in destabilization of the total wave system.