Gravity wave models for the horizontal wave number spectra of atmospheric velocity and density fluctuations

Abstract

Gravity wave models for the horizontal wave number spectra of atmospheric velocity and density fluctuations are derived by assuming that both saturated and unsaturated waves obey the polarization and dispersion relations and that the joint vertical wave number ( m ) and temporal frequency (ω) spectrum is separable. In the wave number region h * = ƒ m * / N ≤ h ≤ m * , where h = ( k 2 + l 2 ) 1/2 , k is the zonal wave number, l is the meridional wave number, ƒ is the inertial frequency, N is the buoyancy frequency, and m * is vertical wave number of the largest scale saturated wave, the model predicts that the two‐dimensional isotropic spectrum is proportional to h −( p +1) and the one‐dimensional spectra are proportional to k −p and l −p when the temporal spectrum is proportional to ω − p . In the saturation region h , k , l , m > m * , the spectra are proportional to h −( q +1) , k −q and l − q when the saturated m spectrum is proportional to m − q . The joint ( k , l , m ) and ( k , l , ω) model spectra are not separable. The models are consistent with existing observations of horizontal wave number spectra in the lower stratosphere and upper mesosphere.