VERTICAL EVOLUTION OF GRAVITY-WAVE SPECTRA AND THE PARAMETERIZATION OF ASSOCIATED WAVE DRAG

Extensions of Weinstock's theory of nonlinear gravity waves and a para meterization of the related momentum deposition are which combines asp ects of Hines' Doppler spreading theory with Weinstock's theory of non linear wave diffusion, treats the low-frequency part of the gravity wa ve spectrum as an additional background flow for higher-frequency wave s. This technique allows one to calculate frequency shifting and wave amplitude damping produced by the interaction with this additional bac kground wind. For a nearly. monochromatic spectrum the parameterizatio n formulae for wave drag coincide with those of Lindzen. It is shown t hat two processes should be distinguished: wave breaking due to instab ilities and saturation due to nonlinear diffusionlike processes. The c riteria for wave breaking and wave saturation in terms of wave spectra are derived. For a saturated spectrum the power spectral density's (P SD) dependence S(m) = AN(2)/m(3) is obtained, where m is the vertical wavenumber and N is the Brunt-Vaisala frequency. Unlike Weinstock's or iginal formulation, our coefficient of proportionality A is a slowly v arying function of m and mean wind. For vertical wavelengths ranging f rom 10 km to 100 m and for typical wind shears, A varies from one half to one ninth. Calculations of spectral evolution with height as well as related profiles of wave drag are shown. These results reproduce ve rtical wavenumber spectral tail slopes which vary near the -3 value re ported by observations. An explanation of these variations is given.