Direct heating rates associated with gravity wave saturation

Abstract

Analysis of filtering out subscale motions is applied for internal gravity waves. This leads to a new perspective of the planetary-scale sensible heat budget of the upper mesosphere/lower thermosphere. In line with previous results of Becker and Schmitz, the present paper recapitulates that the dissipation of gravity wave kinetic energy and the local adiabatic conversion of mean enthalpy into gravity wave kinetic energy cannot be neglected, and that the net effect of both cools the upper mesosphere/lower thermosphere. In addition, the importance of the wave entropy flux—an effect which is ignored in customary gravity wave parameterizations for global circulation models—is stressed. We show that, when evaluated on the basis of Lindzen's saturation assumption, the wave entropy flux convergence behaves like a vertical diffusion of the mean stratification, where the wave-induced diffusion coefficient is involved with a Prandtl number of 2. This result imposes an upper bound of 2 for the effective Prandtl number which scales the combined entropy flux owing to turbulence and gravity waves. The direct heating rates generated by gravity wave saturation are assessed quantitatively, using an idealized general circulation model completed by a Lindzen-type gravity wave parameterization.