Energy Deposition and Turbulent Dissipation Owing to Gravity Waves in the Mesosphere

Abstract

An attempt is made to define the thermodynamics of internal gravity waves breaking in the middle atmosphere on the basis of the energy conservation law for finite fluid volumes. Consistent with established turbulence theory, this method ultimately determines the turbulent dissipation to be equivalent to the frictional heating owing to the Reynolds stress tensor. The dynamic heating due to nonconservative wave propagation, that is, the energy deposition, consists of two terms: namely, convergence of the wave pressure flux and a residual work term that is due to the wave momentum flux and the vertical shear of the mean flow. Only if both heating terms are taken into account does the energy deposition vanish, by definition, for conservative quasi-linear wave propagation. The present form of the energy deposition can also be deduced from earlier studies of Hines and Reddy and from Lindzen. The role of the axiomatically defined heating rates in the heat budget of the middle atmosphere is estimated by numerical experiments using a simple general circulation model (SGCM). The authors employ the theory of Lindzen to parameterize saturation of internal gravity waves, including the first theorem of Eliassen and Palm, to define the wave pressure flux. It is found that in the climatological zonal mean, the residual work and the simulated turbulent dissipation give maximum cooling/heating rates of ?5 K day?1 and +2.5 K day?1 in the summer mesosphere/lower thermosphere. These values are small but not negligible against the major contributions to the heat budget. Filtering out gravity wave perturbations in the thermodynamic equation reveals that the simulated dissipation, which is due to the shear of the planetary-scale flow, does not generally represent the total dissipation. The latter turns out to be dominated by the shear associated with gravity wave perturbations. Taking advantage of Lindzen, the total frictional heating can be calculated and is quantitatively consistent with in situ measurements of Lübken.