Gravity wave breaking in the mesosphere can only be modeled if turbulent heat and momentum fluxes are parameterized reasonably well. In the present study with the ICON-IAP model, subgridscale heat fluxes are either parameterized in a conventional form dependent on the gradient of the potential temperature or on the gradient of the temperature. It is argued that the first option contradicts the second law of thermodynamics with regard to positive thermal entropy production (=dissipation/T). Thermal dissipation has to be distinguished from frictional dissipation, which is present as shear production in parameterization schemes. Diffusion of potential temperature is accompanied by negative thermal entropy production in some regions. This leads to a wave cooling effect and an exaggeration of the mesospheric inversion layer. In contrast, diffusion of temperature conforms with the second law of thermodynamics. The related diffusion coefficients can be obtained from the ones used for theta diffusion and an additional countergradient term, as for instance to be found in non-local closure schemes for turbulence in the planetary boundary layer. This temperature diffusion does not give rise to a wave cooling effect, and the mesospheric inversion layer is not as dominant. A vertical pseudovelocity is defined which highlights the differences between both types of diffusion, and which highlights its proximity to the resolved vertical velocity. Frictional dissipation contributes to heating and more dynamic variability in the breaking level in case of temperature diffusion, but if the potential temperature is diffused, model runs exhibit more cooling in the upper part of the breaking level and more heating in its lower part. The study votes for a clear separation between frictional and thermal dissipation. Both have to be positive independently and not solely as their sum, known as energy deposition.

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*email: gassmann@iap-kborn.de
*Preference: Poster