How is local material entropy production represented in a numerical model?

Abstract

Numerical models of the atmosphere should fulfil fundamental physical laws. The second law of thermodynamics is associated with positive local entropy production and dissipation of available energy. In order to guarantee this positivity in numerical simulations, subgrid‐scale turbulent fluxes of heat, water vapour and momentum are required to depend on numerically resolved gradients in a unique way. The task of parametrization remains to deliver phenomenological coefficients.Inspecting commonly used parametrizations for subgrid fluxes, we find that some of them obey the second law of thermodynamics and some do not. The conforming approaches are Smagorinsky momentum diffusion, phase changes and sedimentation fluxes for hydrometeors. Conventional turbulent heat‐flux parametrizations do not conform with the second law. A new water‐vapour flux formulation is derived from the requirement of locally positive entropy production. The conventional and new water‐vapour fluxes are compared using high‐resolution radiosonde data. Conventional water‐vapour fluxes are wrong by up to 10% and exhibit a negative bias.Two numerical tests (the Boulder windstorm test case and a convective boundary‐layer experiment) are performed with the Icosahedral Nonhydrostatic model at the Institute for Atmospheric Physics (ICON–IAP). The experiments compare conventional and entropy‐consistent heat‐flux parametrizations. Both test cases indicate that negative thermal dissipation can occur for the conventional heat flux. Obviously, the additional energy made available by this negative dissipation to the resolved turbulence is later on dissipated by friction, so that the total dissipation is again comparable, at least for the boundary‐layer experiment.