Symmetric Stress Tensor Formulation of Horizontal Momentum Diffusion in Global Models of Atmospheric Circulation

Abstract

Abstract In climate and weather forecast models, small-scale turbulence in the free atmosphere is usually parameterized by horizontal diffusion of horizontal momentum. This study proposes a formulation that is based on a symmetric stress tensor. The advantage over conventional methods is twofold. First, the Eulerian law of angular momentum conservation is fulfilled. Second, a self-consistent formulation of the momentum and thermodynamic equations of motion becomes possible due to incorporation of the local frictional heating rate, that is, the proper dissipation. The importance of these issues is demonstrated by numerical experiments performed with a simple general circulation model. For example, the new scheme precisely accounts for the irreversible increase of total potential energy during the decay of a baroclinic life cycle. Also the stress generated by horizontal momentum diffusion is found to be significant in the angular momentum budget of multiple life cycle experiments.