Scale-Invariant Formulation of Momentum Diffusion for High-Resolution Atmospheric Circulation Models

Abstract

A new version of the dynamic Smagorinsky model is presented that applies for nonisotropic momentum diffusion in high-resolution atmospheric circulation models. While the horizontal mixing length is computed in accordance with scale invariance in the mesoscale regime of the horizontal energy cascade, the associated dynamic vertical mixing length (DVML) is based on a recently developed scale invariance criterion and represents an application of the scaling laws of stratified macroturbulence. The DVML is validated in high-resolution simulations with the Kühlungsborn mechanistic general circulation model, using triangular spectral truncation at wavenumber 330 and a vertical level spacing of about 200 m in the upper troposphere. For a proper choice of the test filter, the model simulates a realistic horizontal kinetic energy spectrum in the troposphere along with a realistic intensity of the Lorenz energy cycle. This result is obtained without any hyperdiffusion, and it depends only little on whether the vertical mixing length is prescribed or set to the DVML. The globally averaged Smagorinsky parameter is about c S ≅ 0.53. The latitude–height cross sections show that c S maximizes in regions of strong mesoscale kinetic energy.