A generalized formulation of the dynamic Smagorinsky model

A generalized formulation of the Dynamic Smagorinsky Model (DSM) is proposed as a versatile turbulent momentum diffusion scheme for Large-Eddy Simulations. The difference to previous versions of the DSM is a modified test filter range that can be chosen independently from the resolution scale to separate the impact of the test filter on the simulated flow from the impact of the resolution. The generalized DSM (gDSM) in a two-dimensional version is validated in a verification study as a horizontal momentum diffusion scheme with the Kühlungsborn Mechanistic General Circulation Model at high resolution (wavenumber 330) without hyperdiffusion. Three-day averaged results applying three different test filters in the macro-turbulent inertial range are presented and compared with analogous simulations where the standard DSM is used instead. The comparison of the different filters results in all cases in similar globally averaged Smagorinsky parameters cS≃0.35$c_S\simeq0.35$ and horizontal kinetic energy spectra. Hence, the basic assumption of scale invariance underlying the application of the gDSM to parameterize atmospheric turbulence is justified. In addition, the smallest resolved scales contain less energy when the gDSM is applied, thus increasing the stability of the simulation