A Dynamic Mixed Model for General Circulation Models

Abstract

An extension of the dynamic Smgarorinsky model (DSM) is presented. In the so-called dynamic mixed model (DMM), the Leonard stress (i.e., the resolved part of the Reynolds stress) is no longer parameterized in the test filter range by the Smagorinsky model. Instead, it is modeled by the so-called similarity model, which assumes close self-similarity of the resolved and unresolved flow. This implementation is derived first in general and then specifically for spectral models. In the latter case, spectral cut-off filters allow a simple reformulation of the basic tensor equation of the DSM, requiring only the modification of a particular term to obtain the DMM version of the turbulence model.The DMM is then examined in the Kühlungsborn Mechanistic general Circulation Model (KMCM), a spectral CGM, where, starting from the same initial condition, the flow fields are compared in a model run with the DMM and in a control run with the DSM on day zero and day eight. Although most of the results are comparable, there is, already at day zero, a significant difference at the poles: with the DSM, there are certain locations with large values of the Smagorinsky parameter that are not present in the DMM run. This can be explained mathematically by the fact that the convergence of the associated Legendre polynomials in the spectral representation is worse at the poles. Therefore, numerical errors can occur in the spectral transformation, which cancel out in the DMM due to its formulation, allowing the increase of the time steps.

Keywords

• turbulence modelling
• momentum diffusion
• subgrid-scale modelling
• numerical simulation