LARGE-EDDY SIMULATION OF THE TEMPORAL MIXING LAYER USING THE CLARK MODEL

The Clark model for the turbulent stress tensor in large-eddy simulati on is investigated from a theoretical and computational point of view. In order to be applicable to compressible turbulent flows, the Clark model has been reformulated. Actual large-eddy simulation of a weakly compressible, turbulent, temporal mixing layer shows that the eddy-vis cosity part of the original Clark model gives rise to an excessive dis sipation of energy in the transitional regime. On the other hand, the model gives rise to instabilities if the eddy-viscosity part is omitte d and only the ''gradient'' part is retained. A linear stability analy sis of the Burgers equation supplemented with the Clark model is perfo rmed in order to clarify the nature of the instability. It is shown th at the growth-rate of the instability is infinite in the inviscid limi t and that sufficient (eddy-) viscosity can stabilize the model. A mod el which avoids both the excessive dissipation of the original Clark m odel as well as the instability of the ''gradient'' part, is obtained when the dynamic procedure is applied to the Clark model. Large-eddy s imulation using this new dynamic Clark model is found to yield satisfa ctory results when compared with a filtered direct numerical simulatio n. Compared with the standard dynamic eddy-viscosity model, the dynami c Clark model yields more accurate predictions, whereas compared with the dynamic mixed model the new model provides equal accuracy at a low er computational effort.