Dynamic subgrid-scale models in rotating turbulence

Theoretical consideration is presented for the transformation properties of subgrid-scale (SGS) models for the SGS stress tenser in a noninertial frame of reference undergoing rotation. It was previously shown that certain transformation rules should be imposed on SGS stress (transformation rule) (Speziale 1985); namely, the SGS stress is not indifferent to a frame rotation, but the divergence of the SGS stress is frame-indifferent. When conformity of the modeled SGS stress tensor estimated using previous dynamic SGS models (the dynamic Smagorinsky, dynamic mixed and nonlinear models) with these transformation rules was examined (Horiuti 1999), all previous dynamic models were found to violate the rules except for the nonlinear model, when the dynamic procedure was used on the tensor level of the SGS stress tensor. In this study, the dynamic SGS model, in which this drawback was circumvented, was proposed. We considered the dynamic SGS model on the vector level of the SGS stress tensor by taking advantage of elimination of the correction term in the divergence of the SGS stress tenser. It was shown that the proposed model obeys the transformation rules. The result for a posteriori numerical assessment of the proposed model in decaying homogeneous turbulence which is subjected to rotation is presented.