Non-normal effect of the velocity gradient tensor and the relevant subgrid-scale model in compressible turbulent boundary layer

Abstract

The non-normal effects of the velocity gradient tensor (VGT) in a compressible turbulent boundary layer are studied by means of the Schur decomposition of the VGT into its normal and non-normal parts. Based on the analysis of the relative importance of them, it is found that the non-normal part significantly affects the dynamics of the VGT in the wall-bounded turbulent flow and the relevant non-normal effect has a dominant influence on the enstrophy and dissipation. It is revealed that the deviatoric part of the pressure Hessian is associated with the non-normal effect and the isotropic part is associated with the normal effect. The pressure Hessian significantly influences the vortex stretching. The non-normal effect reinforces the preferences for the vorticity vector to align with the intermediate strain-rate eigenvector and to be perpendicular to the extensive and compressive strain-rate eigenvector in the near-wall region. The non-normal effect also reduces the intermediate eigenvalue of the strain-rate tensor. Furthermore, a subgrid scale (SGS) model that separately considers the normal and non-normal effects is proposed based on the above characters and is verified to give a better prediction of the SGS dissipations in the wall-bounded turbulent flow.