Cell aspect ratio dependence of anisotropy measures for resolved and subgrid scale stresses

Discrete approximation of a flow field using anisotropic meshes causes "unphysical" anisotropy of the resolved part of the Reynolds stress tensor and of the subgrid scale stress tensor if common anisotropy measures such asū_īū_j/q²- 1/3δ_ijare used in order to characterize the turbulence structure. By evaluating model spectrum tensors the effect is investigated for isotropic and anisotropic turbulence. The deviation from a physical meaningful anisotropy state depends on various parameters such as the energy spectrum shape near the cutoff in wavespace, the cell aspect ratios, and the range of scales which are resolved. Subgrid kinetic energy must be distributed unequally among the normal stresses on an anisotropic mesh. For example, for aspect ratios Δx:Δy:Δz= 1:8:4, rms fluctuations of subgrid motions are shown to deviate by 9% in isotropic turbulence in the inertial subrange.