Multifractal subgrid-scale modeling for large-eddy simulation. I. Model development and a priori testing

Results are presented from a new approach to modeling the subgrid-scale stresses in large-eddy simulation of turbulent flows, based on explicit evaluation of the subgrid velocity components from a multifractal representation of the subgrid vorticity field. The approach is motivated by prior studies showing that the enstrophy field exhibits multifractal scale-similarity on inertial-range scales in high Reynolds number turbulence. A scale-invariant multiplicative cascade thus gives the spatial distribution of subgrid vorticity magnitudes within each resolved-scale cell, and an additive cascade gives the progressively isotropic decorrelation of subgrid vorticity orientations from the resolved scale Δ to the viscous scale λ_ν. The subgrid velocities are then obtained from Biot-Savart integrals over this subgrid vorticity field. The resulting subgrid velocity components become simple algebraic expressions in terms of resolved-scale quantities, which then allow explicit evaluation of the subgrid stresses τ_ij*. This new multifractal subgrid-scale model is shown in a priori tests to give good agreement for the filtered subgrid velocities, the subgrid stress components, and the subgrid energy production at both low (Re_Δ; ≈ 160) and high (Re_Δ; ≈ 2550) resolved-scale Reynolds numbers. Implementing the model is no more computationally burdensome than traditional eddy-viscosity models. Moreover, evaluation of the subgrid stresses requires no explicit differentiation of the resolved velocity field and is therefore comparatively unaffected by discretization errors.