A new multifractal subgrid-scale model for large-eddy simulation

We present a fundamentally new approach for the modeling of the subgrid-scale stresses for the large-eddy simulation (LES) of turbulent flows, based directly on the spatial distribution of vorticity within the subgrid field. Drawing on a substantial body of theoretical, experimental and computational evidence, we demonstrate that the enstrophy field Q(x, t) ≡ 1/2 ω·ω(x, t) exhibits multifractal scale-similarity in the inertial range of high Reynolds-number turbulence. A multifractal cascade can then be used to describe the spatial distribution of vorticity magnitudes within the subgrid field. An additive cascade can be used to describe the spatial distribution of vorticity orientations, which isotropically decorrelate through the subgrid field from the orientations of the smallest resolved scale Δ in the flow. It is then possible to recast the subgrid velocity contributions to the subgrid stress tensor T_ij as Biot-Savart integrals over the subgrid vorticity field, which permits direct calculation of T_ij. The integral can be simplified using central-limit concepts, and in the high Reynolds-number limit, the subgrid-velocity field reduces to a simple algebraic expression based on quantities available from the resolved scales of the flow. Results from a priori tests are presented indicating good spatial and magnitude agreement for the filtered subgrid velocities u^s9s, the subgrid stress tensor T_ij and the subgrid energy production, P*. The multifractal approach presented here can be extended to model the filtered scalar transport equation and the Reynolds stresses in the Reynolds Averaged Navier-Stokes equation.