Alan A. Wray

The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence

The variational multiscale method is applied to the large eddy simulation (LES) of homogeneous, isotropic flows and compared with the classical Smagorinsky model, the dynamic Smagorinsky model, and direct numerical simulation (DNS) data. Overall, the multiscale method is in better agreement with the DNS data than both the Smagorinsky model and the dynamic Smagorinsky model. The results are somewhat remarkable when one realizes that the multiscale method is almost identical to the Smagorinsky model (the least accurate model!) except for removal of the eddy viscosity from a very small percentage of the lowest modes.

Explicit-filtering large-eddy simulation using the tensor-diffusivity model supplemented by a dynamic Smagorinsky term

Large-eddy simulation (LES) with regular explicit filtering is investigated. The filtered-scale stress due to the explicit filtering is here partially reconstructed using the tensor-diffusivity model: It provides for backscatter along the stretching direction(s), and for global dissipation, both also attributes of the exact filtered-scale stress. The necessary LES truncations (grid and numerical method) are responsible for an additional subgrid-scale stress. A natural mixed model is then the tensor-diffusivity model supplemented by a dynamic Smagorinsky term. This model is reviewed, together with useful connections to other models, and is tested against direct numerical simulation (DNS) of turbulent isotropic decay starting with Re-lambda=90 (thus moderate Reynolds number): LES started from a 256(3) DNS truncated to 64(3) and Gaussian filtered. The tensor-diffusivity part is first tested alone; the mixed model is tested next. Diagnostics include energy decay, enstrophy decay, and energy spectra. After an initial transient of the dynamic procedure (observed with all models), the mixed model is found to produce good results. However, despite expectations based on favorable a priori tests, the results are similar to those obtained when using the dynamic Smagorinsky model alone in LES without explicit filtering. Nevertheless, the dynamic mixed model appears as a good compromise between partial reconstruction of the filtered-scale stress and modeling of the truncations effects (incomplete reconstruction and subgrid-scale effects). More challenging 48(3) LES are also done: Again, the results of both approaches are found to be similar. The dynamic mixed model is also tested on the turbulent channel flow at Re-tau=395. The tensor-diffusivity part must be damped close to the wall in order to avoid instabilities. Diagnostics are mean profiles of velocity, stress, dissipation, and reconstructed Reynolds stresses. The velocity profile obtained using the damped dynamic mixed model is slightly better than that obtained using the dynamic Smagorinsky model without explicit filtering. The damping used so far is however crude, and this calls for further work

Decay of isotropic turbulence at low Reynolds number

Decay of isotropic turbulence is computed using direct numerical simulations. Comparisons with experimental spectra at moderate and low Reynolds numbers (Rλ<70) show good agreement. At moderate to high Reynolds numbers (Rλ≳50), the spectra are found to collapse with Kolmogorov scaling at high wave numbers. However, at low Reynolds numbers (Rλ<50) the shape of the spectra at the Kolmogorov length scales is Reynolds number dependent. Direct simulation data from flowfields of decaying isotropic turbulence are used to compute the terms in the equation for the dissipation rate of the turbulent kinetic energy. The development of the skewness and the net destruction of the turbulence dissipation rate in the limit of low Reynolds numbers are presented. The nonlinear terms are found to remain active at surprisingly low Reynolds numbers.