The subgrid-scale modeling of helicity and energy dissipation in helical turbulence

Yi Li1,2, Charles Meneveau1,2, Gegory Eyink2,3 & Shiyi Chen1,2,4
1 Department of Mechanical Engineering, 2 Center for Environmental and Applied Fluid Mechanics, 3 Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore MD 21218, 4 COE and CCSE, Peking University, Beijing.

ABSTRACT:The subgrid-scale (SGS) modeling of helical, isotropic turbulence in large Eddy Simulation (LES) is investigated by quantifying rates of helicity and energy cascade. Assuming Kolmogorov spectra, the Smagorinsky model with its traditional coefficient is shown to underestimate the helicity dissipation rate by about 40 %. Several two-term helical models are proposed with the model coefficients calculated from simultaneous energy and helicity dissipation balance. The helical models are also extended to include dynamic determination of their coefficients. The models are tested a-priori in isotropic steady helical turbulence. Together with the dynamic Smagorinsky model and the dynamic mixed model, they are also tested a posteriori in both decaying and steady isotropic helical turbulece by comparing results to direct numerical simulations (DNS). The a-priori tests confirm that the Smagorinsky model underestimates SGS helicity dissipation, although quantitative differences with the predictions are observed due to the finite Reynolds number of the DNS. Also, in a-posteriori tests improvement can be achieved for the helicity decay rate with the proposed models, compared with the Smagorinsky model. Overall, however, the effect of the new helical terms added to obtain the correct rate of global helicity dissipation is found to be quite small. Within the small differences, the various versions of the dynamic model provide the results closest to the DNS. The dynamic model's good performance in capturing mean kinetic energy dissipation at the finite Reynolds number of the simulations appears to be the most important aspect in accounting also for accurate prediction of the helicity dissipation.

(2006) Phys. Review E  74, 026310.

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