Subgrid-scale eddy viscosity model for helical turbulence

A novel eddy-viscosity closure is proposed for the subgrid-scale (SGS) stress tensor in large-eddy simulation of helical turbulence. The eddy-viscosity is shown to be proportional to the product of the large-scale velocity strain rate tensor and the symmetric part of the large-scale vorticity gradient (or vorticity strain rate tensor) based on a SGS helicity dissipation balance and a spectral relative helicity relation. The new SGS model is first tested and validated in simulation of homogeneous and isotropic helical turbulence. The statistical results demonstrate that the present model can predict both the energy and helicity spectra more precisely than the dynamic Smagorinsky model and a mixed helical model as compared with the results calculated in direct numerical simulation. Then, a compressible version of the new SGS model is parameterized and utilized to simulate the compressible flow past a circular cylinder. It is found that the present eddy-viscosity model can reproduce the skin friction force much more accurately than the standard Smagorinsky model, and can simulate more realistic flow structures in the near wake of the cylinder than the detached-eddy simulation approach. The surprising findings in simulation of flow past a circular cylinder suggest that the inclusion of contribution from helicity in SGS modeling is important for large-eddy simulation of separated turbulent flows.