Refined subgrid-scale model for large-eddy simulation of helical turbulence.

A refined two-term helical subgrid-scale (SGS) stress model with respect to that suggested by Li et al. [Phys. Rev. E 74, 026310 (2006)] is designed for large-eddy simulation (LES) of helical turbulence. The model coefficients in the new model are verified a priori to be scale invariant in inertial range, which proves that our model is local in scale. A dynamic method based on minimizing the residual resolved energy and helicity dissipations is suggested to simultaneously evaluate the coefficients of the mixed SGS model as the simulation progresses. In addition, an SGS helicity dissipation (or helicity flux) constraint condition is proposed to optimize the mixed two-term model. Both techniques are first tested and validated in the LES of forced isotropic helical turbulence. The statistical results are analyzed and compared with those obtained from the dynamic Smagorinsky model, the traditional dynamic mixed model, and the direct numerical simulation. It is found that the introduction of this dynamic procedure can help overcome the drawback of the traditional dynamic method which can not capture the negative helicity fluxes and SGS dissipations. The probability density functions of the energy flux and the conditioned helicity flux and SGS stress demonstrate that the helicity flux constrained dynamic SGS model can effectively predict the real SGS helical effects on the resolved scales, such as backscatters of energy and helicity, accurate helicity dissipation rate, and so on. The present models are also applied to the simulation of freely decaying isotropic turbulence with no apparent improvement observed in comparison with the traditional SGS models. The underlying reasons for these issues are addressed in detail.