Large eddy simulation with energy and helicity flux constraint

The energy and helicity flux constraints are imposed on the dynamic procedure of LES. The coefficients in the sub-grid scale stress model are determined by minimizing the error $E=\left<(L_{ij}-(T^{mod}_{ij}-\overline{\tau^{mod}_{ij}}))^2 \right>$ in satisfying the Germano identity under the energy and helicity flux constraints $ \left<\tau^{mod}_{ij}\tilde S_{ij}\right>=\Pi_E$, and $\left<\tau^{mod}_{ij}\tilde R_{ij}\right>=\Pi_H$. Both a \emph{priori} test and a \emph{posteriori} test of the present SGS model are performed. Given proper energy and helicity flux functions $\Pi_E$ and $\Pi_H$, this constrained dynamic SGS model not only achieves a good r.m.s approximation of real SGS stress but also preserves the correct energy and helicity flux.