Anisotropic Turbulent Flow Simulations using the Isotropic LANS-$\alpha$ Equations

Direct numerical simulation of most engineering and geophysical turbulent flows requires intensive computations. Large Eddy Simulations (LES), Reynolds Averaged Navier-Stokes Equations (RANS), and the Lagrangian averaged Navier-Stokes-$\alpha$ (LANS-$\alpha$) equations are among the numerical techniques to reduce the computational intensity of turbulent flow calculations. In this talk a {\it dynamic} procedure for the Lagrangian Averaged Navier-Stokes-$\alpha$ (LANS-$\alpha$) equations is developed where the variation in the parameter $\alpha$ in the direction of anisotropy is determined in a self-consistent way from data contained in the simulation itself. In order to evaluate the applicability of the dynamic LANS-$\alpha$ model in anisotropic turbulence, {\it a priori} test of the dynamic LANS-$\alpha$ in channel flows is performed at various Taylor Reynolds numbers between 180 and 550 based on the wall friction velocity to find the variation of $\alpha$ in the wall-normal direction. It is found that in the wall region the parameter $\alpha$ rapidly increases away from the wall and saturates to an almost constant value in the outer region. An appropriate scaling for $\alpha$ is also identified. As a result, the isotropic LANS-$\alpha$ equations can now be easily used in anisotropic channel flows with a universally damped $\alpha$.