A Dynamic α Model for the Lagrangian Averaged Navier-Stokes-α Equations

A dynamic α model for the isotropic incompressible LANS-α equations is proposed in this investigation. To derive this model, the incompressible Navier-Stokes equations are Helmholtz-filtered at the grid and test filter levels. A Germano type identity is derived by comparing the filtered subgrid scale stress terms with those given in LANS-α equations. Considering a constant value of α and averaging in the homogenous directions of the flow results in a nonliner equation for the parameter α, which determine the variation of α in the non-homogeneous directions or time. This nonlinear equation is solved by an iterative technique. Consequently, the parameter α is calculated during the simulation instead a predefined value. The initial tests of this model for the isotropic homogenous forced and decaying turbulence show that energy decay and energy spectra are predicted accurately by the dynamic LANS-α equations. An improvement in the results with dynamic LANS-α model over the coresponding calculations with a fixed α value for isotropic homogenous turbulence has also been observed. To exhibit the application prospecting of dynamic LANS-α model in wall bounded turbulenc simulation, a priori test of this model for turbulent channel flows is initially performed in this study. By a priori test, the parameter α is found to change in the wall normal direction. Near the boundary, the length scale α is seen to depend on the distance to the wall, and away from the boundary, α keeps an approximate constant value. As a result, the turbulent flow is divided into two regions: the constant α region away from the boundary and near wall region. A correct behavior of subgrid scale stress in near wall region is seen to be captured by this dynamic α model. Thus, the current priori tests show a promising application of this model in wall bounded turbulent flow simulation.