Numerical Simulations of the Lagrangian Averaged Navier-Stokes (LANS-$\alpha$) Equations for Forced Homogeneous Isotropic Turbulence

Mohseni, K., S. Shkoller, B. Kosovic and J. E. Marsden

Amer. Inst. Aero. Astro., 2001-2645

Abstract:

The modeling capabilities of the Lagrangian Averaged Navier-Stokes-$\alpha$ equations (LANS-$\alpha$) is investigated in statistically stationary three-dimensional homogeneous and isotropic turbulence. The predictive abilities of the LANS-$\alpha$ equations are analyzed by comparison with DNS data. Two different forcing techniques were implemented to model the energetics of the energy containing scales. The resolved flow is examined by comparison of the energy spectra of the LANS-$\alpha$ and the DNS computations; furthermore, the correlation between the vorticity and the eigenvectors of the rate of the resolved strain tensor is studied. We find that the LANS-$\alpha$ equations captures the gross features of the flow while the wave activity below a given scale $\alpha$ is filtered by the non-linear dispersion.