Lagrangian Averaged Navier-Stokes-alpha (LANS-alpha) Model for Turbulence: Connections to LES and New Directions

Darryl D. Holm, Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory

The Lagrangian Averaged Navier-Stokes-alpha (LANS-alpha) model is a turbulence equation that was developed jointly at Caltech, UC Davis and Los Alamos. It uses

1. Reynolds decomposition(s), Taylor's hypothesis and Lagrangian averages,

2. Hamilton's principle, Averaged Lagrangians and Euler-Poincare equations,

3. Navier-Stokes viscosity in the isotropic case, and a modified anisotropic viscosity otherwise,

to represent the mean dynamical effects of fluctuations on 3D incompressible fluid motion. When the length-scale alpha tends to zero, the LANS-alpha equations reduce to the Navier-Stokes equations. We shall

- Review recent results of the LANS-alpha model

- Discuss its relation to Large Eddy Simulation (LES) models and show comparisons

- Sketch an approach for modifying the LANS-alpha model to include rotation and stratification. This requires abandoning Taylor's hypothesis of "frozen-in" turbulence and deriving a new model that accounts for wave-mean flow interactions in the framework of 1. - 3. above.