NavierStokesalpha model: LES equations with nonlinear dispersion
Abstract
We present a framework for discussing LES equations with nonlinear dispersion. In this framework, we discuss the properties of the nonlinearly dispersive NavierStokesalpha model of incompressible fluid turbulence  also called the viscous CamassaHolm equations and the LANS equations in the literature  in comparison with the corresponding properties of large eddy simulation (LES) equations obtained via the approximateinverse approach. In this comparison, we identify the spatially filtered NSalpha equations with a class of generalized LES similarity models. Applying a certain approximate inverse to this class of LES models restores the Kelvin circulation theorem for the defiltered velocity and shows that the NSalpha model describes the dynamics of the defiltered velocity for this class of generalized LES similarity models. We also show that the subgrid scale forces in the NSalpha model transform covariantly under Galilean transformations and under a change to a uniformly rotating reference frame. Finally, we discuss in the spectral formulation how the NSalpha model retains the local interactions among the large scales, retains the nonlocal sweeping effects of large scales on small scales, yet attenuates the local interactions of the small scales amongst themselves.
 Publication:

arXiv eprints
 Pub Date:
 March 2001
 arXiv:
 arXiv:nlin/0103036
 Bibcode:
 2001nlin......3036D
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 15 pages, no figures, Special LES volume of ERCOFTAC bulletin, to appear in 2001