The Navier-Stokes-alpha model of fluid turbulence
Abstract
We review the properties of the nonlinearly dispersive Navier-Stokes-alpha (NS- α) model of incompressible fluid turbulence - also called the viscous Camassa-Holm equations in the literature. We first re-derive the NS- α model by filtering the velocity of the fluid loop in Kelvin’s circulation theorem for the Navier-Stokes equations. Then we show that this filtering causes the wavenumber spectrum of the translational kinetic energy for the NS- α model to roll off as k-3 for kα>1 in three dimensions, instead of continuing along the slower Kolmogorov scaling law, k-5/3, that it follows for kα<1. This roll off at higher wavenumbers shortens the inertial range for the NS- α model and thereby makes it more computable. We also explain how the NS- α model is related to large eddy simulation (LES) turbulence modeling and to the stress tensor for second-grade fluids. We close by surveying recent results in the literature for the NS- α model and its inviscid limit (the Euler- α model).
- Publication:
-
Physica D Nonlinear Phenomena
- Pub Date:
- May 2001
- DOI:
- 10.1016/S0167-2789(01)00191-9
- arXiv:
- arXiv:nlin/0103037
- Bibcode:
- 2001PhyD..152..505F
- Keywords:
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- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 22 pages, 1 figure. Dedicated to V. E. Zakharov on the occasion of his 60th birthday. To appear in Physica D