On a Leray-alpha model of turbulence Academic Article uri icon


  • In this paper we introduce and study a new model for threedimensional turbulence, the Leray model. This model is inspired by the Lagrangian averaged NavierStokes model of turbulence (also known NavierStokes model or the viscous CamassaHolm equations). As in the case of the Lagrangian averaged NavierStokes model, the Leray model compares successfully with empirical data from turbulent channel and pipe flows, for a wide range of Reynolds numbers. We establish here an upper bound for the dimension of the global attractor (the number of degrees of freedom) of the Leray model of the order of ( L / l d ) 12/7 , where L is the size of the domain and l d is the dissipation lengthscale. This upper bound is much smaller than what one would expect for threedimensional models, i.e. ( L / l d ) 3 . This remarkable result suggests that the Leray model has a great potential to become a good subgridscale largeeddy simulation model of turbulence. We support this observation by studying, analytically and computationally, the energy spectrum and show that in addition to the usual k 5/3 Kolmogorov power law the inertial range has a steeper powerlaw spectrum for wavenumbers larger than 1/ . Finally, we propose a Prandtllike boundarylayer model, induced by the Leray model, and show a very good agreement of this model with empirical data for turbulent boundary layers.

published proceedings


author list (cited authors)

  • Cheskidov, A., Holm, D. D., Olson, E., & Titi, E. S.

citation count

  • 210

complete list of authors

  • Cheskidov, A||Holm, DD||Olson, E||Titi, ES

publication date

  • March 2005