A modified-Leray-alpha subgrid scale model of turbulence Academic Article uri icon


  • Inspired by the remarkable performance of the Leray- (and the Navier-Stokes alpha (NS-), also known as the viscous Camassa-Holm) subgrid scale model of turbulence as a closure model to Reynolds averaged equations (RANS) for flows in turbulent channels and pipes, we introduce in this paper another subgrid scale model of turbulence, the modified Leray- (ML-) subgrid scale model of turbulence. The application of the ML- to infinite channels and pipes gives, due to symmetry, similar reduced equations as Leray- and NS-. As a result the reduced ML- model in infinite channels and pipes is equally impressive as a closure model to RANS equations as NS- and all the other alpha subgrid scale models of turbulence (Leray- and Clark-). Motivated by this, we present an analytical study of the ML- model in this paper. Specifically, we will show the global well-posedness of the ML- equation and establish an upper bound for the dimension of its global attractor. Similarly to the analytical study of the NS- and Leray- subgrid scale models of turbulence we show that the ML- model will follow the usual k-5/3 Kolmogorov power law for the energy spectrum for wavenumbers in the inertial range that are smaller than 1/ and then have a steeper power law for wavenumbers greater than 1/ (where > 0 is the length scale associated with the width of the filter). This result essentially shows that there is some sort of parametrization of the large wavenumbers (larger than 1/) in terms of the smaller wavenumbers. Therefore, the ML- model can provide us another computationally sound analytical subgrid large eddy simulation model of turbulence. 2006 IOP Publishing Ltd and London Mathematical Society.

published proceedings


author list (cited authors)

  • Ilyin, A. A., Lunasin, E. M., & Titi, E. S.

citation count

  • 98

complete list of authors

  • Ilyin, AA||Lunasin, EM||Titi, ES

publication date

  • March 2006