A modified-Leray-alpha subgrid scale model of turbulence
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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.
author list (cited authors)
Ilyin, A. A., Lunasin, E. M., & Titi, E. S.
complete list of authors
Ilyin, AA||Lunasin, EM||Titi, ES