G.A. Degrazia, A.B. Nunes, P. Satyamurty, O.C. Acevedo, H.F. de Campos Velho, U. Rizza, J.C. Carvalho (2006): Heisenberg's Turbulent Spectral Transfer Theory for Sub-grid Scaling in LES Models, PanAmerican Workshop on Applied and Computational Mathematics, 23-28 July, Huatulco (Oaxaca), Mexico.

Abstract: A turbulent subfilter viscosity for large eddy simulation (LES) models is proposed, based on Heisenberg´s mechanism of energy transfer. Such viscosity is described in terms of a cutoff wavenumber, leading to relationships for the grid mesh spacing, for a convective boundary layer. The limiting wavenumber represents a sharp filter separating large and small scales of a turbulent flow and, henceforth, Heisenberg´s model agrees with the physical foundation of LES models. The comparison between Heisenberg´s turbulent viscosity and the classical ones, based on Smagorinsky´s parameterization, shows that both procedures lead to similar subgrid exchange coefficients. With this result, the turbulence resolution length scale and the vertical mesh spacing are expressed only in terms of the longitudinal mesh spacing. Through the employment of spectral observational data in the convective boundary layer, the mesh spacings, the filter width and the subfilter eddy viscosity are described in terms of the convective boundary layer height. The present development shows that Heisenberg´s theory naturally establishes a physical criterium that connects the subgrid terms to the large-scale dimensions of the system.