Calculation of shear stresses in the Fourier–Galerkin formulation of turbulent channel flows: projection, the Dirichlet filter and conservation

We consider turbulent channel flows computed with DNS and LES employing a Fourier–Galerkin method. We show that the balance of total mean shear stress, a measure of conservation of the numerical method, is satisfied only weakly (i.e., in an integral sense), rather than strongly (i.e., pointwise). A study of filters induced by projectors reveals that a certain filter, the Dirichlet filter, provides a tool for extracting shear stresses that are strongly conservative. Numerical results support the theory and demonstrate that spurious oscillations, present in the unfiltered stresses, are also suppressed. 2003 Elsevier Science B.V. All rights reserved.