Functional Modeling (Isotropic Case)
It would be illusory to try to describe the structure of the scales of motion and the interactions in all imaginable configurations, in light of the very large disparity of physical phenomena encountered. So we have to restrict this description to cases which by nature include scales that are too small for today’s computer facilities to solve them entirely, and which are at the same time accessible to theoretical analysis. This description will therefore be centered on the inter-scale interactions in the case of fully developed isotropic homogeneous turbulence1, which is moreover the only case accessible by theoretical analysis and is consequently the only theoretical framework used today for developing subgrid models. Attempts to extend this theory to anisotropic and/or inhomogeneous cases are discussed in Chap. 5. The text will mainly be oriented toward the large-eddy simulation aspects. For a detailed description of the isotropic homogeneous turbulence properties, which are reviewed in Appendix A, the reader may refer to the works of Lesieur  and Batchelor .
KeywordsFunctional Modeling Effective Viscosity Inertial Range Subgrid Scale Smagorinsky Model
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