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10/03/06 Colloquium
Professor Eleftherios Gkioulekas
Mathematics Department
University of Central Florida
Mathematics Department
University of Central Florida
On the Elimination of the Sweeping Interactions from Theories of Hydrodynamic Turbulence
Abstract: The problem of eliminating the sweeping interactions has been a thorn on all efforts aimed at developing analytical theories of three-dimensional hydrodynamic turbulence for many decades. Proposals for addressing this problem have been given by Kraichnan, Yakhot and Giles, and more recently the quasi-Lagrangian formulation of Belinicher and L'vov. In my talk, I will argue that Lagrangian transformations, such as the quasi-Lagrangian formulation of Belinicher and L'vov, do not prove that the sweeping interactions can be neglected in the inertial range; they only introduce implicitly the assumption that the sweeping interactions are negligible. I will discuss the relevant theoretical issues. The sweeping interactions are linked with the renormalization of the MSR theory of the Navier-Stokes equatoons, the problem of the self-consistency of local homogeneity, and the derivation of the $4/5$-law.