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.