Vorticity equation of 2D-hydrodynamics, Vlasov steady-state kinetic equation and developed turbulence

Abstract

The issues discussed in this paper relate to the description of developed two-dimensional turbulence, when the mean values of characteristics of steady flow stabilize. More exactly, the problem of a weak limit of vortex distribution in twodimensional flow of an ideal fluid at time tending to infinity is considered. Relations between the vorticity equation and the well-known Vlasov equation are discussed. © 2008 Springer.