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Vorticity equation of 2D-hydrodynamics, Vlasov steady-state kinetic equation and developed turbulence. (English) Zbl 1207.76111
Borisov, Alexey V. (ed.) et al., IUTAM symposium on Hamiltonian dynamics, vortex structures, turbulence. Proceedings of the IUTAM symposium held in Moscow, Russia, 25–30 August, 2006. Dordrecht: Springer (ISBN 978-1-4020-6743-3/hbk). IUTAM Bookseries 6, 27-37 (2008).
Summary: 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 two-dimensional 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.
For the entire collection see [Zbl 1130.76005].
MSC:
76M35 Stochastic analysis applied to problems in fluid mechanics
76B47 Vortex flows for incompressible inviscid fluids
76F55 Statistical turbulence modeling
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