Abstract
The statistical dynamics of a set of point vortices is investigated. The method of N.N. Bogolubov (1965) is employed and the BBGKY hierarchy is derived. It is shown that most physical quantities of interest, e.g. the velocity field, the pressure, and the interaction energy, are given in terms of a few reduced distribution functions. We also show how the introduction of the vortex dipole chaos assumption permits one to derive a kinetic equation for a ‘gas’ of vortex dipoles. The analysis of the observations of two-dimensional turbulent flows, made by experiments and direct numerical simulations, reveals that the kinetic theory of point vortex dipoles can be used, in conjunction with a scaling theory, to provide a hybrid theory of two-dimensional turbulence with no adjustable parameters.
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Schedule a callMore From: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
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