Abstract
A family of statistical vortex equilibria and related quasi-equilibria in models of classical incompressible flow is analyzed; it is suggested that these equilibria constitute approximate models of the inertial scales in turbulence. Inertial exponents γ are calculated; the equilibrium that has maximum entropy has a spectrum close to the Kolmogorov spectrum. At maximum entropy, the vortex filaments have axes that are self-avoiding random walks. The velocity statistics are non-Gaussian even at equilibrium. The classical vortex system is contrasted with a quantum vortex system; it is shown that classical vortex folding is a manifestation of the Kosterlitz-Thouless transition mechanism. Universality properties of the inertial exponent are discussed, as is the effect of a strong cascade on vortex reconnection. A relation with some recent work on the λ transition in superfluidity is pointed out.
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