Vortex equilibria in turbulence theory and quantum analogues

• Published in: Physica. D 1991-09, Vol.52 (2), p.403-414
• Main Authors: Chorin, Alexandre Joel, Akao, James H.
• Format: Article
• Language: English
• Subjects: Classical and quantum physics: mechanics and fields; Classical mechanics of continuous media: general mathematical aspects; Exact sciences and technology; Physics
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/0167-2789(91)90136-W

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.