Phenomenological Determination of Scaling Exponents in Two-Dimensional Decaying Turbulence : Condensed Matter and Statistical Physics

概要

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In the second stage of two-dimensional decaying turbulence, statistical quantities such as the average vortex size and the enstrophy, etc. develop algebraically with time. In particular, the number of vortices decreases as N(t) 〜t^<-ξ> with a certain positive exponent ξ. The evolution of other quantities is determined in terms of the exponent ξ. In this paper, to phenomenologically determine ξ, the authors emphasize the importance of taking into account the Hamiltonian dynamical advection of vortices to the scaling consideration proposed by Carnevale et al. [Phys. Rev. Lett. 66 (1991), 2735]. The analysis based on the Hamiltonian dynamics yields the value ξ = 2/3, which is in a good agreement with numerical and experimental results 0.7〜0.75. The present theory is compared with the studies on the determination of ξ proposed by Benzi et al. [J. of Phys. A21 (1988), 1221] and McWilliams [J. Fluid Mech. 219 (1990), 361].
理論物理学刊行会の論文
1997-12-25