Circulation-Strain Sum Rule in Stochastic Magnetohydrodynamics

Details Circulation-Strain Sum Rule in Stochastic Magnetohydrodynamics Circulation-Strain Sum Rule in Stochastic Magnetohydrodynamics

2000-11-24

arxiv.org/abs/cond-mat/0011417v3

Phys. Rev. E 65, 036302 (2002).

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages; LaTex file Improved version, both at the technical level and regarding physical interpretation of results

Scientific paper

10.1103/PhysRevE.65.036302

We study probability density functions (pdfs) of the circulation of velocity and magnetic fields in magnetohydrodynamics, computed for a circular contour within inertial range scales. The analysis is based on the instanton method as adapted to the Martin-Siggia-Rose field theory formalism. While in the viscous limit the expected gaussian behaviour of fluctuations is indeed verified, the case of vanishing viscosity is not suitable of a direct saddle-point treatment. To study the latter limit, we take into account fluctuations around quasi-static background fields, which allows us to derive a sum rule relating pdfs of the circulation observables and the rate of the strain tensor. A simple inspection of the sum rule definition leads straightforwardly to the algebraic decay $\rho(\Gamma) \sim 1/ \Gamma^2$ at the circulation pdf tails.

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