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Circulation-Strain Sum Rule in Stochastic Magnetohydrodynamics

L. Moriconi·F. A. S. Nobre
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Abstract

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 $ρ(Γ) \sim 1/ Γ^2$ at the circulation pdf tails.

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L. Moriconi, F. A. S. Nobre. 2002-03-28. Circulation-Strain Sum Rule in Stochastic Magnetohydrodynamics. https://doi.org/10.1103/physreve.65.036302

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