Circulation-Strain Sum Rule in Stochastic Magnetohydrodynamics

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 $\rho (\Gamma )\sim 1/{\Gamma }^2$ at the circulation pdf tails.

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

References in corpus (6)

• Turbulence without pressure
• Instantons in Burgers Equation
• Instantons and Intermittency
• Kolmogorov turbulence in a random-force-driven Burgers equation: anomalous scaling and probability density functions
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Cited by in corpus (1)

• Eddy-Viscous Modeling and the Topology of Extreme Circulation Events in Three-Dimensional Turbulence