Instantons in a Lagrangian model of turbulence

Abstract

The role of instantons is investigated in the Lagrangian model for the velocity gradient evolution known as the Recent Fluid Deformation approximation. After recasting the model into the path-integral formalism, the probability distribution function is computed along with the most probable path in the weak noise limit through the saddle-point approximation. Evaluation of the instanton solution is implemented numerically by means of the iteratively Chernykh-Stepanov method. In the case of the longitudinal velocity gradient statistics, due to symmetry reasons, the number of degrees of freedom can be reduced to one, allowing the pdf to be evaluated analytically as well, thereby enabling a prediction of the scaling of the moments as a function of Reynolds number. It is also shown that the instanton solution lies on the Vieillefosse line concerning the RQ-plane. We illustrate how instantons can be unveiled in the stochastic dynamics performing a conditional statistics.

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• The large deviation approach to statistical mechanics
• Lagrangian dynamics and statistical geometric structure of turbulence
• Modeling the pressure Hessian and viscous Laplacian in Turbulence: comparisons with DNS and implications on velocity gradient dynamics
• Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations
• Relevance of instantons in Burgers turbulence
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Cited by in corpus (2)

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