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We perform a detailed analytical study of the Recent Fluid Deformation (RFD)model for the onset of Lagrangian intermittency, within the context of theMartin-Siggia-Rose-Janssen-de Dominicis (MSRJD) path integral formalism. Themodel is based, as a key point, upon local closures for the pressure Hessianand the viscous dissipation terms in the stochastic dynamical equations for thevelocity gradient tensor. We carry out a power counting hierarchicalclassification of the several perturbative contributions associated tofluctuations around the instanton-evaluated MSRJD action, along the lines ofthe cumulant expansion. The most relevant Feynman diagrams are then integratedout into the renormalized effective action, for the computation of velocitygradient probability distribution functions (vgPDFs). While the subleadingperturbative corrections do not affect the global shape of the vgPDFs in anappreciable qualitative way, it turns out that they have a significant role inthe accurate description of their non-Gaussian cores.

Instantons and Fluctuations in a Lagrangian Model of Turbulence