Title: Instantons and Fluctuations in a Lagrangian Model of Turbulence,
Abstract: We perform a detailed analytical study of the Recent Fluid Deformation (RFD)
model for the onset of Lagrangian intermittency, within the context of the
Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) path integral formalism. The
model is based, as a key point, upon local closures for the pressure Hessian
and the viscous dissipation terms in the stochastic dynamical equations for the
velocity gradient tensor. We carry out a power counting hierarchical
classification of the several perturbative contributions associated to
fluctuations around the instanton-evaluated MSRJD action, along the lines of
the cumulant expansion. The most relevant Feynman diagrams are then integrated
out into the renormalized effective action, for the computation of velocity
gradient probability distribution functions (vgPDFs). While the subleading
perturbative corrections do not affect the global shape of the vgPDFs in an
appreciable qualitative way, it turns out that they have a significant role in
the accurate description of their non-Gaussian cores.