Instantons, fluctuations and singularities in the supercritical stochastic nonlinear Schroedinger equation

Abstract

Recently, Josserand et al. proposed a stochastic nonlinear Schroedinger model for finite-time singularity-mediated turbulence [Phys. Rev. Fluids 5, 054607 (2020)]. Here, we use instanton calculus to quantify the effect of extreme fluctuations on the statistics of the energy dissipation rate. While the contribution of the instanton alone is insufficient, we obtain excellent agreement with direct simulations when including Gaussian fluctuations and the corresponding zero mode. Fluctuations are crucial to obtain the correct scaling when quasi-singular events govern the turbulence statistics.

5 pages, 3 figures, 5 pages appendix