Green's function-stochastic methods framework for probing nonlinear evolution problems: Burger's equation, the nonlinear Schrödinger's equation, and hydrodynamic organization of near-molecular-scale vorticity

► Systematic approach for physically probing nonlinear and random evolution problems. ► Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. ► Organization of near-molecular scale vorticity mediated by hydrodynamic modes. ► Framework allows calculation of vorticity evolution within random strain fields.