Instantons, Fluctuations, and Singularities in the Supercritical Stochastic Nonlinear Schrödinger Equation.

Recently, Josserand et al. proposed a stochastic nonlinear Schrödinger model for finite-time singularity-mediated turbulence [Phys. Rev.

Spontaneous symmetry breaking for extreme vorticity and strain in the three-dimensional Navier-Stokes equations.

We investigate the spatio-temporal structure of the most likely configurations realizing extremely high vorticity or strain in the stochastically forced three-dimensional incompressible Navier-Stokes equations. Most likely configurations are computed by numerically finding the highest probability velocity field realizing an extreme constraint as solution of a large optimization problem. High-vorticity configurations are identified as pinched vortex filaments with swirl, while high-strain configurations correspond to counter-rotating vortex rings.

Instanton based importance sampling for rare events in stochastic PDEs.

We present a new method for sampling rare and large fluctuations in a nonequilibrium system governed by a stochastic partial differential equation (SPDE) with additive forcing. To this end, we deploy the so-called instanton formalism that corresponds to a saddle-point approximation of the action in the path integral formulation of the underlying SPDE. The crucial step in our approach is the formulation of an alternative SPDE that incorporates knowledge of the instanton solution such that we are able to constrain the dynamical evolutions around extreme flow configurations only.

Multiscale velocity correlations in turbulence and Burgers turbulence: Fusion rules, Markov processes in scale, and multifractal predictions.

We compare different approaches towards an effective description of multiscale velocity field correlations in turbulence. Predictions made by the operator-product expansion, the so-called fusion rules, are placed in juxtaposition to an approach that interprets the turbulent energy cascade in terms of a Markov process of velocity increments in scale. We explicitly show that the fusion rules are a direct consequence of the Markov property provided that the structure functions exhibit scaling in the inertial range.

Single-Particle Motion and Vortex Stretching in Three-Dimensional Turbulent Flows.

Three-dimensional turbulent flows are characterized by a flux of energy from large to small scales, which breaks the time reversal symmetry. The motion of tracer particles, which tend to lose energy faster than they gain it, is also irreversible. Here, we connect the time irreversibility in the motion of single tracers with vortex stretching and thus with the generation of the smallest scales.