Computational Mathematics and Scientific Computing Seminar

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Predicting Extreme Events in Fluid Turbulence with the Instanton Formalism: Numerical Computation of Large Deviation Minimizers

Speaker: Tobias Grafke, CIMS

Location: Warren Weaver Hall 1302

Date: Oct. 30, 2015, 10 a.m.

Synopsis:

Rare but extreme events are known to have dramatic influence on the statistics of turbulent flows, but are notoriously hard to handle both analytically and numerically. About 15 years ago, for systems like passive advection and Burgers turbulence, alternative approaches were taken with methods borrowed from field theory, most notably the instanton approach, but full analytical treatment of turbulence remains elusive. In this talk, a numerical method is presented to effectively compute minimizers of the Freidlin-Wentzell action functional that arises in the context of large deviation theory applied to stochastically forced fluid dynamical equations. The presented method is then used to calculate expectations dominated by noise-induced excursions from deterministically stable fixpoints in hydrodynamical equations to gain knowledge on statistics of rare events and the interplay between the nonlinear dynamics and the stochastic forcing. In the course of the talk it will be demonstrated that the numerical method is suitable for computing the minimizing trajectory for degenerately forced systems with a very high number of degrees of freedom which are frequently encountered in multi-dimensional turbulent flows.