Extreme events in fluid dynamics -- Instantons in turbulent flows

Understanding intermittency in turbulent flows is still an outstanding open problem in classical physics. More than 15 years ago, for systems like passive advection and Burgers turbulence, the door for attacking this issue was opened with methods borrowed from field theory, most notably the instanton approach. Yet, conflicting measurements have let to a controversy around the usefulness and applicability of instantons in turbulent systems. In this talk, a novel method is presented to effectively compute minimizers of the Freidlin-Wentzell action functional that arises in the context of large deviation theory for stochastic partial differential equations. The presented method is then applied 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 particular it is applied to predict tail exponents of PDFs of turbulent flow quantities. This allows to solve the discrepancy between measurements and theory that was open for the last 15 years and reinstate instanton calculus in turbulence setups.