[1506.08745] The instanton method and its numerical implementation in fluid mechanics

[ Authors ]
Tobias Grafke, Rainer Grauer, Tobias Schäfer
[ Abstract ]
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional fluid dynamical problems. We illustrate these ideas using the two-dimensional Burgers equation and the three-dimensional Navier-Stokes equations.

U.S. team prepares for 2015 Trial des Nations

U.S. team prepares for 2015 Trial des Nations

The U.S. team is gearing up for the 2015 Fédération Internationale de Motocyclisme Trial des Nations in Tarragona, Spain, on Sept. 19-20. The American Motorcyclist Association and the North American Trials Council are pleased to welcome Bryan Roper, Andrew Putt, Logan Bolopue and Daniel Blanc-Gonnet to the U.S. men’s team, with Quinn Wentzel as the alternate. The U.S. women’s team will include…

View On WordPress

Happy five year #anniversary to my beautiful #mcm @jacob_wentzel . You’re the love of my life and I can’t wait to spend the rest of our lives together. Thank you for always supporting me even when I’m grumpy.