Efficient Computation of Instantons for Multi-Dimensional Turbulent Flows with Large Scale Forcing (Communications in Computational Physics, 2018)
Extreme events play a crucial role in fluid turbulence. Inspired by methodsfrom field theory, these extreme events, their evolution and probability can be computedwith help of the instanton formalism as minimizers of a suitable action functional.Due to the high number of degrees of freedom in multi-dimensional fluid flows,traditional global minimization techniques quickly become prohibitive in their memoryrequirements. We outline a novel method for finding the minimizing trajectory ina wide class of problems that typically occurs in turbulence setups, where the underlyingdynamical system is a non-gradient, non-linear partial differential equation, andthe forcing is restricted to a limited length scale. We demonstrate the efficiency of thealgorithm in terms of performance and memory by computing high resolution instantonfield configurations corresponding to viscous shocks for 1D and 2D compressibleflows.