Efficient Computation of Instantons for Multi-Dimensional Turbulent Flows with Large Scale Forcing

TL;DR

This paper introduces a novel, memory-efficient algorithm for computing instantons in multi-dimensional turbulent flows with large scale forcing, enabling the analysis of extreme events in complex fluid systems.

Contribution

A new method for finding instanton trajectories in high-dimensional, non-gradient fluid flow problems with limited forcing scales, improving computational feasibility.

Findings

Successfully computed high-resolution instanton configurations for 1D and 2D flows.

Demonstrated improved performance and reduced memory usage compared to traditional methods.

Validated the approach on viscous shock scenarios in compressible flows.

Abstract

Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with 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 memory requirements. We outline a novel method for finding the minimizing trajectory in a wide class of problems that typically occurs in turbulence setups, where the underlying dynamical system is a non-gradient, non-linear partial differential equation, and the forcing is restricted to a limited length scale. We demonstrate the efficiency of the algorithm in terms of performance and memory by computing high resolution instanton field configurations corresponding to viscous shocks for 1D and 2D compressible flows.