Toward computing sensitivities of average quantities in turbulent flows

TL;DR

This paper introduces the space-split sensitivity (S3) algorithm, a novel method designed to compute sensitivities of average quantities in chaotic turbulent flows, overcoming limitations of existing approaches.

Contribution

The paper presents the derivation and validation of the S3 algorithm, a new efficient sensitivity analysis method for chaotic systems like turbulent flows, applicable under certain stationary distribution assumptions.

Findings

S3 algorithm shows good agreement with finite-difference results in low-dimensional chaotic maps.

Current sensitivity methods face limitations in chaotic turbulent flows, which S3 aims to overcome.

Numerical examples demonstrate the potential of S3 for more complex systems.

Abstract

Chaotic dynamical systems such as turbulent flows are characterized by an exponential divergence of infinitesimal perturbations to initial conditions. Therefore, conventional adjoint/tangent sensitivity analysis methods that are successful with RANS simulations fail in the case of chaotic LES/DNS. In this work, we discuss the limitations of current approaches, including ensemble-based and shadowing-based sensitivity methods, that were proposed as alternatives to conventional sensitivity analysis. We propose a new alternative, called the space-split sensitivity (S3) algorithm, that is computationally efficient and addresses these limitations. In this work, the derivation of the S3 algorithm is presented in the special case where the system converges to a stationary distribution that can be expressed with a probability density function everywhere in phase-space. Numerical examples of low-dimensional chaotic maps are discussed where S3 computation shows good agreement with finite-difference results, indicating potential for the development of the method in more generality.