DNS-based measurement of the mean impulse response of homogeneous isotropic turbulence

TL;DR

This paper introduces a DNS-based method to measure the mean impulse response of homogeneous isotropic turbulence using white-noise forcing, providing new insights into turbulence response functions and their theoretical approximations.

Contribution

The paper presents a novel DNS technique for measuring turbulence response functions, bridging spectral closure theories and empirical data.

Findings

Good agreement with Kraichnan's advection model

Response function characterized in the dissipative subrange

Validation of Fluctuation-Dissipation Relation approximation

Abstract

A technique for measuring the mean impulse response function of stationary homogeneous isotropic turbulence is proposed. Such measurement is carried out here on the basis of Direct Numerical Simulation (DNS). A zero-mean white-noise volume forcing is used to probe the turbulent flow, and the response function is obtained by accumulating the space-time correlation between the white forcing and the velocity field. This technique to measure the turbulent response in a DNS numerical experiment is a new research tool in that field of spectral closures where the linear response concept is invoked either by resorting to renormalized perturbations theories or by introducing the well-known Fluctuation-Dissipation Relation (FDR). Though the results obtained in the present work are limited to relatively low values of the Reynolds number, a preliminary analysis is possible. Both the characteristic form and the time scaling properties of the response function are investigated in the universal subrange of dissipative wavenumbers; a comparison with the response approximation given by the FDR is proposed through the independent DNS measurement of the correlation function. Very good agreement is found between the measured response and Kraichnan's description of random energy-range advection effects.