The influence of energy-containing scales on the distribution of spectral energy transfers

TL;DR

This paper introduces a new method to analyze mode-to-mode energy transfers in turbulence, revealing that the distribution of intense transfers is primarily influenced by energy-containing scales rather than triad locality.

Contribution

It presents a novel approach based on a potential function to predict energy transfer distributions, distinguishing itself from previous shell-filtered methods.

Findings

Intense energy transfer regions are determined by the spectral location of energy-containing scales.

Energy exchanges with the energy-containing range are suppressed but still occur as residuals.

The results align with EDQNM theory, confirming the cascade process.

Abstract

We present computations of individual mode-to-mode energy transfers from direct numerical simulations of homogeneous isotropic turbulence. Unlike previous approaches based on shell-filtered velocity fields, this method distinguishes between the energy exchanged by each pair of modes within a triad. We introduce a potential function based on the energy content of the modes involved and show that it predicts the distribution of intense energy transfers in the vicinity of the sampling mode considered. By performing simulations with forcing applied at intermediate wavenumbers, we demonstrate that the region of most intense transfers is determined by the spectral location of the energy-containing scales rather than by the local or nonlocal character of the triad. Direct energy exchanges with the energy-containing range are suppressed by geometric constraints from the divergence-free condition, but persist as residuals when the sampling mode is close to the energy-containing scales. The comparison with an estimator derived from EDQNM theory shows good agreement and recovers the forward, scale-local nature of energy transfer consistent with the cascade picture.