A modified Lin equation for the energy balance in isotropic turbulence

TL;DR

This paper introduces a modified Lin equation that incorporates filtered-partitioned transfer spectra, offering a new theoretical framework to better understand energy processes in isotropic turbulence.

Contribution

It presents a novel form of the Lin equation that accounts for filtered-partitioned transfer spectra, addressing the scale paradox in turbulence.

Findings

Provides a new formulation of the energy balance equation.

Addresses the scale paradox in turbulence.

Lays groundwork for improved theoretical and numerical analysis.

Abstract

A new form of the well known Lin equation for the energy balance in isotropic turbulence is given which takes account of the filtered-partitioned transfer spectra which were used to resolve the scale paradox. It is argued that this new formulation provides a new starting point for both theoretical and numerical methods which may lead to a better understanding of the underlying energy processes in turbulence.