Canonical Turbulence Theory

TL;DR

This paper develops a theoretical framework for canonical turbulent flows, deriving symmetric transport equations for Reynolds stresses and proposing a new scaling approach, enabling more efficient analysis of complex turbulence.

Contribution

It introduces a formalism that decouples fluctuations from mean flow, providing a symmetric set of transport equations and a new scaling method for Reynolds stresses in canonical geometries.

Findings

Derivation of symmetric transport equations for Reynolds stresses.

Introduction of a turbulence scaling in dissipation space.

Potential for more efficient algorithms for complex flows.

Abstract

A theoretical analysis is presented for turbulent flows, applicable for canonical (channel, boundary-layer and free jet) geometries. Momentum and energy balance for a control volume moving at the local mean velocity decouples the fluctuation from the mean velocities, resulting in a symmetric set of transport equations for the Reynolds normal and shear stresses. In this formalism, gradients of the fluctuating velocities represent flux vectors, easily verifiable using the available DNS data. A derivative of this transport concept is the scaling for the Reynolds stresses in the dissipation space. Combining with the statistical energy distribution function, a full prescription of turbulent flows is enabled in the basic canonical geometries. Based on this theoretical foundation, more complex flow configurations may be addressed with far more efficient algorithms.