Scaling bounds on dissipation in turbulent flows

TL;DR

This paper introduces a rigorous method to estimate energy dissipation rates in turbulent flows directly from fluid dynamics equations, validated on various flow types.

Contribution

A novel analytical approach for bounding dissipation in turbulent flows, applicable to multiple flow configurations.

Findings

Successfully estimates dissipation rates in shear and channel flows.

Extends to Rayleigh–Bénard and porous medium convection.

Provides bounds consistent with physical expectations.

Abstract

We present a new rigorous method for estimating statistical quantities in fluid dynamics such as the (average) energy dissipation rate directly from the equations of motion. The method is tested on shear flow, channel flow, Rayleigh--B\'enard convection and porous medium convection.