Dissipation Scaling and Structural Order in Turbulent Channel Flows

TL;DR

This paper introduces a new perspective on turbulence scaling in channel flows, revealing how dissipation and structural features evolve with Reynolds number, enabling profile reconstruction and improved understanding of turbulence dynamics.

Contribution

It presents a novel dissipative scaling framework and self-similarity approach for turbulent channel flows, allowing profile reconstruction across Reynolds numbers and insights into turbulence structure.

Findings

Total turbulence kinetic energy remains constant when normalized by friction velocity squared.

Total dissipation increases linearly with Reynolds number.

Self-similar profiles enable reconstruction at any Reynolds number.

Abstract

Scaling and structural evolutions are contemplated in a new perspective for turbulent channel flows. The total integrated turbulence kinetic energy remains constant when normalized by the friction velocity squared, while the total dissipation increases linearly with respect to the Reynolds number. This serves as a global constraint on the turbulence structure. Motivated by the flux balances in the root turbulence variables, we also discover dissipative scaling for u2 and v2, respectively through its first and second gradients. This self-similarity allows for profile reconstructions at any Reynolds numbers based on a common template, through a simple multiplicative operation. Using these scaled variables in the Lagrangian transport equation derives the Reynolds shear stress, which in turn computes the mean velocity profile. The self-similarities along with the transport equations render possible succinct views of the turbulence dynamics and computability of the full structure in channel flows.