Dissipation scaling and structural order in turbulent channel flows

Abstract

Scaling and structural evolutions are contemplated in a new perspective for turbulent channel flows. The total integrated turbulence kinetic energy and the total dissipation can be viewed as global constraints on the turbulence structure, leading to predictable, ordered scaling for u′2 and v′2 through its first and second gradients, respectively. This self-similarity allows for profile reconstructions at any Reynolds numbers based on a common template through simple multiplicative operations. Using these scaled variables in the Lagrangian transport equation derives the Reynolds shear stress, which in turn computes the mean velocity profile through the Reynolds-averaged Navier-Stokes equation. The dissipation scaling along with the transport equations renders succinct views of the turbulence dynamics and its structural characteristics. In this way, variable profiles can be analytically reconstructed, which bears potential implications toward solvability and computability of turbulent flows in canonical and other geometries.