Velocity and Energy Profiles In Two- vs. Three-Dimensional Channels: Effects of Inverse vs. Direct Energy Cascade

TL;DR

This paper compares velocity and energy profiles in ideal two- and three-dimensional turbulent channel flows, highlighting how inverse energy cascade in 2D leads to significantly different and more energetic flow characteristics than in 3D.

Contribution

It introduces a model for ideal 2D channel flow with a second conserved variable, emphasizing the impact of inverse cascade on flow profiles and energy scaling.

Findings

2D channel flow is more energetic than 3D, with energy increasing logarithmically with Reynolds number.

Profiles of velocity and energy differ qualitatively between 2D and 3D flows.

Inverse cascade in 2D causes distinct flow behavior compared to direct cascade in 3D.

Abstract

In light of some recent experiments on quasi two-dimensional (2D) turbulent channel flow we provide here a model of the ideal case, for the sake of comparison. The ideal 2D channel flow differs from its 3D counterpart by having a second quadratic conserved variable in addition to the energy, and the latter has an inverse rather than a direct cascade. The resulting qualitative differences in profiles of velocity, V, and energy, K, as a function of the distance from the wall are highlighted and explained. The most glaring difference is that the 2D channel is much more energetic, with K in wall units increasing logarithmically with the Reynolds number $\Ret$ instead of being $\Ret$-independent in 3D channels.