Turbulent Couette Flow:An analytical solution

TL;DR

This paper presents an analytical solution for turbulent plane Couette flow derived from Navier-Stokes equations, highlighting the effects of unsteady Lagrangian diffusion on velocity profiles and identifying key flow layers.

Contribution

It introduces a novel analytical approach to turbulent Couette flow that accounts for unsteady Lagrangian diffusion and matches experimental velocity measurements.

Findings

Identification of three flow layers, including a viscosity-dominated wall layer and a log-law layer.

Good correlation between predicted and experimental time-averaged velocities.

Analytical solution captures key features of turbulent Couette flow.

Abstract

A simple analytical solution for turbulent plane Couette flow is obtained from a subset of the Navier-Stokes equations. This approach analyses the effect of the unsteady state Lagrangian diffusion of viscous momentum on the smoothed phase velocity. Three initial velocity profiles at the start of a turbulent wall cycle are considered. The predictions adequate identify the existence of three layers usually observed in turbulent flow fields, in particular a viscosity dominated wall layer and a log-law layer. Experimental measurements of time-averaged velocity are also well correlated. Key words: Couette flow, turbulent, attractors, analytical solution, Lagrangian partial derivative, time scale, initial conditions