Related Experiment Video
Updated: Jul 8, 2026

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics
Published on: August 27, 2013
Streamwise localization of traveling wave solutions in channel flow
Joshua Barnett1, Daniel R Gurevich1, Roman O Grigoriev1
1School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA.
Abstract:
Channel flow of an incompressible fluid at Reynolds numbers above 2400 possesses a number of different spatially localized solutions that approach laminar flow far upstream and downstream. We use one such relative time-periodic solution, which corresponds to a spatially localized version of a Tollmien-Schlichting wave, to illustrate how the upstream and downstream asymptotics can be computed analytically. In particular, we show that for these spanwise uniform states the asymptotics predict the exponential localization that has been observed for numerically computed solutions of several canonical shear flows but never properly understood theoretically.
Related Concept Videos
Traveling Waves: Lossless Lines
Bernoulli's Equation for Flow Along a Streamline
Eulerian and Lagrangian Flow Descriptions
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
Uniform Depth Channel Flow
Uniform Depth Channel Flow: Problem Solving
Rapidly Varying Flow

