Streamwise localization of traveling wave solutions in channel flow

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.

References in corpus (6)

• Computational Study of Turbulent-Laminar Patterns in Couette Flow
• Lower branch coherent states in shear flows: transition and control
• Streamwise and doubly-localised periodic orbits in plane Poiseuille flow
• A doubly-localized equilibrium solution of plane Couette flow
• Turbulent-laminar patterns in shear flows without walls
• Streamwise decay of localized states in channel flow

Cited by in corpus (6)

• Transition to turbulence in shear flows
• Small scale exact coherent structures at large Reynolds numbers in plane Couette flow
• Self-sustainment of coherent structures in counter-rotating Taylor-Couette flow
• Propagation mechanism of localized wave packet in plane-Poiseuille flow
• Analysis and modeling of localized invariant solutions in pipe flow
• Pattern preservation during the decay and growth of localized wave packet in two-dimensional channel flow