Streamwise decay of localized states in channel flow
arXiv:1609.06514 · doi:10.1103/PhysRevE.94.041101
Abstract
Channel flow, the pressure driven flow between parallel plates, has exact coherent structures that show various degrees of localization. For states which are localized in streamwise direction but extended in spanwise direction, we show that they are exponentially localized, with decay constants that are different on the upstream and downstream side. We extend the analysis of Brand and Gibson [J. Fluid Mech. 750, R1 (2014)] for stationary states to the case of advected structures that is needed here, and derive expressions for the decay in terms of eigenvalues and eigenfunctions of certain second order differential equations. The results are in very good agreement with observations on exact coherent structures of different transversal wave lengths.
arXiv commentMinor changes
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Cited by in corpus (6)
- Statistical transition to turbulence in plane channel flow
- Transition to turbulence in shear flows
- Small scale exact coherent structures at large Reynolds numbers in plane Couette flow
- Propagation mechanism of localized wave packet in plane-Poiseuille flow
- Streamwise localization of traveling wave solutions in channel flow
- Analysis and modeling of localized invariant solutions in pipe flow