Direct resonances in Orr-Sommerfeld problems
type: Item
instance of: scholarly article
title: Direct resonances in Orr-Sommerfeld problems
zbMATH Open document ID: 0619.76068
DOI: 10.1007/BF01177057
author: B. George
published in: Acta Mechanica
publication date: 1986-01-01T00:00:00Z
review text: In the present paper direct resonances in Orr-Sommerfeld problems are investigated. The author shows that spatial direct resonances between discrete Orr-Sommerfeld modes are possible in plane Poiseuille flows and boundary-layer type flows if three-dimensional disturbances are considered. It is demonstrated that the corresponding response increases with increasing Reynolds number. Concerning plane Poiseuille flow turbulence sets in before this response becomes large enough. For boundary-layer type flows the response can be rather large already in the laminar flow domain. The author points out that this phenomenon should be observable. He suggests to study the possibility of direct resonances between other modes particularly in view of the laminar-turbulent transition process.
Mathematics Subject Classification ID: 76E99
Mathematics Subject Classification ID: 76F99
zbMATH DE Number: 4005866
zbMATH Keywords: vorticity modes
zbMATH Keywords: direct resonances
zbMATH Keywords: Orr-Sommerfeld problems
zbMATH Keywords: spatial direct resonances
zbMATH Keywords: discrete Orr-Sommerfeld modes
zbMATH Keywords: plane Poiseuille flows
zbMATH Keywords: boundary-layer type flows
zbMATH Keywords: three-dimensional disturbances
zbMATH Keywords: response
zbMATH Keywords: turbulence
zbMATH Keywords: laminar flow
zbMATH Keywords: laminar-turbulent transition process
MaRDI profile type: Publication
cites work: A Nonlinear Theory for the Generation of Water Waves by Wind
cites work: Direct Resonance In Nonlinear Wave Systems
cites work: The Evolution of Waves Near Direct-Resonance Conditions
cites work: Nonlinear waves near a cut-off frequency in an acoustic duct – a numerical study
cites work: A New Mechanism For Linear and Nonlinear Hydrodynamic Instability
cites work: On the generation of spatially growing waves in a boundary layer
cites work: On the eigenvalues of the Orr-Sommerfeld equation
cites work: The stability of steady and time-dependent plane Poiseuille flow
cites work: Initial-value problem for boundary layer flows
cites work: Resonant growth of three-dimensional disturbances in plane Poiseuille flow
cites work: A resonance mechanism in plane Couette flow
cites work: Absolute and convective instabilities in free shear layers
cites work: Algebraic growth of disturbances in a laminar boundary layer
cites work: A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer
cites work: Accurate solution of the Orr–Sommerfeld stability equation
cites work: A spectral method for external viscous flows
full work available at URL: https://doi.org/10.1007/bf01177057
OpenAlex ID: W2086613128
description: scientific article; zbMATH DE number 4005866