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Linear stability analysis of flow in a periodically grooved channel
Author(s) -
Adachi T.,
Uehara H.
Publication year - 2003
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.456
Subject(s) - reynolds number , laminar flow , instability , mathematics , hydrodynamic stability , hele shaw flow , flow (mathematics) , eigenvalues and eigenvectors , open channel flow , hopf bifurcation , linear stability , mechanics , bifurcation , physics , mathematical analysis , geometry , turbulence , nonlinear system , quantum mechanics
Abstract We have conducted the linear stability analysis of flow in a channel with periodically grooved parts by using the spectral element method. The channel is composed of parallel plates with rectangular grooves on one side in a streamwise direction. The flow field is assumed to be two‐dimensional and fully developed. At a relatively small Reynolds number, the flow is in a steady‐state, whereas a self‐sustained oscillatory flow occurs at a critical Reynolds number as a result of Hopf bifurcation due to an oscillatory instability mode. In order to evaluate the critical Reynolds number, the linear stability theory is applied to the complex laminar flow in the periodically grooved channel by constituting the generalized eigenvalue problem of matrix form using a penalty‐function method. The critical Reynolds number can be determined by the sign of a linear growth rate of the eigenvalues. It is found that the bifurcation occurs due to the oscillatory instability mode which has a period two times as long as the channel period. Copyright © 2003 John Wiley & Sons, Ltd.