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Instability in Parallel Flows Revisited
Author(s) -
Friedlander Susan,
Howard Louis
Publication year - 1998
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00083
Subject(s) - inviscid flow , instability , shear flow , generalization , flow (mathematics) , nonlinear system , mathematics , plane (geometry) , shear (geology) , mechanics , physics , mathematical analysis , classical mechanics , geometry , geology , petrology , quantum mechanics
An example of an unstable inviscid plane parallel shear flow with classical boundary conditions is presented. The complete unstable spectrum is exhibited using techniques of continued fractions for the shear flow with profile U ( y )=cos m y . For such flows spectral instability implies nonlinear instability. A three‐dimensional generalization is discussed.