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An Upper Bound on the Growth Rate of a Linear Instability in a Homogeneous Shear Flow
Author(s) -
Hickernell Fred J.
Publication year - 1985
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 - 10.1002/sapm198572187
Subject(s) - upper and lower bounds , instability , homogeneous , linear growth , vorticity , growth rate , shear flow , mathematics , shear (geology) , flow (mathematics) , physics , mechanics , mathematical analysis , geometry , vortex , geology , combinatorics , petrology
Temporally growing modes of the linearized equations of motion for homogeneous shear flows in the beta‐plane are considered. A new upper bound on their rate of growth is derived. This bound is related to the necessary criterion for linear instability derived by Fjørtoft [1]. As a flow stabilizes due to increased beta‐effect or decreased basic‐state vorticity gradient, the upper bound on the growth rate decreases to zero. For more stable flows this newly derived bound is tighter than that derived by Høiland [2].