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Nonlinear Waves in a Shear Flow with a Vorticity Discontinuity
Author(s) -
Pullin D. I.,
Jacobs P. A.
Publication year - 1986
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/sapm198675177
Subject(s) - vorticity , inviscid flow , discontinuity (linguistics) , amplitude , shear flow , mechanics , nonlinear system , stagnation point , vorticity equation , potential vorticity , crest , classical mechanics , physics , mathematical analysis , mathematics , vortex , optics , heat transfer , quantum mechanics
We consider nonlinear finite‐amplitude progressive shear‐flow waves on a basic velocity profile consisting of two coflowing layers of inviscid equal‐density fluid, each of uniform but different vorticity. The problem is formulated as a nonlinear integral equation describing the shape of the vorticity discontinuity in a frame of reference in which the flow is steady. Numerical solutions to this equation are presented for a range of values of the vorticity ratio Ω. For 1 > © ≥ − 1 the theoretical maximum wave amplitude occurs when the wave crest forms a 90° corner which just touches the appropriate critical‐layer stagnation point. The linearized stability of the progressive wave states to arbitrary subharmonic isovortical disturbances is studied numerically. The results indicate stability at moderate values of the wave amplitude.