Large-amplitude long waves in a shear flow

Melvin E. Stern*, Nathan Paldor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Large amplitude disturbances in a boundary layer shear flow are considered in an inviscid and long-wave theory. Initially weak horizontal convergences are concentrated and amplified in time, v→∞ thereby increasing the maximum normal velocity (v) until it becomes comparable with the horizontal velocity. The effect is first demonstrated in a two-dimensional model having piecewise uniform vorticity. The leading edge of the compact disturbance propagates downstream more rapidly than the trailing edge, but no "quiet" zone appears in the center. Instead and a tendency for wavebreaking occurs. The evolving large v pattern is consistent with observations of the laminar spike just prior to its breakdown. The long-wave theory is generalized to three-dimensional motions, and the effect of an initial span wise divergence is such as to rationalize the initial vorticity assumed in the two-dimensional model.

Original languageEnglish
Pages (from-to)906-919
Number of pages14
JournalPhysics of Fluids
Volume26
Issue number4
DOIs
StatePublished - 1983
Externally publishedYes

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