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Transient Nonlinear Disturbances and Shelves in a Stratified Fluid Layer
Author(s) -
Skopovi Ivan,
Akylas T. R.
Publication year - 2004
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/j.1467-9590.2004.01527.x
Subject(s) - nonlinear system , amplitude , stratified flows , mechanics , euler equations , stratified flow , breaking wave , bounded function , euler's formula , transient (computer programming) , internal wave , kondratiev wave , physics , classical mechanics , geology , wave propagation , mathematics , mathematical analysis , quantum mechanics , computer science , operating system , turbulence
We revisit the classical problem of internal wave propagation in a stratified fluid layer bounded by rigid walls and point out a mechanism by which unsteady locally confined disturbances generate far‐field shelves. Carrying the standard expansion procedure to fourth order in the wave amplitude reveals that weakly nonlinear long waves of a certain mode shed, in general, lower‐ and higher‐mode shelves, which propagate upstream and downstream with the corresponding long‐wave speeds. This phenomenon is brought about by the combined effect of nonlinear interactions and the presence of transience in the main disturbance. While the shelves accompanying small‐amplitude waves are relatively weak, numerical solutions of the full Euler equations indicate that shelves induced by unsteady disturbances of finite amplitude close to breaking can be quite significant.