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Evolution Equations for Weakly Nonlinear, Long Internal Waves in a Rotating Fluid
Author(s) -
Grimshaw R.
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/sapm19857311
Subject(s) - physics , nonlinear system , rossby radius of deformation , rossby number , internal wave , rossby wave , classical mechanics , radius , internal tide , dispersion (optics) , rotation (mathematics) , evolution equation , korteweg–de vries equation , mechanics , mathematical analysis , mathematics , optics , geometry , turbulence , quantum mechanics , computer security , atmospheric sciences , computer science
Evolution equations are derived for weakly nonlinear, long internal waves in a frame of reference rotating about the vertical axis. When the internal Rossby radius is at most comparable with the wavelength, the evolution equation is a Korteweg‐de Vries equation for shallow fluids, and its counterpart for deep fluids. To leading order the transverse structure is that for a linear internal Kelvin wave. For weaker rotation when effects due to the internal Rossby radius are comparable with the effects due to nonlinearity and dispersion, the evolution equation is a rotation‐modified two dimensional Korteweg‐de Vries equation for shallow fluids, or its counterpart for deep fluids. Some comparisons are made with the recent experiments of Maxworthy (1983).