摘要:

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 (

ISSN:0022-2526    

DOI:10.1002/sapm19857311

年代:1985

数据来源: WILEY

摘要:

The properties of steady, periodic, deep‐water gravity waves on a linear shear current are investigated. Numerical solutions for all waveheights, up to and including the limiting ones, are computed from a formulation which involves only the wave profile (parametrized in a natural way) and some constants of the motion. It is found that for some shear currents the highest waves are not necessarily those waves with sharp crests known as extreme waves. Furthermore a certain nonuniqueness in the sense of a fold is shown to exist, and a new type of limiting wave is discovered. For both small‐amplitude waves and extreme waves the numerical results are compared with theoretical predicti

ISSN:0022-2526    

DOI:10.1002/sapm198573135

年代:1985

数据来源: WILEY

摘要:

In thermohaline convection and a number of other systems, both direct and oscillatory modes of instability are possible. Should these modes coalesce at some point in parameter space, nonlinear instabilities are likely to be more dramatic in the neighborhood of such a point than elsewhere. A finite‐amplitude evolution equation describing such events is derived here by the method of multiple scales. The results are compared with those obtained previously for model systems and by other methods. The direct resonance point of view is found to provide some new insights. A generalization to allow for slow spatial modulation of the amplitude is given and, among other possibilities, solitary‐wave solutions are obtaina

ISSN:0022-2526    

DOI:10.1002/sapm198573159

年代:1985

数据来源: WILEY

摘要:

In long rectangular Hele‐Shaw cells the Saffman‐Taylor instability generates steady advancing fingers of the less viscous fluid. The structure of these fingers is determined by the solution of a system of nonlinear integrodifferential equations for two unknown functions of the curvilinear coordinate defined along the boundary of the finger. The surface tension appears in these equations through a dimensionless coefficient calledk. I analyze the solution when this coefficient tends to infinity. In this limit, the inviscid fluid tends to fill almost completely the cell, except for a thin layer of viscous fluid left on the sides of thickness of order

ISSN:0022-2526    

DOI:10.1002/sapm198573175

年代:1985

数据来源: WILEY