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  • 1
    Electronic Resource
    Electronic Resource
    Resonant forcing of coastally trapped waves in a continuously stratified ocean (1990)
    Springer
    Pure and applied geophysics 133 (1990), S. 635-664 
    Details
    ISSN: 1420-9136
    Keywords: Resonant forcing ; coastally trapped waves ; KdV equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract In a previous paper (Grimshaw, 1987) the resonant forcing of coastally trapped waves was discussed in the barotropic case. In order to extend that theory to more realistic situations, we have considered the analogous theory whereby a longshore current interacts with a longshore topographic feature, or the forcing is due to longshore wind stress, for the case of the continuously stratified ocean. As in the previous theory, near resonance, when a long-wave phase speed is close to zero (in the reference frame of the forcing), the wave motion is governed by a forced evolution equation of the KdV-type. The behaviour of the wave field is characterized by three parameters representing the bandwidth for resonance, the forcing amplitude and the dissipation. We have evaluated these parameters in various practical cases, and found that the bandwidths, which scale with α1/2 when the forcing has dimensionless amplitude α, can often be quite broad. Typically the second, third, or higher, modes may be resonant. Concurrently, the dissipation is also usually significant, leading to a steady state balance between the forcing, dissipation and nonlinear terms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00876226
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  • 2
    Electronic Resource
    Electronic Resource
    Solitary waves in a compressible fluid (1980)
    Springer
    Pure and applied geophysics 119 (1980), S. 780-797 
    Details
    ISSN: 1420-9136
    Keywords: Internal waves in compressible fluid/incompressible fluid ; Internal solitary waves
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Evolution equations for long nonlinear internal waves in a compressible fluid are derived, with the aim of comparing these equations with their counterparts in an incompressible fluid. Both the Korteweg-de Vries equation, and the deep fluid equation are discussed, for both dry and moist atmospheres. It is shown that the effects of compressibility, or non-Boussinesq terms, are generally small, but measurable, and are manifested mainly in the nonlinear term of the evolution equation. For the case of a moist atmosphere the effect of a gain in energy by latent heat release is compared with the energy lost by radiation damping.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01131255
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  • 3
    Electronic Resource
    Electronic Resource
    Transformation of a soliton at a point of zero nonlinearity (1997)
    Springer
    JETP letters 65 (1997), S. 120-125 
    Details
    ISSN: 1090-6487
    Keywords: 05.45.+b
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The transformation of a soliton in a zone with a sign-changing nonlinearity has been investigated on the basis of the Korteweg-de Vries equation. It is shown that after passage through the critical zone a soliton with opposite polarity is formed in the wave field and, together with the previously known mechanism of secondary-soliton generation as a result of a pedestal formed at the adiabatic stage, there also exists another mechanism which is associated with the transformation of the wave in a zone of variable nonlinearity after the critical point. It is shown that both mechanisms make approximately the same contribution to the secondary-soliton energetics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1134/1.567336
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  • 4
    Electronic Resource
    Electronic Resource
    Dynamics of a KdV soliton due to periodic forcing
    Amsterdam : Elsevier
    Physics Letters A 179 (1993), S. 291-298 
    Details
    ISSN: 0375-9601
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/0375-9601(93)90681-O
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  • 5
    Electronic Resource
    Electronic Resource
    Wave Action and Wave-Mean Flow Interaction, with Application to Stratified Shear Flows (1984)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Fluid Mechanics 16 (1984), S. 11-44 
    Details
    ISSN: 0066-4189
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.fl.16.010184.000303
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  • 6
    Electronic Resource
    Electronic Resource
    Extreme interfacial waves (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 2802-2807 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Numerical solutions are presented for large-amplitude interfacial waves of extreme form on the interface between two fluids of different densities in the Boussinesq approximation. The flow in the lower fluid is irrotational, but the upper fluid may have constant, nonzero vorticity. Only symmetric waves are calculated. The results suggest limiting wave profiles for which separate portions of the interface touch, forming stagnant zones of one fluid imbedded in the other fluid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865477
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  • 7
    Electronic Resource
    Electronic Resource
    Nonlinear instability at the interface between two viscous fluids (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 37-45 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Co-current flow of two viscous fluids in a channel is linearly unstable to long wavelength disturbances. The weakly nonlinear evolution of this instability is examined. It is shown that, because of surface tension and nonlinear effects, the interface can either return to its original undisturbed state or evolve to some finite amplitude steady state.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865160
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  • 8
    Electronic Resource
    Electronic Resource
    Two-dimensional disturbance growth of linearly stable viscous shear flows (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 1424-1432 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Instability of fluid flow has long been linked with the eigenvalues of the Orr-Sommerfeld equation. Recently, it has been shown that even though all eigenvalues may be stable, it is still possible to have disturbance growth. This is because the Orr-Sommerfeld operator is non-normal. We identify which eigenmodes are important in two-dimensional disturbance growth. We find a relationship between maximum growth and growth caused by the adjoint of the leading eigenmode for both plane Poiseuille flow and plane Couette flow. The work points to a connection between the occurrence of the first degeneracy of the Orr-Sommerfeld operator and the first appearance of disturbance growth. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868919
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  • 9
    Electronic Resource
    Electronic Resource
    Finite-amplitude solitary waves at the interface between two homogeneous fluids (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 3550-3559 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Numerical solutions are presented for finite-amplitude interfacial waves. Only symmetric waves are calculated. Two cases are considered. In the first case the waves are free-surface solitary waves propagating on a basic flow with uniform vorticity. Large-amplitude waves of extreme form are calculated for a range of values of the basic vorticity. In the second case the waves are propagating on the interface between two homogeneous fluids of different densities, which are otherwise at rest. Again large-amplitude waves of extreme form are calculated for a range of values of the basic density ratio. In particular, in the Boussinesq limit when the density ratio is nearly unity, solitary waves of apparently unlimited amplitude can be found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866922
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  • 10
    Electronic Resource
    Electronic Resource
    Transcritical flow of a stratified fluid: The forced extended Korteweg–de Vries model (2002)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 14 (2002), S. 755-774 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Transcritical, or resonant, flow of a stratified fluid over an obstacle is studied using a forced extended Korteweg–de Vries model. This model is particularly relevant for a two-layer fluid when the layer depths are near critical, but can also be useful in other similar circumstances. Both quadratic and cubic nonlinearities are present and they are balanced by third-order dispersion. We consider both possible signs for the cubic nonlinear term but emphasize the less-studied case when the cubic nonlinear term and the dispersion term have the same-signed coefficients. In this case, our numerical computations show that two kinds of solitary waves are found in certain parameter regimes. One kind is similar to those of the well-known forced Korteweg–de Vries model and occurs when the cubic nonlinear term is rather small, while the other kind is irregularly generated waves of variable amplitude, which may continually interact. To explain this phenomenon, we develop a hydraulic theory in which the dispersion term in the model is omitted. This theory can predict the occurrence of upstream and downstream undular bores, and these predictions are found to agree quite well with the numerical computations. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1429962
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