Particle paths in small amplitude solitary waves with negative vorticity

Journal of Mathematical Analysis and Applications (Impact Factor: 1.12). 11/2011; 398(1). DOI: 10.1016/j.jmaa.2012.08.052
Source: arXiv

ABSTRACT We investigate the particle trajectories in solitary waves with vorticity,
where the vorticity is assumed to be negative and decrease with depth. We show
that the individual particle moves in a similar way as that in the irrotational
case if the underlying laminar flow is favorable, that is, the flow is moving
in the same direction as the wave propagation throughout the fluid, and show
that if the underlying current is not favorable, some particles in a
sufficiently small solitary wave move to the opposite direction of wave
propagation along a path with a single loop or hump .

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We provide the qualitative flow pattern beneath a solitary water wave by describing the individual particle trajectories.
    Quarterly of Applied Mathematics 01/2010; 68(1). DOI:10.1090/S0033-569X-09-01166-1 · 0.54 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: A general method is presented for the exact treatment of analytical problems that have solutions representing solitary waves. The theoretical framework of the method is developed in abstract first, providing a range of fixed-point theorems and other useful resources. It is largely based on topological concepts, in particular the fixedpoint index for compact mappings, and uses a version of positive-operator theory referred to Frechet spaces. Then three exemplary problems are treated in which steadily propagating waves of permanent form are known to be represented. The first covers a class of one-dimensional model equations that generalizes the classic Korteweg-de Vries equation. The second concerns two-dimensional wave motions in an incompressible but density-stratified heavy fluid. The third problem describes solitary waves on water in a uniform canal.
    Philosophical Transactions of The Royal Society B Biological Sciences 06/1990; 331(1617):195-244. DOI:10.1098/rsta.1990.0065 · 6.31 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction (See also 35Q30, 35Q53) 76M23 Vortex methods 76M28 Particle methods and lattice-gas methods 76U05 Rotating fluids
    Nonlinearity 01/2008; 21(5). DOI:10.1088/0951-7715/21/5/012 · 1.20 Impact Factor
Show more


1 Download
Available from