Article

Linear water waves with vorticity: Rotational features and particle paths

Department of Mathematics, Lund University, PO Box 118, 221 00 Lund, Sweden; Dipartimento di Matematica, Viale Morgagni 67/A, 50134 Firenze, Italy
Journal of Differential Equations (Impact Factor: 1.48). 01/2008; DOI: 10.1016/j.jde.2008.01.012
Source: arXiv

ABSTRACT We study steady linear gravity waves of small amplitude travelling on a current of constant vorticity. For positive vorticity the situation resembles that of Stokes waves, but if the vorticity is large enough the particle trajectories are affected. For negative vorticity we show that there may appear internal waves and vortices, wherein the particle trajectories are not ellipses.

1 Bookmark
 · 
57 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We survey recent results on particle trajectories within steady two-dimensional water waves. Particular emphasis is placed on the linear and exact mathematical theory of periodic and symmetric waves, and the effects of a (possibly rotational) background current. The different results vindicate and detail the classical Stokes drift, and also show the transition of orbits when waves propagate into running water. The classical approximation, depicting the trajectories as closed ellipses, is shown to be a mathematical rarity. 2000 Mathematics Subject Classification. 35Q35, 37N10, 76B15, 76F10.
    Discrete and Continuous Dynamical Systems-series B - DISCRETE CONTIN DYN SYS-SER B. 01/2009; 12(3).
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper concerns linear standing gravity water waves on finite depth. We obtain qualitative and quantitative understanding of the particle paths within the wave.
    Journal of Nonlinear Mathematical Physics - J NONLINEAR MATH PHYS. 01/2008; 15.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In order to obtain quite precise information about the shape of the particle paths below small-amplitude gravity waves travelling on irrotational deep water, analytic solutions of the nonlinear differential equation system describing the particle motion are provided. All these solutions are not closed curves. Some particle trajectories are peakon-like, others can be expressed with the aid of the Jacobi elliptic functions or with the aid of the hyperelliptic functions. Remarks on the stagnation points of the small-amplitude irrotational deep-water waves are also made.
    Journal of Mathematical Fluid Mechanics 02/2012; 15(1). · 1.42 Impact Factor

Full-text (3 Sources)

View
44 Downloads
Available from
May 28, 2014