3 research outputs found
Fractional Fourier approximations for potential gravity waves on deep water
In the framework of the canonical model of hydrodynamics, where fluid is
assumed to be ideal and incompressible, waves are potential, two-dimensional,
and symmetric, the authors have recently reported the existence of a new type
of gravity waves on deep water besides well studied Stokes waves (Phys. Rev.
Lett., 2002, v. 89, 164502). The distinctive feature of these waves is that
horizontal water velocities in the wave crests exceed the speed of the crests
themselves. Such waves were found to describe irregular flows with stagnation
point inside the flow domain and discontinuous streamlines near the wave
crests. Irregular flows produce a simple model for describing the initial stage
of the formation of spilling breakers when a localized jet is formed at the
crest following by generating whitecaps.
In the present work, a new highly efficient method for computing steady
potential gravity waves on deep water is proposed to examine the above results
in more detail. The method is based on the truncated fractional approximations
for the velocity potential in terms of the basis functions
, being a free parameter. The
non-linear transformation of the horizontal scale is additionally applied to concentrate a numerical emphasis on the
crest region of a wave for accelerating the convergence of the series.
Fractional approximations were employed for calculating both steep Stokes waves
and irregular flows. For lesser computational time, the advantage in accuracy
over ordinary Fourier expansions in terms the basis functions was found to be from one to ten decimal orders depending on the
wave steepness and flow parameters.Comment: 14 pages, 8 figures, submitted to Nonlinear Processes in Geophysic
Steep sharp-crested gravity waves on deep water
A new type of steady steep two-dimensional irrotational symmetric periodic
gravity waves on inviscid incompressible fluid of infinite depth is revealed.
We demonstrate that these waves have sharper crests in comparison with the
Stokes waves of the same wavelength and steepness. The speed of a fluid
particle at the crest of new waves is greater than their phase speed.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let