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| Titel |
Fractional Fourier approximations for potential gravity waves on deep water |
| VerfasserIn |
V. P. Lukomsky, I. S. Gandzha |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 10, no. 6 ; Nr. 10, no. 6, S.599-614 |
| Datensatznummer |
250008216
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| Publikation (Nr.) |
 copernicus.org/npg-10-599-2003.pdf |
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| Zusammenfassung |
| 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 (Lukomsky et al., 2002b). 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. In the present work, a new highly
efficient method for computing steady potential
gravity waves on deep water is proposed to examine
the character of singularity of irregular flows in
more detail. The method is based on the truncated fractional
approximations for the velocity potential in terms of
the basis functions 1/(1 - exp(y0 -
y -
ix))n, y0 being a free parameter. The
non-linear transformation of the horizontal scale x = c
- g
sin c,
0 < g
< 1, is additionally applied
to concentrate a numerical emphasis on the crest
region of a wave for accelerating the convergence of the series.
For lesser computational time, the advantage in accuracy over
ordinary Fourier expansions in terms of the basis functions
exp(n(y + ix)) was found to be from one to ten
decimal orders for steep Stokes waves and up to one
decimal digit for irregular flows. The data obtained
supports the following conjecture: irregular waves
to all appearance represent a family of
sharp-crested waves like the limiting Stokes wave
but of lesser amplitude. |
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