Journal ArticleDOI
Numerical solution of the exact equations for capillary-gravity waves
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In this paper, a numerical method is presented for the computation of two-dimensional periodic progressive surface waves propagating under the combined influence of gravity and surface tension, where the dynamic boundary equation is used in its exact nonlinear form.Abstract:
A numerical method is presented for the computation of two-dimensional periodic progressive surface waves propagating under the combined influence of gravity and surface tension. The dynamic boundary equation is used in its exact nonlinear form. The procedure involves a boundary-integral formulation coupled with a Newtonian iteration. Solutions of high accuracy can be achieved over much of the range of wavelengths and heights including limiting waves. A number of different continuous families of solutions have been produced, all of which ultimately exhibit closed bubbles at their troughs. The so-called critical wavelengths are less important than have been previously assumed; the number of possible wave forms does increase with increasing wavelength, however.read more
Citations
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On the motion of bubbles in capillary tubes
TL;DR: The average thickness of the wetting film left behind during the slow passage of an air bubble in a water-filled capillary tube of circular cross-section has been determined experimentally as a function of bubble speed and bubble length as mentioned in this paper.
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Capillary rollers and bores
TL;DR: In this paper, the authors studied the occurrence of parasitic capillaries on the forward face of moderately short gravity waves, especially those with wavelengths 5 to 50 cm; see Figure la.
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Free-surface flow over a semicircular obstruction
TL;DR: In this paper, the steady flow of a fluid over a semicircular obstacle on the bottom of a stream is discussed, along with a numerical method for the solution of the fully nonlinear problem.
Journal ArticleDOI
Capillary Effects on Surface Waves
Marc Perlin,William W. Schultz +1 more
TL;DR: In this article, the authors concentrate on the rich effects that surface tension has on free and forced surface waves for linear, nonlinear, and especially strongly nonlinear waves close to or at breaking or their limiting form.
Journal ArticleDOI
Solitary and Periodic Gravity-Capillary Waves of Finite Amplitude,
TL;DR: In this article, two-dimensional solitary and periodic waves in water of finite depth were considered and it was shown that elevation solitary waves cannot be obtained as the continuous limit of periodic waves as the wavelength tends to infinity.
References
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Journal ArticleDOI
An exact solution for progressive capillary waves of arbitrary amplitude
TL;DR: In this article, an exact solution for two-dimensional progressive waves of arbitrary amplitude on a fluid of unlimited depth, when only surface tension and not gravity is taken into account as the restoring force, was found in a fairly simple form.
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Computer extension and analytic continuation of stokes expansion for gravity waves
TL;DR: In this paper, Stokes' infinitesimal-wave expansion for steady progressive free-surface waves has been extended to high order using a computer to perform the coefficient arithmetic, which is valid for any finite value of the wavelength and solutions of high accuracy can be obtained for most values of the wave height and water depth.
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Steep gravity waves in water of arbitrary uniform depth
TL;DR: In this paper, the speed, momentum, energy and other integral properties are calculated accurately by means of series expansions in terms of a perturbation parameter whose range is known precisely and encompasses waves from the lowest to the highest possible.
Journal ArticleDOI
Integral properties of periodic gravity waves of finite amplitude
TL;DR: In this paper, a number of exact relations for periodic water waves of finite amplitude in water of uniform depth were proved and the mean fluxes of mass, momentum and energy were shown to be equal to 2T(4T-3F) and (3T-2V) crespectively, where T and V denote the kinetic and potential energies and c is the phase velocity.