scholarly journals THE SPIRAL WAVEMAKER FOR LITTORAL DRIFT STUDIES

1972 ◽  
Vol 1 (13) ◽  
pp. 34 ◽  
Author(s):  
Robert A. Dalrymple ◽  
Robert G. Dean
Keyword(s):  
Water Waves ◽  
Small Amplitude ◽  
Angle Of Incidence ◽  
Long Beach ◽  
Shallow Water Waves ◽  
Littoral Drift ◽  
Amplitude Wave ◽  
End Effects ◽  
Small Circle ◽  
Theoretical Developments

A technique for simulating an infinitely long beach in the laboratory is introduced, with the objective of eliminating end effects usually present with short straight beach sections. The technique involves the spiral wavemaker generating waves in the center of a circular basin. The wavemaker, consisting of a vertical right-circular cylinder oscillating in a small circle about its axis, is described in detail. Theoretical developments, using small-amplitude wave assumptions, show that the surface wave crests generated by the wavemaker may be described, at a particular time, as an Archimedian-type of spiral, with the wavemaker at its origin. Also, the crests impinge on the circular beach everywhere at the same angle of incidence. Experiments with a prototype spiral wavemaker verify the theory, with close results for shallow water waves. Littoral drift applications of the wavemaker are given.

Sloshing in Regular Polygonal Basins—Frequencies, Modes, and Tileability

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Helmholtz Equation ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
Small Amplitude ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Mode Shapes ◽  
Shallow Water Waves ◽  
First Time

Abstract The classical theory of small amplitude shallow water waves is applied to regular polygonal basins. The natural frequencies of the basins are related to the eigenvalues of the Helmholtz equation. Exact solutions are presented for triangular, square, and circular basins while pentagonal, hexagonal, and octagonal basins are solved, for the first time, by an efficient Ritz method. The first five eigenvalues of each basin are tabulated and the corresponding mode shapes are discussed. Tileability conditions are presented. Some modes (eigenmodes) can be tiled into larger domains.

scholarly journals WATER WAVES PROPAGATING ON BEACHES OF ARBITRARY SHAPE

1982 ◽  
Vol 1 (18) ◽  
pp. 51
Author(s):  
Y.Y. Chen ◽  
H.H. Hwung
Keyword(s):  
Water Waves ◽  
Small Amplitude ◽  
Arbitrary Shape ◽  
Water Surface ◽  
Wave Motion ◽  
Progressive Wave ◽  
Amplitude Wave ◽  
Theoretical Derivation ◽  
Beach Slope ◽  
Sloping Beach

When a small amplitude wave climbing along an arbitrary sloping beach from deep water toward the shore, the variation of characteristics in the process of wave motion has been described in this paper. From the results of theoretical derivation, it is found out that the variation of water surface and amplitude are function of beach slope) and dimensionless distance (kx~) from the shore. And under the condition of the beach slope is a = 0 and a = °o that the solution will become a progressive wave and a standing wave respectively.

scholarly journals Recovery of steady periodic wave profiles from pressure measurements at the bed

2013 ◽  
Vol 714 ◽  
pp. 463-475 ◽  
Author(s):  
D. Clamond ◽  
A. Constantin
Keyword(s):  
Water Waves ◽  
Water Wave ◽  
Small Amplitude ◽  
Periodic Wave ◽  
Classical Solutions ◽  
Periodic Waves ◽  
Pressure Measurements ◽  
Governing Equations ◽  
Shallow Water Waves ◽  
Wave Profiles

AbstractWe derive an equation relating the pressure at the flat bed and the profile of an irrotational steady water wave, valid for all classical solutions of the governing equations for water waves. This permits the recovery of the surface wave from pressure measurements at the bed. Although we focus on periodic waves, the extension to solitary waves is straightforward. We illustrate the usefulness of the equation beyond the realm of linear theory by investigating the regime of shallow-water waves of small amplitude and by presenting a numerical example.

RESPONSE CHARACTERISTICS OF GRAVEL BEACH FROM THE VIEWPOINT OF SHALLOW WATER WAVES AND MOVEMENT OF GRAVELS

2020 ◽  
Vol 76 (2) ◽  
pp. I_565-I_570
Author(s):  
Shin-ichi AOKI ◽  
Tomoki HAMANO ◽  
Taishi NAKAYAMA ◽  
Eiichi OKETANI ◽  
Takahiro HIRAMATSU ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Response Characteristics ◽  
Gravel Beach

Integrable Models

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Fluid Mechanics ◽  
Soliton Solution ◽  
Water Waves ◽  
Heisenberg Model ◽  
Kdv Equation ◽  
Short Review ◽  
Lax Pair ◽  
Shallow Water Waves ◽  
Initial Value ◽  
The Kdv Equation

Some exceptional situations in fluid mechanics can be modeled by equations that are analytically solvable. The most famous example is the Korteweg–de Vries (KdV) equation for shallow water waves in a channel. The exact soliton solution of this equation is derived. The Lax pair formalism for solving the general initial value problem is outlined. Two hamiltonian formalisms for the KdV equation (Fadeev–Zakharov and Magri) are explained. Then a short review of the geometry of curves (Frenet–Serret equations) is given. They are used to derive a remarkably simple equation for the propagation of a kink along a vortex filament. This equation of Hasimoto has surprising connections to the nonlinear Schrödinger equation and to the Heisenberg model of ferromagnetism. An exact soliton solution is found.

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