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.

On the recovery of solitary wave profiles from pressure measurements

2012 ◽  
Vol 699 ◽  
pp. 376-384 ◽  
Author(s):  
A. Constantin
Keyword(s):  
Solitary Wave ◽  
Explicit Formula ◽  
Large Amplitude ◽  
Water Wave ◽  
Pressure Measurements ◽  
Pressure Data ◽  
Governing Equations ◽  
Wave Profiles

AbstractWe derive an explicit formula that permits the recovery of the profile of an irrotational solitary water wave from pressure data measured at the flat bed of the fluid domain. The formula is valid for the governing equations and applies to waves of small and large amplitude.

scholarly journals SHOALING AND REFLECTION OF NONLINEAR SHALLOW WATER WAVES

1986 ◽  
Vol 1 (20) ◽  
pp. 60 ◽  
Author(s):  
Padmaraj Vengayil ◽  
James T. Kirby
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Water Waves ◽  
Water Wave ◽  
Periodic Waves ◽  
Shallow Water Waves ◽  
Reflected Waves ◽  
Wave Shoaling ◽  
Backward Propagation ◽  
Resonant Reflection

The formulation for shallow water wave shoaling and refraction diffraction given by Liu et al (1985) is extended to include reflected waves. The model is given in the form of coupled K-P equations for forward and backward propagation. Shoaling on a plane beach is studied using the forward-propagating model alone. Non-resonant reflection of a solitary wave from a slope and resonant reflection of periodic waves by sinusoidal bars are then studied.

Shallow water wave generation by unsteady flow

1968 ◽  
Vol 31 (4) ◽  
pp. 779-788 ◽  
Author(s):  
J. E. Ffowcs Williams ◽  
D. L. Hawkings
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Water Wave ◽  
Small Amplitude ◽  
Point Of View ◽  
Sound Waves ◽  
Aerodynamic Sound ◽  
Shallow Layer ◽  
Sound Theory ◽  
Water Simulation

Small amplitude waves on a shallow layer of water are studied from the point of view used in aerodynamic sound theory. It is shown that many aspects of the generation and propagation of water waves are similar to those of sound waves in air. Certain differences are also discussed. It is concluded that shallow water simulation can be employed in the study of some aspects of aerodynamically generated sound.

scholarly journals New multi-soliton solutions of Whitham-Broer-Kaup shallow-water-wave equations

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 137-144 ◽  
Author(s):  
Sheng Zhang ◽  
Mingying Liu ◽  
Bo Xu
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Water Wave ◽  
Wave Equations ◽  
Soliton Solutions ◽  
Bilinear Forms ◽  
Shallow Water Waves ◽  
Bilinear Method ◽  
Shallow Water Wave ◽  
Shallow Water Wave Equations

In this paper, new and more general Whitham-Broer-Kaup equations which can describe the propagation of shallow-water waves are exactly solved in the framework of Hirota?s bilinear method and new multi-soliton solutions are obtained. To be specific, the Whitham-Broer-Kaup equations are first reduced into Ablowitz- Kaup-Newell-Segur equations. With the help of this equations, bilinear forms of the Whitham-Broer-Kaup equations are then derived. Based on the derived bilinear forms, new one-soliton solutions, two-soliton solutions, three-soliton solutions, and the uniform formulae of n-soliton solutions are finally obtained. It is shown that adopting the bilinear forms without loss of generality play a key role in obtaining these new multi-soliton solutions.

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 X-type Soliton, Resonance Y-type Soliton and Hybrid Solutions of a (2+1)-dimensional Hirota-Satsuma-Ito System for the Shallow Water Waves

2021 ◽  
Author(s):  
Yuan Shen ◽  
Bo Tian ◽  
Tian-Yu Zhou ◽  
Xiao-Tian Gao
Keyword(s):  
Shallow Water ◽  
Symbolic Computation ◽  
Water Waves ◽  
Water Wave ◽  
Soliton Solutions ◽  
Hirota Method ◽  
Shallow Water Waves ◽  
Soliton Resonance ◽  
Hybrid Solutions

Abstract Water waves are observed in the rivers, lakes, oceans, etc. Under investigation in this paper is a (2+1)-dimensional Hirota-Satsuma-Ito system arising in the shallow water waves. Via the Hirota method and symbolic computation, we derive some X-type and resonance Y-type soliton solutions. We also work out some hybrid solutions consisting of the resonance Y-type solitons, solitons, breathers and lumps. Graphics we present reveal that the hybrid solutions consisting of the resonance Y-type solitons and solitons/breathers/lumps describe the interactions between the resonance Y-type solitons and solitons/breathers/lumps, respectively. The obtained results rely on the water-wave coefficient in that system.

scholarly journals A fractal variational theory of the Broer-Kaup system in shallow water waves

2021 ◽  
pp. 87-87
Author(s):  
Wei-Wei Ling ◽  
Pin-Xia Wu
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Water Wave ◽  
Variational Formulation ◽  
Inverse Method ◽  
Variational Theory ◽  
Shallow Water Waves ◽  
Solution Structures ◽  
Fractal Space ◽  
Variational Formulations

The Broer-Kaup equation is one of many equations describing some phenomena of shallow water wave. There are many errors in scientific research because of the existence of the non-smooth boundaries. In this paper, we generalize the Broer-Kaup equation to the fractal space and establish fractal variational formulations through the semi-inverse method. The acquired fractal variational formulation reveals conservation laws in an energy form in the fractal space and suggests possible solution structures of the morphology of the solitary waves.

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.

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