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.

Transmission of water waves through small apertures

1972 ◽  
Vol 55 (1) ◽  
pp. 149-161 ◽  
Author(s):  
D. C. Guiney ◽  
B. J. Noye ◽  
E. O. Tuck
Keyword(s):  
Shallow Water ◽  
Transmission Coefficient ◽  
Water Waves ◽  
Water Wave ◽  
Wave Transmission ◽  
Exact Theory ◽  
Vertical Barrier ◽  
Wave Transmission Coefficient

The water-wave transmission coefficient for a small slit in a thick vertical barrier is obtained theoretically and verified both experimentally and by comparison with an exact theory for the case of zero thickness. Similar shallow-water results are presented.

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.

Multi-Layer Modeling of Wave Groups From Deep to Shallow Water

2003 ◽  
Author(s):  
Patrick Lynett ◽  
Philip L.-F. Liu ◽  
Hwung-Hweng Hwung ◽  
Wen-Son Ching
Keyword(s):  
Shallow Water ◽  
Deep Water ◽  
Water Waves ◽  
Water Wave ◽  
Linear Wave ◽  
Layer Model ◽  
Wave Groups ◽  
Good Linear ◽  
Model Equations ◽  
Linear Accuracy

A set of model equations for water wave propagation is derived by piecewise integration of the primitive equations of motion through N arbitrary layers. Within each layer, an independent velocity profile is determined. With N separate velocity profiles, matched at the interfaces of the layers, the resulting set of equations have N+1 free parameters, allowing for an optimization with known analytical properties of water waves. The optimized two-layer model equations show good linear wave characteristics up to kh ≈8, while the second-order nonlinear behavior is well captured to kh ≈6. The three-layer model shows good linear accuracy to kh ≈14, and the four layer to kh ≈20. A numerical algorithm for solving the model equations is developed and tested against nonlinear deep-water wave-group experiments, where the kh of the carrier wave in deep water is around 6. The experiments are set up such that the wave groups, initially in deep water, propagate up a constant slope until reaching shallow water. The overall comparison between the multi-layer model and the experiment is quite good, indicating that the multi-layer theory has good nonlinear, as well has linear, accuracy for deep-water waves.

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.

Trapping of water waves above a round sill

1983 ◽  
Vol 132 ◽  
pp. 105-118 ◽  
Author(s):  
Yuriko Renardy
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Small Amplitude ◽  
Three Dimensional ◽  
Substantial Effect ◽  
Dimensional Problem ◽  
Shallow Water Theory ◽  
Resonant Frequencies ◽  
Wave Trapping ◽  
Linear Shallow Water Theory

The three-dimensional problem of wave trapping above a submerged round sill was first analysed by Longuet-Higgins on the basis of a linear shallow-water theory. The large responses predicted by the theory were, however, not well borne out by the experiments of Barnard, Pritchard & Provis, and this has motivated a more detailed study of the problem. A full linear theory for both inviscid and weakly viscous fluid, without any shallow-water assumptions, is presented here. It reveals important limitations on the use of shallow-water theory and the reasons for them. In particular, while the qualitative features of wave trapping are similar to those of shallow-water theory, the nearly resonant frequencies differ significantly, and, since the resonances are narrow, the observed amplitudes at a given frequency differ greatly. The geometry is strongly indicative of long waves, and the dispersion relation appears quite consistent with that, but the part of the motion at wavenumbers that are not small has, despite the small amplitude, a substantial effect on the response to excitation.

scholarly journals Variational principle of the Whitham-Broer-Kaup equation in shallow water wave with fractal derivatives

2021 ◽  
pp. 19-19
Author(s):  
Wei-Wei Ling ◽  
Pin-Xia Wu
Keyword(s):  
Variational Principle ◽  
Shallow Water ◽  
Solitary Waves ◽  
Water Waves ◽  
Water Wave ◽  
Variational Formulation ◽  
Inverse Method ◽  
Solution Structure ◽  
Shallow Water Waves ◽  
Fractal Space

The Whitham-Broer-Kaup equation exists widely in shallow water waves, but unsmooth boundary seriously affects the properties of solitary waves and has certain deviations in scientific research. The aim of this paper is to introduce its modification with fractal derivatives in a fractal space and to establish a fractal variational formulation by the semi-inverse method. The obtained fractal variational principle shows conservation laws in an energy form in the fractal space and also hints its possible solution structure.

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