Mechanisms for the generation of edge waves over a sloping beach

1988 ◽  
Vol 186 ◽  
pp. 379-391 ◽  
Author(s):  
D. V. Evans
Keyword(s):  
Water Wave ◽  
Wave Theory ◽  
Dominant Mode ◽  
Mode Shapes ◽  
Edge Waves ◽  
Longshore Current ◽  
Linear Water Wave Theory ◽  
Pressure Distributions ◽  
Sloping Beach ◽  
Standing Edge Waves

Two mechanisms for the generation of standing edge waves over a sloping beach are described using classical linear water-wave theory. The first is an extension of the result of Yih (1984) to a class of localized bottom protrusions on a sloping beach in the presence of a longshore current. The second is a class of longshore surface-pressure distributions over a beach. In both cases it is shown that Ursell-type standing edge-wave modes can be generated in an appropriate frame of reference. Typical curves of the mode shapes are presented and it is shown how in certain circumstances the dominant mode is not the lowest.

On the excitation of edge waves on beaches

1977 ◽  
Vol 79 (2) ◽  
pp. 273-287 ◽  
Author(s):  
A. A. Minzoni ◽  
G. B. Whitham
Keyword(s):  
Shallow Water ◽  
Incident Wave ◽  
Water Wave ◽  
Wave Train ◽  
Wave Theory ◽  
Edge Waves ◽  
Shallow Water Theory ◽  
Shallow Water Approximation ◽  
Complete Discussion ◽  
Standing Edge Waves

The excitation of standing edge waves of frequency ½ω by a normally incident wave train of frequency ω has been discussed previously (Guza & Davis 1974; Guza & Inman 1975; Guza & Bowen 1976) on the basis of shallow-water theory. Here the problem is formulated in the full water-wave theory without making the shallow-water approximation and solved for beach angles β = π/2N, where N is an integer. The work confirms the shallow-water results in the limit N [Gt ] 1, shows the effect of larger beach angles and allows a more complete discussion of some aspects of the problem.

Existence of edge waves along three-dimensional periodic structures

2010 ◽  
Vol 659 ◽  
pp. 225-246 ◽  
Author(s):  
SERGEY A. NAZAROV ◽  
JUHA H. VIDEMAN
Keyword(s):  
Water Wave ◽  
Periodic Structures ◽  
Three Dimensional ◽  
Wave Theory ◽  
Trace Operator ◽  
Sufficient Condition ◽  
Volume Integral ◽  
Edge Waves ◽  
Linear Water Wave Theory ◽  
Infinite Array

Existence of edge waves travelling along three-dimensional periodic structures is considered within the linear water-wave theory. A condition ensuring the existence is derived by analysing the spectrum of a suitably defined trace operator. The sufficient condition is a simple inequality comparing a weighted volume integral, taken over the submerged part of an element in the infinite array of identical obstacles, to the area of the free surface pierced by the obstacle. Various examples are given, and the results are extended to edge waves along periodic coastlines and over a periodically varying ocean floor.

scholarly journals Three-dimensional water-wave scattering in two-layer fluids

2000 ◽  
Vol 423 ◽  
pp. 155-173 ◽  
Author(s):  
J. R. CADBY ◽  
C. M. LINTON
Keyword(s):  
Water Wave ◽  
Lower Layer ◽  
Three Dimensional ◽  
Single Layer ◽  
Wave Theory ◽  
Finite Depth ◽  
Wave Radiation ◽  
Infinite Layer ◽  
Linear Water Wave Theory ◽  
Submerged Sphere

We consider, using linear water-wave theory, three-dimensional problems concerning the interaction of waves with structures in a fluid which contains a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of greater density. For such a situation time-harmonic waves can propagate with two different wavenumbers K and k. In a single-layer fluid there are a number of reciprocity relations that exist connecting the various hydrodynamic quantities that arise, and these relations are systematically extended to the two-fluid case. The particular problems of wave radiation and scattering by a submerged sphere in either the upper or lower layer are then solved using multipole expansions.

Edge waves over a shelf: full linear theory

1984 ◽  
Vol 142 ◽  
pp. 79-95 ◽  
Author(s):  
D. V. Evans ◽  
P. Mciver
Keyword(s):  
Shallow Water ◽  
Wide Class ◽  
Shallow Water Equations ◽  
Water Waves ◽  
Explicit Solution ◽  
Mode Shapes ◽  
Edge Waves ◽  
Wave Solutions ◽  
Linearized Theory ◽  
Sloping Beach

Edge-wave solutions to the linearized shallow-water equations for water waves are well known for a variety of bottom topographies. The only explicit solution using the full linearized theory describes edge waves over a uniformly sloping beach, although the existence of such waves has been established for a wide class of bottom geometries. In this paper the full linearized theory is used to derive the properties of edge waves over a shelf. In particular, curves are presented showing the variation of frequency with wavenumber along the shelf, together with some mode shapes for a particular shelf geometry.

scholarly journals WATER WAVE SCATTERING BY A THIN VERTICAL SUBMERGED PERMEABLE PLATE

2021 ◽  
Vol 26 (2) ◽  
pp. 223-235
Author(s):  
Rupanwita Gayen ◽  
Sourav Gupta ◽  
Aloknath Chakrabarti
Keyword(s):  
Integral Equation ◽  
Water Waves ◽  
Water Wave ◽  
Wave Theory ◽  
Hypersingular Integral Equation ◽  
Cauchy Type ◽  
Hypersingular Integral ◽  
Permeable Plate ◽  
Linear Water Wave Theory ◽  
Surface Water Waves

An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock’s expansion of water wave potential, the associated boundary value problem is reduced to a second kind hypersingular integral equation of order 2. The unknown function of the hypersingular integral equation is expressed as a product of a suitable weight function and an unknown polynomial. The associated hypersingular integral of order 2 is evaluated by representing it as the derivative of a singular integral of the Cauchy type which is computed by employing an idea explained in Gakhov’s book [7]. The values of the reflection coefficient computed with the help of present method match exactly with the previous results available in the literature. The energy identity is derived using the Havelock’s theorems.

scholarly journals Approximation Models For Water Wave Equations

2019 ◽  
Vol 7 (08) ◽  
Author(s):  
Leonard Bezati ◽  
Shkelqim Hajrulla ◽  
Kristofor Lapa
Keyword(s):  
Phase Velocity ◽  
Water Waves ◽  
Water Wave ◽  
Wave Equations ◽  
Kdv Equation ◽  
Wave Theory ◽  
Finite Volume Methods ◽  
Linear Water Wave Theory ◽  
The Best Approximation ◽  
Non Linear

Abstract: In this work we are interested in developing approximate models for water waves equation. We present the derivation of the new equations uses approximation of the phase velocity that arises in the linear water wave theory. We treat the (KdV) equation and similarly the C-H equation. Both of them describe unidirectional shallow water waves equation. At the same time, together with the (BBM) equation we propose, we provide the best approximation of the phase velocity for small wave numbers that can be obtained with second and third-order equations. We can extend the results of [3, 4].  A comparison between the methods is mentioned in this article. Key words:  C-H equation, KdV equation, approximation, water wave equation, numerical methods. --------------------------------------------------------------------------------------------------------------------- [3]. D. J. Benney, “Long non-linear waves in fluid flows,” Journal of Mathematical           Physics, vol. 45, pp. 52–63, 1966. View at Google Scholar · View at Zentralblatt MATH  [4]. Bezati, L., Hajrulla, S., & Hoxha, F. (2018). Finite Volume Methods for Non-Linear          Eqs. International Journal of Scientific Research and Management, 6(02), M-  2018. 

The nonlinear excitation of synchronous edge waves by a monochromatic wave normally approaching a plane beach

1995 ◽  
Vol 301 ◽  
pp. 251-268 ◽  
Author(s):  
P. Blondeaux ◽  
G. Vittori
Keyword(s):  
Energy Transfer ◽  
Water Wave ◽  
Three Dimensional ◽  
Wave Theory ◽  
Monochromatic Wave ◽  
Edge Waves ◽  
Nonlinear Stability Analysis ◽  
Nonlinear Excitation ◽  
Incoming Wave ◽  
Weakly Nonlinear

The possible excitation of synchronous edge waves by a monocromatic wave normally approaching a plane beach is studied. Use is made of the full three-dimensional water wave theory but only beach angles β = π/(2N), where N is an integer, are considered. A weakly nonlinear stability analysis is used to investigate the interaction of subharmonic, synchronous and 3/2-frequency edge waves with the incoming wave field. It is shown that values of β exist for which an energy transfer from the incoming wave to the synchronous edge waves takes place through the intermediary of the subharmonic components.

Standing edge waves reinvestigated: A comparison between two different bathymetries

2019 ◽  
Vol 234 (1) ◽  
pp. 108-126
Author(s):  
Dong Shao ◽  
Gang Jiang ◽  
Zirui Zheng ◽  
Yun Xing
Keyword(s):  
Water Depth ◽  
Water Surface ◽  
Initial Position ◽  
Trapped Modes ◽  
Edge Waves ◽  
Wave Refraction ◽  
Theoretical Predictions ◽  
Run Up ◽  
Sloping Beach ◽  
Standing Edge Waves

As a result of wave refraction caused by variable water depth within enclosed or semi-enclosed nearshore areas like harbors and bays, standing edge waves play an important part in the circulation patterns. The bathymetries of these areas may fall into two categories as follows: one is a reflective beach with a moving shoreline where the waves run up and down and the other has a certain water depth at a fixed backwall. A comparison of the standing edge waves trapped on these two types of bathymetries is made. Analytical investigations show that the trapped modes may behave dissimilarly on each type of bathymetry, especially for relatively high modes when the bathymetry is not simply a constantly sloping beach but a piecewise one. Wave patterns induced by water surface disturbances of the numerical simulations are analyzed with wavelet spectra. Frequencies of different components of the standing edge waves are compared with theoretical predictions. The results of the bathymetry with a reflective backwall are consistent with the findings of previous studies. For the case with a moving shoreline, several very low modes of the standing edge waves can survive and persist into a steady state, whereas higher modes may suffer from a quick attenuation. The occurrence of the trapped modes is revealed sensitive to the initial position of the water surface agitations in this case.

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