The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory

2010 ◽  
Vol 87 (3-4) ◽  
pp. 430-435 ◽  
Author(s):  
S. Yu. Dobrokhotov ◽  
M. Rouleux
Keyword(s):  
Water Wave ◽  
Wave Theory ◽  
Linear Water Wave Theory

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.

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.

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. 

scholarly journals Radiated Force due to Surge Motion by a Pair of Submerged Cylinder in Water

2019 ◽  
Vol 8 (10) ◽  
pp. 3205-3210
Keyword(s):  
Water Wave ◽  
Expansion Method ◽  
Wave Theory ◽  
Finite Depth ◽  
Added Mass ◽  
Damping Coefficient ◽  
Hydrodynamic Coefficients ◽  
Linear Water Wave Theory ◽  
Eigenfunction Expansion Method ◽  
Submerged Cylinder

Evaluation of hydrodynamic coefficients due to surge of submerged structure is great significant to designing a device which can be consider as a device of wave energy. In the present work, a theoretical approach is developed to describe radiation of water wave by fully submerged cylinder placed above a submerged circular plate in water of finite depth which is based on linear water wave theory The radiation problem due to surge motion by this pair of cylinders have investigated with the suspicion of linear water wave theory. To determine the radiated potentials in every area, we utilize the eigenfunction expansion method and variables separation method. Finally, we derived the analytical expressions of Hydrodynamic coefficients i. e. added mass and damping coefficient due to surge and associated unknown coefficients are calculated by utilizing the matching conditions between the physical and virtual boundaries. A set of added mass and damping coefficient have presented graphically for various radius of the submerge cylinder.

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.

Hydrodynamic characteristics of bodies in channels

1993 ◽  
Vol 252 ◽  
pp. 647-666 ◽  
Author(s):  
C. M. Linton ◽  
D. V. Evans
Keyword(s):  
Water Depth ◽  
Water Wave ◽  
Vertical Plate ◽  
Wave Theory ◽  
Analytic Solutions ◽  
Mode Frequency ◽  
Hydrodynamic Characteristics ◽  
Trapped Modes ◽  
Trapped Mode ◽  
Linear Water Wave Theory

The effect of channel walls on the hydrodynamic characteristics of fixed or oscillating bodies is discussed using classical linear water wave theory. Particular attention is paid to the occurrence of trapped modes persisting local to the fixed body and which are manifested in a non-uniqueness of the corresponding forced problem at the trapped mode frequency. The general ideas are illustrated by consideration of two simple geometries for which semi-analytic solutions are available, namely a circular cylinder either partly immersed or extending throughout the water depth, and a thin vertical plate parallel to the channel walls which extends throughout the water depth. Conclusions are drawn concerning the conditions under which trapped modes may exist and their effect on the hydrodynamic characteristics of more general bodies.

Wave scattering by a fixed submerged platform over a step bottom

2017 ◽  
Vol 233 (1) ◽  
pp. 93-107 ◽  
Author(s):  
Ramnarayan Mondal ◽  
Ken Takagi
Keyword(s):  
Water Wave ◽  
Wave Scattering ◽  
Rectangular Cross Section ◽  
Vertical Wall ◽  
Expansion Method ◽  
Wave Theory ◽  
Geometrical Parameters ◽  
Linear Water Wave Theory ◽  
Expansion Formulae ◽  
Submerged Body

This study deals with oblique and normal water wave scattering by a fixed submerged body of rectangular cross section which is infinite in length and finite in width. The fluid domain is considered as infinite as well as semi-infinite in nature. The study is carried out under the assumption of small amplitude linear water wave theory. It is considered that the bottom has a step and the submerged body is considered in shallower water depth region. The velocity potential is derived using the eigenfunction expansion method. The unknown constants, which appear in the expansion formulae, are obtained using orthogonal relation along with the boundary conditions at the interfaces. The wave-induced hydrodynamic forces acting on the submerged body and vertical wall are computed for different geometrical parameters. The wave reflection coefficient and the free surface motion are also calculated to see the wave phenomena around the submerged body.

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