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.

scholarly journals Trapped modes around a row of circular cylinders in a channel

1999 ◽  
Vol 386 ◽  
pp. 259-279 ◽  
Author(s):  
T. UTSUNOMIYA ◽  
R. EATOCK TAYLOR
Keyword(s):  
Expansion Method ◽  
Wave Theory ◽  
Multipole Expansion ◽  
Circular Cylinders ◽  
Large Radius ◽  
Trapped Modes ◽  
Resonant Phenomenon ◽  
Trapped Mode ◽  
Linear Water Wave Theory ◽  
Multipole Expansion Method

Trapped modes around a row of bottom-mounted vertical circular cylinders in a channel are examined. The cylinders are identical, and their axes equally spaced in a plane perpendicular to the channel walls. The analysis has been made by employing the multipole expansion method under the assumption of linear water wave theory. At least the same number of trapped modes is shown to exist as the number of cylinders for both Neumann and Dirichlet trapped modes, with the exception that for cylinders having large radius the mode corresponding to the Dirichlet trapped mode for one cylinder will disappear. Close similarities between the Dirichlet trapped modes around a row of cylinders in a channel and the near-resonant phenomenon in the wave diffraction around a long array of cylinders in the open sea are discussed. An analogy with a mass–spring oscillating system is also presented.

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.

Passive trapped modes in the water-wave problem for a floating structure

2010 ◽  
Vol 657 ◽  
pp. 456-477 ◽  
Author(s):  
C. J. FITZGERALD ◽  
P. MCIVER
Keyword(s):  
Water Wave ◽  
Finite Energy ◽  
Frequency Domain Analysis ◽  
Trapped Modes ◽  
Wave Problem ◽  
Floating Structure ◽  
Water Wave Problem ◽  
Floating Structures ◽  
Trapped Mode ◽  
Motion Modes

Trapped modes in the linearized water-wave problem are free oscillations of an unbounded fluid with a free surface that have finite energy. It is known that such modes may be supported by particular fixed structures, and also by certain freely floating structures in which case there is, in general, a coupled motion of the fluid and structure; these two types of mode are referred to respectively as sloshing and motion trapped modes, and the corresponding structures are known as sloshing and motion trapping structures. Here a trapped mode is described that shares characteristics with both sloshing and motion modes. These ‘passive trapped modes’ are such that the net force on the structure exerted by the fluid oscillation is zero and so, in the absence of any forcing, the structure does not move even when it is allowed to float freely. In the paper, methods are given for the construction of passive trapping structures, a mechanism for exciting the modes is outlined using frequency-domain analysis, and the existence of the passive trapped modes is confirmed by numerical time-domain simulations of the excitation process.

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.

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