scholarly journals Scattering of oblique waves in a two-layer fluid

2002 ◽  
Vol 461 ◽  
pp. 343-364 ◽  
Author(s):  
C. M. LINTON ◽  
J. R. CADBY
Keyword(s):  
Lower Layer ◽  
Wave Theory ◽  
Finite Depth ◽  
Oblique Waves ◽  
Infinite Layer ◽  
Linear Water Wave Theory ◽  
Time Harmonic ◽  
Multipole Expansions ◽  
Horizontal Cylinders ◽  
Horizontal Circular Cylinder

We consider problems based on linear water wave theory concerning the interaction of oblique waves with horizontal cylinders in a fluid consisting of 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. The particular problems of wave scattering by a horizontal circular cylinder in either the upper or lower layer are solved using multipole expansions.

scholarly journals The interaction of waves with horizontal cylinders in two-layer fluids

1995 ◽  
Vol 304 ◽  
pp. 213-229 ◽  
Author(s):  
C. M. Linton ◽  
M. McIver
Keyword(s):  
Lower Layer ◽  
Single Layer ◽  
Wave Theory ◽  
Finite Depth ◽  
Scattering Problems ◽  
Infinite Layer ◽  
Linear Water Wave Theory ◽  
Interaction Of Waves ◽  
Reciprocity Relations ◽  
Horizontal Cylinders

We consider two-dimensional problems based on linear water wave theory concerning the interaction of waves with horizontal cylinders in a fluid consisting of 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. These relations are systematically extended to the two-fluid case. It is shown that for symmetric bodies the solutions to scattering problems where the incident wave has wavenumber K and those where it has wavenumber k are related so that the solution to both can be found by just solving one of them. The particular problems of wave scattering by a horizontal circular cylinder in either the upper or lower layer are then solved using multipole expansions.

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.

scholarly journals Hydrodynamic Forces on a Submerged Circular Cylinder in Two-layer Fluid with an Ice-cover

2021 ◽  
Vol 23 (08) ◽  
pp. 282-294
Author(s):  
Manomita Sahu ◽  
◽  
Dilip Das ◽  
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Flexural Rigidity ◽  
Lower Layer ◽  
Wave Theory ◽  
Finite Depth ◽  
Ice Cover ◽  
Hydrodynamic Forces ◽  
Wave Number ◽  
Infinite Layer

We consider problems based on linear water wave theory concerning the interaction of wave with horizontal circular cylinder submerged in two-layer ocean consisting of a upper layer of finite depth bounded above by an ice-cover and below by an infinite layer of fluid of greater density, the ice-cover being modelled as an elastic plate of very small thickness. Using the method of multipoles, we formulate the problems of hydrodynamic forces on a submerged cylinder in either the upper or the lower layer. The vertical and horizontal forces on the circular cylinder are obtained and depicted graphically against the wave number for various values of flexural rigidity of ice-cover to show the effect of the presence of ice-cover on these quantities. Also when the flexural rigidity and surface density of the ice-cover are taken to be zero, the ice-cover tends to a free-surface. Then all the forces are the same as in the case of two-layer fluid with free surface.

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.

Comparisons of Simulation Methods for Motions of a Moored Body in Waves

1985 ◽  
Vol 107 (1) ◽  
pp. 34-41
Author(s):  
M. Takagi ◽  
K. Saito ◽  
S. Nakamura
Keyword(s):  
Wave Theory ◽  
Simulation Methods ◽  
Convolution Integral ◽  
Linear Water Wave Theory ◽  
Initial Stage ◽  
Constant Coefficients ◽  
Exciting Forces ◽  
Linear Differential ◽  
Experimental Values ◽  
The Time Domain

Based on the linear water wave theory, numerical simulations are carried out for motions in waves of a body moored by a nonlinear-type mooring system. Numerical results obtained by using the equation of motion described in the time domain with a convolution integral (C.I. method) are compared with those of the second-order linear differential equation with constant coefficients (C. C. method). These results are also compared with experimental values measured from the initial stage when the action of exciting forces starts and the validity of C.I. method is discussed.

EFFECTS OF SURFACE TENSION ON TRAPPED MODES IN A TWO-LAYER FLUID

2015 ◽  
Vol 57 (2) ◽  
pp. 189-203 ◽  
Author(s):  
S. SAHA ◽  
S. N. BORA
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Circular Cylinder ◽  
Boundary Value Problems ◽  
Finite Depth ◽  
Trapped Modes ◽  
Trapped Waves ◽  
Linearized Theory ◽  
Horizontal Circular Cylinder ◽  
Effect Of Surface

We consider a two-layer fluid of finite depth with a free surface and, in particular, the surface tension at the free surface and the interface. The usual assumptions of a linearized theory are considered. The objective of this work is to analyse the effect of surface tension on trapped modes, when a horizontal circular cylinder is submerged in either of the layers of a two-layer fluid. By setting up boundary value problems for both of the layers, we find the frequencies for which trapped waves exist. Then, we numerically analyse the effect of variation of surface tension parameters on the trapped modes, and conclude that realistic changes in surface tension do not have a significant effect on the frequencies of these.

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.

Contributions to the theory of stokes waves

1955 ◽  
Vol 51 (4) ◽  
pp. 713-736 ◽  
Author(s):  
S. C. De
Keyword(s):  
Wave Height ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Wave Theory ◽  
Finite Depth ◽  
Volume Flow ◽  
Steady Flows ◽  
Total Head ◽  
Stokes Waves ◽  
Fifth Order

ABSTRACTThe well-known Stokes theory (9, 10) of waves of permanent form in water of finite depth has been extended to the fifth order of approximation. The solutions have been first obtained in the form of equations for the space coordinates x and y as functions of the velocity potential Φ and stream function ψ. Expressions for the complex potential W in terms of the complex variable z ( = x + iy), the form of the wave profile, and the square of the wave velocity have been obtained to the fifth order.Expressions for the three physical quantities Q, R and S, where Q is the volume flow rate per unit span, R is the energy per unit mass (i.e. g times the total head, measuring heights from the bottom and pressures from atmospheric) and S is the momentum flow rate per unit spaa, corrected for pressure forces and divided by density, have been obtained to the fifth order. The values for the dimensionless quantities r = R/Rc and s = S/Sc, where Rc and Sc refer to the values of R and S for a critical stream of volume flow Q, are tabulated for certain values of the ratios mean depth to wavelength and amplitude to wavelength. The values of r and s thus obtained have been used to calculate the ratios of mean depth to wavelength and of wave height to wavelength according to the cnoidal wave theory as recently presented by Benjamin and Light-hill(1), and the results are found to be in satisfactory agreement with that from Stokes's theory for waves longer than six times the depth.The (r, s) diagram introduced in the recent work of Benjamin and Lighthill(1) has been further considered, and the unshaded part of the diagram referred to in that paper has been mapped with a network of curves for constant values of the ratios of mean depth to wavelength and of wave height to wavelength (Fig. 2). The third barrier to the existence of steady flows, corresponding to ‘waves of greatest height’ referred to in that paper, has also been indicated in Fig. 2.

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