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 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 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 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.

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.

Oceanic warm cloud layers within multilevel cloud systems observed by satellite measurements

2020 ◽  
Author(s):  
Qi Liu ◽  
Yuhao Ding ◽  
Ping Lao
Keyword(s):  
Double Layer ◽  
Radiative Forcing ◽  
Lower Layer ◽  
Numerical Models ◽  
Three Dimensional ◽  
Single Layer ◽  
Layer System ◽  
Cloud Systems ◽  
Warm Cloud ◽  
Double Layer System

<p>Low-level warm clouds are a major component in multilayered cloud systems and are generally hidden from the top-down view of satellites with passive measurements. By using spaceborne radar data with fine vertical resolution, this study conducts an investigation on oceanic warm clouds embedded in multilayered structures. The occurrences of warm cloud overlapping and the geometric features of several kinds of warm cloud layers are examined. It is found that there are three main types of cloud systems that involve warm cloud layers, including warm single layer clouds, cold-warm double layer clouds and warm-warm double layer clouds. The two types of double layer clouds account for 23% and in the double layer occurrences warm-warm double layer subsets contribute about 13%. The global distribution patterns of these three types differ from each other. Single-layer warm clouds and the lower warm clouds in the cold-warm double layer system have nearly identical geometric parameters, while the upper and lower layer warm clouds in the warm-warm double layer system are distinct from the previous two forms of warm cloud layers. In contrast to the independence of the two cloud layers in cold-warm double layer system, the two kinds of warm cloud layers in the warm-warm double layer system may be coupled. The distance between the two layers in the warm-warm double layer system is weakly dependent on cloud thickness. Given the upper and lower cloud layer with moderate thickness around 1 km, the cloudless gap reaches its maximum exceeding 600 m. As the two cloud layers become even thinner or thicker, the cloudless gap decreases in thickness. It is believed that such knowledge on cloud overlapping is critical for fully understanding the distribution of warm clouds in three-dimensional space. The results derived in this study could help validating cloud results of numerical models, which are indeed three-dimensional in nature. They could also be used to improve the estimation of cloud radiative forcing, since it is affected by cloud occurrences and especially their vertical structures. It should be pointed out that solid explanations for the above cloud features cannot be presented by only using these satellite data themselves. </p>

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.

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