Cloaking a vertical cylinder via homogenization in the mild-slope equation

2016 ◽  
Vol 796 ◽  
Author(s):  
G. Dupont ◽  
S. Guenneau ◽  
O. Kimmoun ◽  
B. Molin ◽  
S. Enoch
Keyword(s):  
Free Surface ◽  
Conformal Mapping ◽  
Water Waves ◽  
Vertical Cylinder ◽  
Far Field ◽  
Physical Constraints ◽  
Mild Slope Equation ◽  
The Mean ◽  
Drift Force ◽  
Linear Water Waves

We describe a method to construct devices which allows a vertical rigid cylinder to be cloaked for any far-field observer in the case of linear water waves. An adaptation of parameters given by a geometric transform performed in the mild-slope equation is achieved via homogenization. The final device, which respects the physical constraints of the problem, is obtained with a conformal mapping. The result of this algorithm is a structure surrounding the vertical cylinder, composed of an annular region with varying bathymetry and with rigid vertical objects piercing the free surface. An approximate cloaking is achieved, which implies a reduction of the mean drift force acting on the cylinder.

Accurate refraction–diffraction equations for water waves on a variable-depth rough bottom

2001 ◽  
Vol 449 ◽  
pp. 301-311 ◽  
Author(s):  
YEHUDA AGNON ◽  
EFIM PELINOVSKY
Keyword(s):  
Water Waves ◽  
Mean Field ◽  
Variable Coefficients ◽  
Test Case ◽  
Random Roughness ◽  
Operator Calculus ◽  
Mild Slope Equation ◽  
The Mean ◽  
Model Equations ◽  
Systematic Derivation

The extended mild-slope equation and the modified mild-slope equation have been used successfully to study refraction–diffraction of linear water waves by steep bottom roughness. Their consistency has been questioned. A systematic derivation of these model equations exposes and illuminates their rationale. Their good performance stems from an accurate representation of (Class I) Bragg resonance. As a benchmark test case, we consider scattering by a sloping bottom with random roughness. The rates of scattering found for the mean field in both of the approximate models agree exactly with the full theory for scattering by small roughness. This greatly improves the limited agreement which was found for the mild-slope equation, and establishes the validity of the above model equations. The study involves operator calculus, a powerful method for simplifying problems with variable coefficients. The augmented mild-slope equation serves to consistently derive accurate model equations.

scholarly journals Second Order Diffraction of Water Waves by a Bottom Mounted Vertical Circular Cylinder and Some Related Numerical Problems

2006 ◽  
Vol 129 (1) ◽  
pp. 68-70
Author(s):  
Oguz Yilmaz
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Circular Cross Section ◽  
Vertical Cylinder ◽  
Second Order ◽  
Published Data ◽  
Hankel Transformation ◽  
Third Order ◽  
Improper Integral ◽  
Order Diffraction

A Hankel transformation is used to obtain the second order diffraction solution of vertical cylinder of circular cross section. The improper integral over the free surface is tackled carefully. The singularity at the free surface is overcome effectively using a third order nonlinear transformation. Numerical results for free surface elevations compare well with the published data.

A note on the vertical distribution of momentum transport in water waves

2015 ◽  
Vol 44 (4) ◽  
Author(s):  
Jerzy Kołodko ◽  
Gabriela Gic-Grusza
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Continuous Distribution ◽  
Classical Problem ◽  
Ocean Dynamics ◽  
Momentum Transport ◽  
Generalized Function ◽  
Dirac Delta ◽  
The Mean ◽  
Transport Flux

AbstractIn this paper, the classical problem of horizontal waveinduced momentum transport is analyzed once again. A new analytical approach has been employed to reveal the vertical variation of this transport in the Eulerian description.In mathematical terms, this variation is shown to have (after “smoothing out” the surface corrugation) the character of a generalized function (distribution) and is described by a classical function in the water depths and by an additional Dirac-delta-function component on the averaged free surface.In terms of physics, the considered variation consists of two entities: (i) a continuous distribution of the mean momentum transport flux density (tensorial radiation pressure) over the entire water column, and (ii) an additional momentum transport flux concentrated on the mean free surface level (tensorial radiation surface pressure). Simple analytical formulae describing this variation have been derived.This allowed a conventional expression to be derived, describing the depth-integrated excess of horizontal momentum flux due to the presence of waves (the so-called “radiation stress”), confirming to some extent the correctness of the whole analysis carried out.The results obtained may be important to the ocean dynamics, especially in view of their possible application in the field of hydrodynamics of wave-dominated coastal zones.

scholarly journals Mean drift forces on arrays of bodies due to incident long waves

1987 ◽  
Vol 185 ◽  
pp. 469-482 ◽  
Author(s):  
P. McIver
Keyword(s):  
Water Waves ◽  
Low Frequency ◽  
Frequency Limit ◽  
Numerical Work ◽  
Single Body ◽  
Force Ratio ◽  
Wide Range ◽  
The Mean ◽  
Drift Force ◽  
Vertical Cylinders

The scattering of long water waves by an array of bodies is investigated using the method of matched asymptotic expansions. Two particular geometries are considered: a group of vertical cylinders extending throughout the depth and a group of floating hemispheres. From these solutions, the low-frequency limit of the ratio of the mean drift force on a group of N bodies to that on a single body is calculated. For a wide range of circumstances this drift-force ratio is N2, which is in agreement with previous numerical work. Further drift-force enhancement is possible for certain configurations of vertical cylinders.

Approximations to wave trapping by topography

1996 ◽  
Vol 325 ◽  
pp. 357-376 ◽  
Author(s):  
P. G. Chamberlain ◽  
D. Porter
Keyword(s):  
Water Waves ◽  
Two Dimensional ◽  
Trapped Modes ◽  
Wave Trapping ◽  
Mild Slope Equation ◽  
Precise Shape ◽  
Different Depths ◽  
Linear Water Waves ◽  
Local Irregularity

The trapping of linear water waves over two-dimensional topography is investigated by using the mild-slope approximation. Two types of bed profile are considered: a local irregularity in a horizontal bed and a shelf joining two horizontal bed sections at different depths. A number of results are derived concerning the existence of trapped modes and their multiplicity. It is found, for example, that the maximum number of modes which can exist depends only on the gross properties of the topography and not on its precise shape. A range of problems is solved numerically, to inform and illustrate the analysis, using both the mild-slope equation and the recently derived modified mild-slope equation.

scholarly journals A plethora of generalised solitary gravity–capillary water waves

2015 ◽  
Vol 784 ◽  
pp. 664-680 ◽  
Author(s):  
Didier Clamond ◽  
Denys Dutykh ◽  
Angel Durán
Keyword(s):  
Free Surface ◽  
Conformal Mapping ◽  
Euler Equations ◽  
Complex Plane ◽  
Solitary Waves ◽  
Infinite Number ◽  
Water Waves ◽  
Efficient Algorithm ◽  
Capillary Water

The present study describes, first, an efficient algorithm for computing solutions in terms of capillary–gravity solitary waves of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of an infinite number of generalised solitary waves (solitary waves with undamped oscillatory wings). Using conformal mapping, the unknown fluid domain, which is to be determined, is mapped into a uniform strip of the complex plane. In the transformed domain, a Babenko-like equation is then derived and solved numerically.

Nonlinear wave loads on a slender vertical cylinder

1995 ◽  
Vol 289 ◽  
pp. 179-198 ◽  
Author(s):  
O. M. Faltinsen ◽  
J. N. Newman ◽  
T. Vinje
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Vertical Cylinder ◽  
Nonlinear Effects ◽  
Total Force ◽  
Surface Boundary ◽  
Wave Loads ◽  
Wave Load ◽  
Outer Domain ◽  
Wave Slope

The diffraction of water waves by a vertical circular cylinder is considered in the regime where the wave amplitude A and cylinder radius a are of the same order, and both are small compared to the wavelength. The wave slope is small, and a conventional linear analysis applies in the outer domain far from the cylinder. Significant nonlinear effects exist in the complementary inner domain close to the cylinder, associated with the free-surface boundary condition. Using inner coordinates scaled with respect to a, it is shown that the leading-order nonlinear contribution to the velocity potential includes terms proportional to both A2a and A3. The wave load which acts on the cylinder near the free surface includes second- and third-harmonic components which are proportional respectively to A2a2 and A3a. In a conventional perturbation analysis, where A [Lt ] a, these components would be ordered in magnitude corresponding to the different powers of A, but here they are of the same order. The second- and third-order components of the total force are of comparable magnitude for practical values of the wave slope.

Rankine and Fourier-Kochin Representation of Near-Field Ship Waves

2002 ◽  
Vol 46 (01) ◽  
pp. 63-79
Author(s):  
Francis Noblesse
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Near Field ◽  
Boundary Surface ◽  
Diffraction Radiation ◽  
Offshore Structure ◽  
Ship Waves ◽  
Time Harmonic ◽  
The Mean ◽  
Elementary Waves

New fundamental analytical representations of the near-held potential how that corresponds to a given how at a surface bounding a potential-how region are given for three classes of free-surface hows in deep water: diffraction-radiation of regular water waves by an offshore structure, steady ship waves, and time-harmonic ship waves (diffraction-radiation with forward speed). These near-held how representations, called Rankine and Fourier-Kochin representations, define the how in terms of distributions of Rankine singularities and Fourier-Kochin distributions of elementary waves over the boundary surface and its intersection with the mean free surface. The Rankine and Fourier-Kochin near-held how representations involve only simple ordinary functions. These how representations extend the previously given Fourier-Kochin representations of waves.

scholarly journals An alternative approach to study irrotational periodic gravity water waves

2021 ◽  
Vol 72 (4) ◽  
Author(s):  
Biswajit Basu ◽  
Calin I. Martin
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Water Wave ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Stagnation Points ◽  
Alternative Approach ◽  
New Formulation ◽  
Bounded Below ◽  
Surface Dynamic

AbstractWe are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.

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