Hydrodynamic Interactions of the Truncated Porous Vertical Circular Cylinder With Water Waves

2018 ◽  
Author(s):  
Charaf Ouled Housseine ◽  
Sime Malenica ◽  
Guillaume De Hauteclocque ◽  
Xiao-Bo Chen
Keyword(s):  
Circular Cylinder ◽  
Porous Body ◽  
Wave Diffraction ◽  
Water Waves ◽  
Expansion Method ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Diffraction Radiation ◽  
Linear Potential ◽  
Eigenfunction Expansion Method

Wave diffraction-radiation by a porous body is investigated here. Linear potential flow theory is used and the associated Boundary Value Problem (BVP) is formulated in frequency domain within a linear porosity condition. First, a semi-analytical solution for a truncated porous circular cylinder is developed using the dedicated eigenfunction expansion method. Then the general case of wave diffraction-radiation by a porous body with an arbitrary shape is discussed and solved through Boundary Integral Equation Method (BIEM). The main goal of these developments is to adapt the existing diffraction-radiation code (HYDROSTAR) for that type of applications. Thus the present study of the porous cylinder consists a validation work of (BIEM) numerical implementation. Excellent agreement between analytical and numerical results is observed. Porosity influence on wave exciting forces, added mass and damping is also investigated.

Effective Estimation of Water Waves Scattering by Double-Row Pile Breakwaters

2012 ◽  
Author(s):  
Omid Nejadkazem ◽  
Ahmad Reza Mostafa Gharabaghi
Keyword(s):  
Water Waves ◽  
Wave Length ◽  
Expansion Method ◽  
Optimum Number ◽  
Intermediate Water ◽  
Double Row ◽  
Eigenfunction Expansion Method ◽  
Efficient Performance ◽  
Efficient Calculation ◽  
Efficient Prediction

This paper describes various hydraulic characteristic of double-row pile breakwaters (DPB). Applying an eigenfunction expansion method, a numerical method have been developed that can compute wave transmission, reflection, and other hydraulic characteristics. To verify the validity of developed prediction, laboratory experiments of Isaascson et al. (1999) have been utilized. Then for an efficient calculation, optimum number of necessary evanescent waves for an effective and efficient prediction is discussed for various hydraulic quantities of interest. In a nutshell, for an effective and efficient performance of the DPB, intermediate water wave and porosity range of [0.2 0.3] are recommended. Relative distance between two barriers must be set depending on significant wave length of design.

Rigorous accounting diffraction on non-plane gratings irradiated by non-planar waves

2021 ◽  
Author(s):  
Leonid I. Goray
Keyword(s):  
Plane Wave ◽  
Wave Diffraction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Transverse Magnetic ◽  
Incident Field ◽  
Boundary Integral ◽  
Cylindrical Waves ◽  
Plane Wave Diffraction

Abstract The modified boundary integral equation method (MIM) is considered a rigorous theoretical application for the diffraction of cylindrical waves by arbitrary profiled plane gratings, as well as for the diffraction of plane/non-planar waves by concave/convex gratings. This study investigates two-dimensional (2D) diffraction problems of the filiform source electromagnetic field scattered by a plane lamellar grating and of plane waves scattered by a similar cylindrical-shaped grating. Unlike the problem of plane wave diffraction by a plane grating, the field of a localised source does not satisfy the quasi-periodicity requirement. Fourier transform is used to reduce the solution of the problem of localised source diffraction by the grating in the whole region to the solution of the problem of diffraction inside one Floquet channel. By considering the periodicity of the geometry structure, the problem of Floquet terms for the image can be formulated so that it enables the application of the MIM developed for plane wave diffraction problems. Accounting of the local structure of an incident field enables both the prediction of the corresponding efficiencies and the specification of the bounds within which the approximation of the incident field with plane waves is correct. For 2D diffraction problems of the high-conductive plane grating irradiated by cylindrical waves and the cylindrical high-conductive grating irradiated by plane waves, decompositions in sets of plane waves/sections are investigated. The application of such decomposition, including the dependence on the number of plane waves/sections and radii of the grating and wave front shape, was demonstrated for lamellar, sinusoidal and saw-tooth grating examples in the 0th & –1st orders as well as in the transverse electric and transverse magnetic polarisations. The primary effects of plane wave/section partitions of non-planar wave fronts and curved grating shapes on the exact solutions for 2D and three-dimensional (conical) diffraction problems are discussed.

Water Wave Diffraction and Radiation by a Submerged Horizontal Circular Cylinder in Front a Vertical Wall

2020 ◽  
Author(s):  
Ai-jun Li ◽  
Yong Liu
Keyword(s):  
Circular Cylinder ◽  
Analytical Solutions ◽  
Wave Diffraction ◽  
Water Wave ◽  
Vertical Wall ◽  
Horizontal Cylinder ◽  
Linear Potential ◽  
Polar Coordinate ◽  
Horizontal Circular Cylinder ◽  
Unbounded Fluid

Abstract This article studies water wave diffraction and radiation by a submerged horizontal circular cylinder in front of a vertical wall under the assumption of linear potential flow theory. Based on the image principle, the hydrodynamic problem of a horizontal cylinder in front of a vertical wall is transformed into an equivalent problem involving symmetrical cylinders in a horizontally unbounded fluid domain. Then, analytical solutions for the present physical problem are developed using the method of multipole expansions combined with the shift of polar coordinate systems. The wave exciting forces on the cylinder as well as the added mass and radiation damping due to the cylinder oscillation are calculated. The analytical solutions converge very rapidly with the increasing truncated number of multipoles. Calculation examples are presented to examine the effects of different parameters on the hydrodynamic quantities of the cylinder. Results indicate that the hydrodynamic quantities of the cylinder in front of a vertical wall greatly differ from those in a horizontally unbounded fluid domain.

scholarly journals Mathematical Modeling of Partial-Porous Circular Cylinders with Water Waves

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Min-Su Park ◽  
Weoncheol Koo
Keyword(s):  
Water Waves ◽  
Body Wave ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Expansion Method ◽  
The Body ◽  
Circular Cylinders ◽  
Exterior Region ◽  
Eigenfunction Expansion Method ◽  
Body Regions

The interaction of water waves with partially porous-surfaced circular cylinders was investigated. A three-dimensional numerical modeling was developed based on the complete mathematical formulation of the eigenfunction expansion method in the potential flow. Darcy’s law was applied to describe the porous boundary. The partial-porous cylinder is composed of a porous-surfaced body near the free surface, and an impermeable-surfaced body with an end-capped rigid bottom below the porous region. The optimal ratio of the porous portion to the impermeable portion can be adopted to design an effective ocean structure with minimal hydrodynamic impact. To scrutinize the hydrodynamic interactions inNpartial-porous circular cylinders, the computational fluid domain is divided into three regions: an exterior region,Ninner porous body regions, andNregions beneath the body. Wave excitation forces and wave run-up on multibodied partial-porous cylinders are calculated and compared for various porous-portion ratios and wave conditions, all of which significantly influence the hydrodynamic property.

Nonlinear radiated and diffracted waves due to the motions of a submerged circular cylinder

1999 ◽  
Vol 382 ◽  
pp. 263-282 ◽  
Author(s):  
YUMING LIU ◽  
QIANG ZHU ◽  
DICK K. P. YUE
Keyword(s):  
Circular Cylinder ◽  
High Harmonic ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
The Body ◽  
Leading Order ◽  
Near Surface ◽  
Diffracted Waves ◽  
Nonlinear Potential ◽  
Incident Waves

We study the high-harmonic surface wave associated with nonlinear diffraction and radiation of gravity waves by a near-surface circular cylinder. Based on nonlinear potential-flow theory, we show analytically, using a boundary-integral equation method, that: (a) for a circular motion of the cylinder, the leading-order outgoing radiated waves at any harmonic are generated only in one direction; (b) for a cylinder free to respond to regular incident waves, the total leading-order scattered waves at any harmonic are two orders smaller upstream of the body. These theoretical results are substantially confirmed by direct time-domain simulations of the problem.

The quest for a three-dimensional theory of ship-wave interactions

1991 ◽  
Vol 334 (1634) ◽  
pp. 213-227 ◽  
Keyword(s):  
Steady State ◽  
Velocity Field ◽  
Water Waves ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Analytic Solutions ◽  
Boundary Integral ◽  
Ship Motions ◽  
Strip Theory ◽  
Forward Translation

The radiation and diffraction of water waves by ships can be analysed in classical terms from potential theory. The linearized formulation is well studied, but robust numerical implementations have been achieved only in cases where the vessel is stationary or oscillating about a fixed mean position. Slender-body approximations have been used to rationalize and extend the strip theory of ship motions, providing analytic solutions and guidance in the development of more general numerical methods. The governing equations are reviewed, with emphasis on the interactions between the steady-state velocity field due to the ship’s forward translation and the perturbations due to its unsteady motions in waves. Recent computations based on the boundary-integral-equation method are described, and encouraging results are noted. There is growing evidence that the influence of the steady-state velocity field is important, and the degree of completeness required to account for the steady field depends on the fullness of the ship. Benchmark computations are needed to test theories and computer programs without the uncertainty inherent in experimental comparisons.

Oblique interaction between water waves and a partially submerged rectangular breakwater

2019 ◽  
Vol 234 (1) ◽  
pp. 154-169 ◽  
Author(s):  
R. B. Kaligatla ◽  
N. M. Prasad ◽  
S. Tabssum
Keyword(s):  
Water Waves ◽  
Eigenfunction Expansion ◽  
Wave Scattering ◽  
Wave Reflection ◽  
Expansion Method ◽  
Algebraic Equations ◽  
Eigenfunction Expansion Method ◽  
Balance Relation ◽  
Orthogonal Property ◽  
The One

A problem of oblique wave scattering by a rectangular breakwater floating in water of uneven depth is solved by applying matched eigenfunction expansion method. Three positions of breakwater are considered. The width and draft of breakwater are assumed to be finite, whereas its length is infinite. Breakwater is studied in the settings of without backwall and with a backwall. By using matching conditions at interface boundaries and making use of orthogonal property of eigenfunctions, the problem is converted to a system of algebraic equations. Breakwater’s position is proposed for which wave reflection, transmission, and force on wall are optimized. The breakwater with certain width and draft reflects more wave energy than the one with zero-draft. In the case of absence of wall, breakwater at lee side to the step induces least transmission of waves. In the case of presence of wall, suitable position of breakwater is suggested based on a range of wave frequency to mitigate force on wall. Optimum distances between wall and breakwater are found to attain less force on wall. Using Green’s identity, energy balance relation is derived to check accuracy in results. The findings are likely to be useful to assess the performance of a breakwater in different positions in water of uneven depth.

Hydroelastic Response of a Floating Mat-Type Structure in Oblique, Shallow-Water Waves

1999 ◽  
Vol 43 (04) ◽  
pp. 241-254
Author(s):  
R. Cengiz Ertekin ◽  
Jang Whan Kim
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Wave Equations ◽  
Plate Theory ◽  
Integral Equation Method ◽  
Field Method ◽  
Boundary Integral ◽  
Incoming Wave ◽  
Level I ◽  
Hydroelastic Response

The linear, Level I Green-Naghdi (GN) theory is developed to study the hydroelastic behavior of a rectangular airport or runway whose draft is "small" and which floats in a near-shore area. The new theoretical and numerical model uses the linear, shallow-water wave equations of the GN type for the fluid dynamics and the thin-plate theory for the structural dynamics. The governing equations are matched at the juncture boundary and the resulting partial differential equations are solved by the boundary-integral-equation method, and the finite-difference method is used for discretizing the boundary conditions at the edges of the plate. The method devised here is proven to be very efficient in a parametric study of the hydroelastic response of a mat-type floating runway in regular, oblique waves. The main parameters varied in the problem are the stiffness, length and beam of the mat. The deflections of the mat are calculated for various incoming wave frequencies and heading angles in water of "shallow" depth. The results are compared with the available experimental data and numerical calculations by others. The mean drift loads on the mat are also calculated by following Maruo's far-field method.

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