scholarly journals Shear Current Effects on Monochromatic Water Waves Crossing Trenches

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Jun-Whan Lee ◽  
Koo-Yong Park ◽  
Yong-Sik Cho
Keyword(s):  
Water Waves ◽  
Expansion Method ◽  
Reflection Coefficients ◽  
Reflection And Transmission ◽  
Eigenfunction Expansion Method ◽  
Proper Number ◽  
Shear Current ◽  
Incident Wave Angle ◽  
Wave Angle ◽  
Resonant Reflection

The reflection coefficients of monochromatic water waves over trenches with shear current are estimated analytically. The diffraction of waves by an abrupt depth change and shear current is formulated by the matched eigenfunction expansion method. The proper number of steps and evanescent modes are proposed by a series of convergence tests. The accuracy of the predicted reflection coefficients is checked by estimating the wave energy. Reflection and transmission characteristics are studied for various shear current conditions. The different combinations of strength, width of shear current, and incident wave angle with constant water depth topography are examined. The optimal figure of the trench with shear current is obtained by estimating the reflection coefficients for various sloped transitions. The resonant reflection of the water waves is found by multiarrayed optimal trenches and the interaction of sinusoidally varying topography with shear current.

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.

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.

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.

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.

scholarly journals Theoretical Hydrodynamic Analysis of a Surface-Piercing Porous Cylindrical Body

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 320
Author(s):  
Dimitrios N. Konispoliatis ◽  
Ioannis K. Chatjigeorgiou ◽  
Spyridon A. Mavrakos
Keyword(s):  
Water Waves ◽  
Wave Attenuation ◽  
Three Dimensional ◽  
Cylindrical Body ◽  
Expansion Method ◽  
Wave Theory ◽  
Linear Wave ◽  
Wave Loads ◽  
Dimensional Solution ◽  
Eigenfunction Expansion Method

In the present study, the diffraction and the radiation problems of water waves by a surface-piercing porous cylindrical body are considered. The idea conceived is based on the capability of porous structures to dissipate the wave energy and to minimize the environmental impact, developing wave attenuation and protection. In the context of linear wave theory, a three-dimensional solution based on the eigenfunction expansion method is developed for the determination of the velocity potential of the flow field around the cylindrical body. Numerical results are presented and discussed concerning the wave elevation and the hydrodynamic forces on the examined body for various values of porosity coefficients. The results revealed that porosity plays a key role in reducing/controlling the wave loads on the structure and the wave run-up, hence porous barriers can be set up to protect a marine structure against wave attack.

Scattering of Water Waves by a Pair of Semi-Infinite Barriers

1975 ◽  
Vol 42 (4) ◽  
pp. 777-779 ◽  
Author(s):  
P. L.-F. Liu
Keyword(s):  
Transmission Coefficient ◽  
Incident Wave ◽  
Water Waves ◽  
Asymptotic Theory ◽  
Three Dimensional ◽  
Incident Wavelength ◽  
Water Motion ◽  
Incident Wave Angle ◽  
Progressive Waves ◽  
Wave Angle

Three-dimensional water waves are incident upon a pair of semi-infinite parallel vertical thin barriers. Assuming that the opening between the barriers is small compared with the incident wavelength, an asymptotic theory is developed for the resulting water motion. Between the barriers uniform progressive waves propagate into the channel. The transmission coefficient is found to be insensitive to the incident wave angle and the separation between the barriers.

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

Resonant reflection of surface water waves by periodic sandbars

1985 ◽  
Vol 152 ◽  
pp. 315-335 ◽  
Author(s):  
Chiang C. Mei
Keyword(s):  
Water Waves ◽  
Resonance Condition ◽  
Nonlinear Effects ◽  
Sea Bottom ◽  
Strong Reflection ◽  
Weak Reflection ◽  
Surface Water Waves ◽  
Wave Induced ◽  
Incident Waves ◽  
Resonant Reflection

One of the possible mechanisms of forming offshore sandbars parallel to a coast is the wave-induced mass transport in the boundary layer near the sea bottom. For this mechanism to be effective, sufficient reflection must be present so that the waves are partially standing. The main part of this paper is to explain a theory that strong reflection can be induced by the sandbars themselves, once the so-called Bragg resonance condition is met. For constant mean depth and simple harmonic waves this resonance has been studied by Davies (1982), whose theory, is however, limited to weak reflection and fails at resonance. Comparison of the strong reflection theory with Heathershaw's (1982) experiments is made. Furthermore, if the incident waves are slightly detuned or slowly modulated in time, the scattering process is found to depend critically on whether the modulational frequency lies above or below a threshold frequency. The effects of mean beach slope are also studied. In addition, it is found for periodically modulated wave groups that nonlinear effects can radiate long waves over the bars far beyond the reach of the short waves themselves. Finally it is argued that the breakpoint bar of ordinary size formed by plunging breakers can provide enough reflection to initiate the first few bars, thereby setting the stage for resonant reflection for more bars.

The Quasi-Static Analysis for Two-Dimensional Thin Plates

2011 ◽  
Vol 255-260 ◽  
pp. 166-169
Author(s):  
Li Chen ◽  
Yang Bai
Keyword(s):  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Solution Space ◽  
Expansion Method ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Elastic Plates ◽  
Various Boundary Conditions ◽  
Eigenfunction Expansion Method ◽  
Concentration Phenomena

The eigenfunction expansion method is introduced into the numerical calculations of elastic plates. Based on the variational method, all the fundamental solutions of the governing equations are obtained directly. Using eigenfunction expansion method, various boundary conditions can be conveniently described by the combination of the eigenfunctions due to the completeness of the solution space. The coefficients of the combination are determined by the boundary conditions. In the numerical example, the stress concentration phenomena produced by the restriction of displacement conditions is discussed in detail.

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