scholarly journals POLYNOMIAL APPROXIMATION AND WATER WAVES

1986 ◽  
Vol 1 (20) ◽  
pp. 15 ◽  
Author(s):  
John D. Fenton
Keyword(s):  
Polynomial Approximation ◽  
Water Waves ◽  
Three Dimensional ◽  
Wave Theory ◽  
General Nature ◽  
Linear Wave ◽  
Wave Refraction ◽  
Approximate Wave ◽  
Spatial Approximation ◽  
Wave Problems

A different approach to the solution of water wave problems is considered. Instead of using an approximate wave theory combined with highly accurate global spatial approximation methods, as for example in many applications of linear wave theory, a method is developed which uses local polynomial approximation combined with the full nonlinear equations. The method is applied to the problem of inferring wave properties from the record of a pressure transducer, and is found to be capable of high accuracy for waves which are not too short, even for large amplitude waves. The general approach of polynomial approximation is well suited to problems of a rather more general nature, especially where the geometry is at all complicated. It may prove useful in other areas, such as the nonlinear interaction of long waves, shoaling of waves, and in three dimensional problems, such as nonlinear wave refraction and diffraction.

scholarly journals REFRACTION OF FINITE-HEIGHT AND BREAKING WAVES

1976 ◽  
Vol 1 (15) ◽  
pp. 28 ◽  
Author(s):  
James R. Walker
Keyword(s):  
Three Dimensional ◽  
Wave Theory ◽  
Breaking Waves ◽  
Finite Amplitude ◽  
Primary Objective ◽  
Test Series ◽  
Data Sets ◽  
Linear Wave ◽  
Wave Refraction ◽  
Wave Shoaling

The primary objective of this study was to ascertain the influence of wave height and breaking on wave refraction over a three-dimensional shoal. The subject wave transformations were studied in an hydraulic model. Wave shoaling, decay in the breaker zone, and phase velocities were analyzed in a base test series over a bottom slope of 1:30. A second test series was conducted over a three-dimensional shoal. Wave patterns were photographed and wave heights and celerities were measured. The measurements were compared with wave refraction patterns and coefficients computed by analytical methods. Wave shoaling observed over the constant 1:30 slope was 25 percent greater than predicted by Airy theory at the breaking point for wave steepness H0/L0=.030 and 50 percent greater than predicted for H0/Lo = •002. Shoaling measurements were compared with other empirical data sets, confirming the inadequacy of commonly used practice using linear wave theory near the breaker zone. The celerity measurements indicated that the non-breaking celerity was given by C = (1+.25 H/d)Ca, where Ca is the Airy celerity. The discussion and results give a basic understanding of wave refraction near the breaker zone, supplementing analytical papers on refraction procedures using finite amplitude wave theories.

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.

Dynamic Response of a Porous Seabed and an Offshore Pile to Linear Water Waves

2008 ◽  
Author(s):  
Jian-Fei Lu ◽  
Dong-Sheng Jeng
Keyword(s):  
Dynamic Response ◽  
Water Waves ◽  
Coupled Model ◽  
Expansion Method ◽  
Wave Theory ◽  
Horizontal Displacement ◽  
Element Model ◽  
Wave Force ◽  
Acoustic Medium ◽  
Linear Wave

In this study, a coupled model is proposed to investigate dynamic response of a porous seabed and an offshore pile to ocean wave loadings. Both the offshore pile and the porous seabed are treated as a saturated poro-elastic medium, while the seawater is considered as a conventional acoustic medium. The coupled boundary element model is established by the continuity conditions along the interfaces between the three media. In the system, wave force is considered as an external load and it is evaluated via the wave function expansion method in the context of a linear wave theory. Numerical results show that the increase of the modulus ratio between the pile and the seabed can reduce the horizontal displacement of the pile and the pore pressures of the seabed around the pile. Furthermore, the maximum pore pressure of the seabed usually occurs at the upper part of the seabed around the pile.

Hydroelastic Response of Floating Fuel Storage Modules Placed Side-by-Side

2008 ◽  
Author(s):  
Z. Y. Tay ◽  
C. M. Wang
Keyword(s):  
Numerical Model ◽  
Water Waves ◽  
Plate Theory ◽  
Experimental Tests ◽  
Wave Theory ◽  
Mindlin Plate ◽  
Linear Wave ◽  
Plate Element ◽  
Fuel Storage ◽  
Hydroelastic Response

Presented herein are the hydroelastic responses of two large box-like floating modules that are placed adjacent to each other. These two floating modules form the floating fuel storage facility (FFSF). Owing to the small draft when compared to the length dimensions, the zero-draft assumption is commonly adopted in the modeling of very large floating structures (VLFS) as plates for hydroelastic analysis. However, such an assumption is not applicable to the considered floating modules since the effect of draft on the hydroelastic response is significant when the modules are loaded with fuel. A numerical model taking into account the draft effect is hence developed in order to predict correctly the hydroelastic response and hydrodynamic interactions of floating storage modules placed side-by-side. The floating storage modules are modeled as plates where an improved Mindlin plate element, developed by coupling the reduced integration method and the additional non-conforming modes, is used. Such a plate element does not exhibit spurious modes and shear locking phenomena, thereby making it applicable to both thin and thick plate models. Furthermore, the Mindlin plate theory predicts better stress resultants as compared with its Kirchhoff plate counterpart. The linear wave theory is used to model the water waves. The wave-induced deflections obtained from the numerical model are validated by experimental tests.

scholarly journals Asymptotic expansion of integrals occurring in linear wave theory

1972 ◽  
Vol 7 (1) ◽  
pp. 121-130 ◽  
Author(s):  
P. van den Driessche ◽  
R.D. Braddock
Keyword(s):  
Asymptotic Expansion ◽  
Stationary Phase ◽  
Wave Theory ◽  
Linear Wave ◽  
Phase Point ◽  
One Dimensional ◽  
Special Cases ◽  
Order Of Magnitude ◽  
Leading Term ◽  
Wave Problems

The asymptotic expansion of an integral of the type , is derived in terms of the large parameter t. Functions Φ(k) and ψ(k) are assumed analytic, and ψ(k) may have zeros at a stationary phase point. The usual one dimensional stationary phase and Airy integral terms are found as special cases of a more general result. The result is used to find the leading term of the asymptotic expansion of the double integral. A particular two dimensional Φ(k) relevant to surface water wave problems is considered in detail, and the order of magnitude of the integral is shown to depend on the nature of ψ(k) at the stationary phase point.

Eigenmodes in the water-wave problems for infinite pools with cone-shaped bottom

2016 ◽  
Vol 800 ◽  
pp. 645-665 ◽  
Author(s):  
Mikhail A. Lyalinov
Keyword(s):  
Water Waves ◽  
Mellin Transform ◽  
Point Spectrum ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Functional Difference ◽  
Infinite Domains ◽  
Linearized Theory ◽  
Functional Difference Equations ◽  
Wave Problems

In the framework of the assumptions of the linearized theory of small-amplitude water waves, the eigenfunctions of the point spectrum are studied for boundary-value problems in infinite domains. Special types of three-dimensional infinite water pools characterised by cone-shaped bottoms are considered. By means of an incomplete separation of variables and exploiting the Mellin transform, we reduce construction of the eigenmodes to the study and solution of the problems for some functional difference equations with meromorphic coefficients. The behaviour of the eigenmodes at a singular point of the boundary and the rate of their decay at infinity are also examined.

scholarly journals Three Dimensional Radiated Water Wave with a Submerged Cylinder in Presence of Circular Plate

2019 ◽  
Vol 9 (1) ◽  
pp. 6665-6670
Keyword(s):  
Separation Of Variables ◽  
Surface Condition ◽  
Three Dimensional ◽  
Wave Interaction ◽  
Wave Theory ◽  
Linear Wave ◽  
Energy Device ◽  
Linear Wave Theory ◽  
Bernoulli’S Equation ◽  
Submerged Cylinder

This work deals with the problem of radiated by wave interaction with a couple of submerged cylinders in water which can be considered as a wave energy device and the problem arising from the rotational motion of submerged upper cylinder which one contains in the device. In this work, we approach theoretically to solve the problem based on the method of separation of variables and we derive the radiated velocity potentials numerically based on linear wave theory and eigenfunctions are introduced for each region by using free surface condition. Then we calculate the hydrodynamic coefficients due to rotational of the upper cylinder by using Bernoulli’s equation of pressure by neglecting the atmospheric pressure and unknown constants are calculate by using matched conditions between the regions Finally, we present all numerical results graphically for different radii of the cylinders

A direct method for Bloch wave excitation by scattering at the edge of a lattice. Part II: Finite size effects

2019 ◽  
Vol 72 (3) ◽  
pp. 387-414
Author(s):  
R I Brougham ◽  
I Thompson
Keyword(s):  
Size Effects ◽  
Water Waves ◽  
Direct Method ◽  
Finite Size ◽  
Wave Theory ◽  
Bloch Wave ◽  
General Context ◽  
Linear Wave ◽  
Finite Size Effects ◽  
Scatterer Size

Summary A method for determining the reflection and transmission properties of a periodic structure occupying a half-space, previously developed for lattices formed from point scatterers, is generalized to allow for finite size effects. This facilitates the consideration of much higher frequencies (or more precisely, much higher scatterer size to wavelength ratios), and also a wider range of boundary conditions. The method is presented in a general context of linear wave theory, and physical interpretations are given for acoustics, elasticity, electromagnetism and water waves.

In-Line Forces on Vertical Cylinders in Deepwater Waves

1985 ◽  
Vol 107 (1) ◽  
pp. 18-23
Author(s):  
T. H. Dawson
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Wave Theory ◽  
Stokes Wave ◽  
Wave Forces ◽  
Linear Wave ◽  
Random Waves ◽  
Morison Equation ◽  
Circular Particle ◽  
Wave Cycle

Laboratory measurements of the total in-line forces on a fixed vertical 2-in-dia cylinder in deep-water regular and random waves are given and compared with predictions from the Morison equation. Results show, for regular waves with heights ranging from 2 to 22 in. and frequencies ranging from 0.4 to 0.9 Hz that the Morison equation, with Stokes wave theory and constant drag and inertia coefficients of 1.2 and 1.8, respectively, provides good agreement with the measured maximum wave forces. The force variation over the entire wave cycle is also well represented. The linearized Morison equation, with linear wave theory and the same coefficients likewise provides close agreement with the measured rms wave forces for irregular random waves having approximate Bretschneider spectra and significant wave heights from 5 to 14 in. The success of the constant-coefficient approximation is attributed to a decreased dependence of the coefficients on dimensionless flow parameters as a result of the circular particle motions and large kinematic gradients of the deep-water waves.

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