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 Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

Second-Order Diffraction Loads on Plural Vertical Cylinder With Arbitrary Cross Sections

1987 ◽  
Vol 109 (4) ◽  
pp. 314-319
Author(s):  
K. Masuda ◽  
W. Kato ◽  
H. Ishizuka
Keyword(s):  
Boundary Value Problem ◽  
Cross Sections ◽  
Present Method ◽  
Boundary Value ◽  
Vertical Cylinder ◽  
Wave Force ◽  
Second Order ◽  
Wave Forces ◽  
Order Diffraction ◽  
Rectangular Cylinders

The purpose of the present study is development of a powerful numerical method for calculating second-order diffraction loads on plural vertical cylinder with arbitrary cross sections. According to the present method, second-order wave force can be obtained from a linear radiation potential without solving second-order boundary value problem. The boundary value problem for the radiation potential is solved with the hybrid boundary element method. The computations for circular and rectangular cylinders were carried out and compared with the experiments. In addition, second-order wave forces on twin circular cylinder are calculated with the present method.

The transmission of surface waves under surface obstacles

1961 ◽  
Vol 57 (3) ◽  
pp. 638-668 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Transmission Coefficient ◽  
Cross Section ◽  
Water Waves ◽  
Wave Train ◽  
Circular Cross Section ◽  
Great Distance ◽  
The Body ◽  
Radius Of Curvature

ABSTRACTA train of surface waves (water waves under gravity) is normally incident on a cylinder with horizontal generators fixed near the free surface, and is partially transmitted and partially reflected. At a great distance behind the cylinder the wave motion tends to a regular wave train travelling towards infinity; the ratio of its amplitude to the amplitude of the incident wave is the transmission coefficient . The transmission coefficient is studied when the wavelength is short compared to the dimensions of the body; physically (though not for engineering applications) this is the most interesting range of wavelengths, which corresponds to the range of shadow formation and ray propagation in optics and acoustics. The waves are then confined to a thin layer near the free surface, and the transmission under a partially immersed obstacle is then small. In the calculation the boundary condition at the free surface is linearized, viscosity is neglected, and the motion is assumed to be irrotational.At present the transmission coefficient is known only for a few configurations, all of them relating to infinitely thin plane barriers. A method is now given which is applicable to cylinders of finite cross-section and which is worked out in detail for a half-immersed cylinder of circular cross-section. The solution of the problem is made to depend on the solution of an integral equation which is solved by iteration. Only the first two terms can be obtained with any accuracy, and it appears at first that this is not sufficient to give the leading term in the transmission coefficient at short wavelengths; this difficulty is characteristic of transmission problems. By various mathematical devices which throw light on the mechanism of wave transmission, it is, nevertheless, found possible to prove that the transmission coefficient for waves of short wavelength λ and period 2π/ω incident on a half-immersed circular cylinder of radius a is asymptotically given bywhen N = 2πα/λ = ω2α/g is large. Earlier evidence had pointed towards an exponential law. It is suggested that transmission coefficients of order N−4 are typical for obstacles having vertical tangents and finite non-zero radius of curvature at the points where they meet the horizontal mean free surface. For obstacles having both front and rear face plane vertical to a depth a, is probably of order e−2N approximately; if only one of the two faces is plane vertical, is probably of order e−N approximately. Thus is seen to depend critically on the details of the cross-section.

On higher-order wave theory for submerged two-dimensional bodies

1969 ◽  
Vol 38 (2) ◽  
pp. 415-432 ◽  
Author(s):  
Nils Salvesen
Keyword(s):  
Free Surface ◽  
Wave Theory ◽  
Order Theory ◽  
Wave Drag ◽  
Higher Order ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
Free Surface Waves ◽  
Body Shapes

The importance of non-linear free-surface effects on potential flow past two-dimensional submerged bodies is investigated by the use of higher-order perturbation theory. A consistent second-order solution for general body shapes is derived. A comparison between experimental data and theory is presented for the free-surface waves and for the wave resistance of a foil-shaped body. The agreement is good in general for the second-order theory, while the linear theory is shown to be inadequate for predicting the wave drag at the relatively small submergence treated here. It is also shown, by including the third-order freesurface effects, how the solution to the general wave theory breaks down at low speeds.

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.

Comments on Second-Order Wave Effects on Large-Diameter Vertical Cylinder

1978 ◽  
Vol 22 (04) ◽  
pp. 266-268
Author(s):  
Subrata K. Chakrabarti
Keyword(s):  
Free Surface ◽  
Large Diameter ◽  
Vertical Cylinder ◽  
Wave Interaction ◽  
Scattered Wave ◽  
Second Order ◽  
Surface Boundary ◽  
Order Solution ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Conditions

In a recent paper, Raman et al (RJV) [1] 2 presented a second- order solution for the wave interaction with a large-diameter, bottom-mounted, surface-piercing, fixed vertical cylinder. Earlier, Chakrabarti [2,3] obtained an approximate solution for the vertical cylinder due to Stokes's fifth-order wave. Later, Yamaguchi and Tsuchiya (YT) [4] proposed a second-order solution in a closed form for the wave interaction problem with the vertical cylinder which was examined by Chakrabarti [5]. All these solutions are different due to the assumptions regarding the frequency of the scattered wave and the kinematic free-surface boundary condition. RJV [1] claim that their solution is superior to the earlier solutions because, according to them, it satisfies the nonlinear free-surface boundary conditions completely.

Sign in / Sign up

Export Citation Format

Share Document