Analytical solutions for long waves on a circular island with combined topographies

Wave Motion ◽  
2012 ◽  
Vol 49 (1) ◽  
pp. 152-164 ◽  
Author(s):  
Tae-Hwa Jung ◽  
Changhoon Lee
Keyword(s):  
Analytical Solutions ◽  
Long Waves ◽  
Circular Island

Analytical solutions for long waves over a circular island

2010 ◽  
Vol 57 (4) ◽  
pp. 440-446 ◽  
Author(s):  
Tae-Hwa Jung ◽  
Changhoon Lee ◽  
Yong-Sik Cho
Keyword(s):  
Analytical Solutions ◽  
Long Waves ◽  
Circular Island

Drifting Force and Moment on Ships in Oblique Waves

1966 ◽  
Vol 10 (01) ◽  
pp. 18-24
Author(s):  
Pung Nien Hu ◽  
King Eng
Keyword(s):  
Potential Theory ◽  
General Expression ◽  
Phase Angle ◽  
Analytical Solutions ◽  
Vertical Axis ◽  
Long Waves ◽  
Elementary Functions ◽  
Oblique Waves ◽  
Side Force ◽  
Yaw Moment

A general expression for the drifting moment about the vertical axis of an oscillating ship in regular oblique waves is derived from the potential theory, following a similar procedure developed by Maruo for drifting force. Explicit analytical solutions for the drifting side force and yaw moment on thin ships in long waves are obtained in terms of simple elementary functions. The effect of the wave frequency, the draft of the ship, the displacement, and the phase angle of the ship oscillation are discussed.

Scattering of long waves around a circular island mounted on a conical shoal

Wave Motion ◽  
1996 ◽  
Vol 23 (4) ◽  
pp. 353-362 ◽  
Author(s):  
Songping Zhu ◽  
Yinglong Zhang
Keyword(s):  
Long Waves ◽  
Circular Island

scholarly journals Generation, Transformation, and Scattering of Long Waves Induced by a Short-Wave Group over Finite Topography

2011 ◽  
Vol 41 (10) ◽  
pp. 1842-1859 ◽  
Author(s):  
Qingping Zou
Keyword(s):  
Analytical Solutions ◽  
Wave Train ◽  
Short Wave ◽  
Long Waves ◽  
Wave Group ◽  
Wave Groups ◽  
Long Wave ◽  
Wave Orbital Velocity ◽  
Variable Water ◽  
Horizontal Bottom

Abstract Second-order analytical solutions are constructed for various long waves generated by a gravity wave train propagating over finite variable depth h(x) using a multiphase Wentzel–Kramers–Brillouin (WKB) method. It is found that, along with the well-known long wave, locked to the envelope of the wave train and traveling at the group velocity Cg, a forced long wave and free long waves are induced by the depth variation in this region. The forced long wave depends on the depth derivatives hx and hxx and travels at Cg, whereas the free long waves depend on h, hx, and hxx and travel in the opposite directions at . They interfere with each other and generate free long waves radiating away from this region. The author found that this topography-induced forced long wave is in quadrature with the short-wave group and that a secondary long-wave orbital velocity is generated by variable water depth, which is in quadrature with its horizontal bottom counterpart. Both these processes play an important role in the energy transfer between the short-wave groups and long waves. These behaviors were not revealed by previous studies on long waves induced by a wave group over finite topography, which calculated the total amplitude of long-wave components numerically without consideration of the phase of the long waves. The analytical solutions here also indicate that the discontinuity of hx and hxx at the topography junctions has a significant effect on the scattered long waves. The controlling factors for the amplitudes of these long waves are identified and the underlying physical processes systematically investigated in this presentation.

scholarly journals An Extended Analytic Solution of Combined Refraction and Diffraction of Long Waves Propagating over Circular Island

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yu-Shu Kuo ◽  
Tai-Wen Hsu ◽  
Chia-Cheng Tsai ◽  
Yu-Hsuan Huang
Keyword(s):  
Wave Scattering ◽  
Analytic Solution ◽  
Complex Variables ◽  
Long Waves ◽  
Wave Refraction ◽  
Long Wave ◽  
Present Solution ◽  
Circular Island ◽  
Frobenius Series ◽  
Independent Parameters

An analytic solution of long waves scattering by a cylindrical island mounted on a permeable circular shoal was obtained by solving the linear long wave equation (LWE). The solution is in terms of the Bessel function expressed by complex variables. The present solution is suitable for arbitrary bottom configurations described by a power function with two independent parameters. For the case of the paraboloidal shoal, there exists a singular point (α=2) which can be removed using Frobenius series, whereαis a real constant. The present solution is reduced to Yu and Zhang’s (2003) solution for impermeable circular shoal. The numerical results show some special features of the combined effect of wave refraction and diffraction caused by a porous circular island. The effect of key parameters of the island dimension, the shoal slope, and permeability on wave scattering was discussed based on the analytic solution.

Analytical solutions for forced long waves on a sloping beach

2003 ◽  
Vol 478 ◽  
pp. 101-109 ◽  
Author(s):  
PHILIP L.-F. LIU ◽  
PATRICK LYNETT ◽  
COSTAS E. SYNOLAKIS
Keyword(s):  
Analytical Solutions ◽  
Atmospheric Pressure ◽  
Numerical Solutions ◽  
Shallow Water Equation ◽  
Analytic Solutions ◽  
Long Waves ◽  
Unknown Variable ◽  
Pressure Distributions ◽  
Forcing Function ◽  
Sloping Beach

We derive analytic solutions for the forced linear shallow water equation of the following form:<?TeX \partial^2 Y \over \partial t^2}-b{\partial \over \partial x}\left(x {\partial Y \over \partial x}\right)={\partial^2 f\over \partial t^2 ?>for x>0, in which Y(x,t) denotes an unknown variable, f(x,t) a prescribed forcing function and b a positive constant. This equation has been used to describe landslide-generated tsunamis and also long waves induced by moving atmospheric pressure distributions. We discuss particular and general solutions. We then compare our results with numerical solutions of the same equation and with the corresponding solutions of the nonlinear depth-integrated equations and discuss them in terms of landslide-generated tsunamis.

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