The Motions of a Ship on a Sloped Seabed

2006 ◽  
Author(s):  
Bas Buchner
Keyword(s):  
Water Depth ◽  
Diffraction Theory ◽  
Added Mass ◽  
Interference Effects ◽  
Large Size ◽  
Correct Calculation ◽  
Exciting Forces ◽  
Wave Exciting Forces ◽  
Local Water ◽  
Drift Forces

In standard diffraction theory it is assumed that the water depth is constant and that the seabed is infinitely large. To account for a local varying bathymetry in shallow water (as it can occur for offshore LNG terminals) it is sometimes considered to introduce a second fixed body on the seabed representing this bathymetry in diffraction theory. Based on the results presented in this paper it can be concluded that this is (without special measures) not possible. The refraction and interference effects are too strong and affect the wave exciting forces on the LNG carrier in an incorrect way. A large size of the second body and smoother edges of this body do not improve the situation. However, a second body in diffraction theory, when chosen properly with respect to size and shape, can contribute to the correct calculation of the added mass and damping of vessels on sloped seabeds as this varies with the local water depth over the length of the vessel. This will clearly affect the motion response of the vessel. This can be seen for instance in the pitch-heave coupling. This will influence the motions of the ship in waves, as well as the resulting drift forces and related mooring loads.

Parametric Study of Mooring Lines on a Small Buoy

2003 ◽  
Author(s):  
Quanming Miao ◽  
Jinzhu Xia
Keyword(s):  
Mooring Line ◽  
Diffraction Radiation ◽  
Hydrodynamic Coefficients ◽  
Analysis Method ◽  
Mooring Lines ◽  
Slow Drift ◽  
Radiation Theory ◽  
Exciting Forces ◽  
Wave Exciting Forces ◽  
Drift Forces

A shallow-draft cylindrical buoy and mooring lines comprise an integrated dynamic system responding to environmental loading due to wind, current and waves in a complex way. In this paper, a time-domain decoupled buoy motion analysis method will be applied to study numerically the effect of the length, pre-tension and coordinates of attached points of the mooring lines on the motions of the buoy and the loads of the mooring lines. The wind and the current speeds are assumed to be constant and the wind and current forces are estimated from empirical formulations. The hydrodynamic coefficients, wave exciting forces and slow drift forces of the buoy are obtained from the 3D diffraction-radiation theory. The numerical results show how the length of the mooring line influences the maximum mooring loads at severe sea. The results also quantitatively show how the pre-tension and the coordinates of attached point of the mooring lines affect the motions and loads of the moored system.

Theory of Short Wave Excitation

1986 ◽  
Vol 30 (03) ◽  
pp. 147-152
Author(s):  
Yong Kwun Chung
Keyword(s):  
Incident Wave ◽  
Characteristic Length ◽  
Finite Depth ◽  
Short Wave ◽  
The Body ◽  
Wave Number ◽  
Floating Body ◽  
Wave Excitation ◽  
Exciting Forces ◽  
Wave Exciting Forces

When the wavelength of the incident wave is short, the total surface potential on a floating body is found to be 2∅ i & O (m-l∅ i) on the lit surface and O (m-l∅ j) on the shadow surface where ~b i is the potential of the incident wave and m the wave number in water of finite depth. The present approximation for wave exciting forces and moments is reasonably good up to X/L ∅ 1 where h is the wavelength and L the characteristic length of the body.

scholarly journals Wave Exciting Forces on Groups of Floating Bodies

1979 ◽  
Vol 1979 (145) ◽  
pp. 79-87 ◽  
Author(s):  
Akira Masumoto ◽  
Yoshio Yamagami ◽  
Ryuji Sakata
Keyword(s):  
Floating Bodies ◽  
Exciting Forces ◽  
Wave Exciting Forces

On the Radiation and Diffraction of Surface Waves by Submerged Spheroids

1989 ◽  
Vol 33 (02) ◽  
pp. 84-92
Author(s):  
G. X. Wu ◽  
R. Eatock Taylor
Keyword(s):  
Degrees Of Freedom ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Added Mass ◽  
Wave Radiation ◽  
Legendre Functions ◽  
Incoming Wave ◽  
Six Degrees Of Freedom ◽  
Damping Coefficients ◽  
Exciting Forces

The problem of wave radiation and diffraction by submerged spheroids is analyzed using linearized three-dimensional potential-flow theory. The solution is obtained by expanding the velocity potential into a series of Legendre functions in a spheroidal coordinate system. Tabulated and graphical results are provided for added mass and damping coefficients of various spheroids undergoing motions in six degrees of freedom. Graphs are also provided for exciting forces and moments corresponding to a range of incoming wave angles.

Ship Motions in Shallow Water

1970 ◽  
Vol 14 (04) ◽  
pp. 317-328 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Incident Wave ◽  
Degrees Of Freedom ◽  
Added Mass ◽  
Exciting Force ◽  
Ship Motions ◽  
Wave System ◽  
Six Degrees Of Freedom ◽  
Damping Coefficients

The problem discussed concerns small motions of a ship, in all six degrees of freedom, but at zero speed of advance, due to an incident wave system in shallow water of depth comparable with the ship's draft. The problem is completely formulated for an arbitrary ship, and is partially solved for the case when the ship is slender and the wavelength much greater than the water depth. Sample numerical computations of heave, pitch, and sway added mass and damping coefficients and the sway exciting force are presented.

Experimental Investigation of the First and Second Order Wave Exciting Forces on a Restrained Body in Long Crested Irregular Waves

2011 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
Suresh Rajendran ◽  
C. Guedes Soares
Keyword(s):  
Experimental Investigation ◽  
Transfer Functions ◽  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Irregular Waves ◽  
Numerical Predictions ◽  
Exciting Forces ◽  
Wave Exciting Forces

The paper presents an experimental investigation of the first order and second order wave exciting forces acting on a body of simple geometry subjected to long crested irregular waves. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is restrained from moving. Second order spectral analysis is applied to obtain the linear spectra, coherence spectra and cross bi-spectra of both the incident wave elevation and of the horizontal and vertical wave exciting forces. Then the linear and quadratic transfer functions (QTF) of the exciting forces are obtained. The QTF obtained from the analysis of irregular wave measurements are compared with results from experiments in bi-chromatic waves and with numerical predictions from a second order potential flow code.

The Effect of Wave Directionality on Low Frequency Motions and Mooring Forces

2009 ◽  
Author(s):  
Olaf J. Waals
Keyword(s):  
Water Depth ◽  
Transfer Functions ◽  
Low Frequency ◽  
Sensitivity Study ◽  
Wave Loads ◽  
Offshore Structure ◽  
Frequency Wave ◽  
Drift Theory ◽  
Mooring Forces ◽  
Drift Forces

Operability of offshore moored ships can be affected by low frequency wave loads. The low frequency motions of a moored ship may limit the uptime of an offshore structure such as an LNG offloading terminal. The wave loads that cause the main excitation of these low frequency motions are usually computed using second order wave drift theory for long crested waves, which assumes that the low frequency components are only related to waves coming from the same direction. In this method short crested seas are dealt with as a summation of long crested seas, but no interaction between the wave components traveling in different directions is usually taken into account. This paper describes the results of a study to the effect of 2nd order low frequency wave loads in directional seas. For this study the drift forces related to the interaction between waves coming from different directions is also included. This is done by computing the quadratic transfer functions (QTF) for all possible combinations of wave components (frequencies and directions). Time traces of drift forces are generated and compared to the results without wave directional interaction after which the motions of an LNG carrier are simulated. A sensitivity study is carried out towards the number of direction steps and the water depth. Finally the motions of an LNG carrier in shallow water (15m water depth) are simulated and mooring forces are compared for various amounts of wave spreading.

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