Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

2008 ◽  
Vol 40 (4) ◽  
pp. 253-272 ◽  
Author(s):  
Dilip Das ◽  
B N Mandal ◽  
A Chakrabarti
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Water Wave ◽  
Wave Theory ◽  
Higher Order ◽  
Surface Boundary ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition

scholarly journals GENERALIZED WAVE THEORY FOR A SLOPING BED

1988 ◽  
Vol 1 (21) ◽  
pp. 12 ◽  
Author(s):  
D.H. Swart ◽  
J.B. Crowley
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Wave Theory ◽  
Breaking Waves ◽  
Surface Boundary ◽  
Data Set ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition ◽  
Horizontal Bottom ◽  
Sloping Bottom

This paper discusses the development from first principles of a first-order solution for non-breaking waves on a gently sloping bottom. The theory is derived in a similar fashion as was done by Swart and Loubser (1978) for vocoidal waves on a horizontal bottom. The resulting covocoidal theory was compared to an extensive data set for waves over a sloping bottom (Nelson, 1981) and is tested for analytical validity. It adheres exactly to continuity and the kinematic free surface boundary condition, and shows comparable errors in the dynamic free surface boundary condition to that found for the better, general horizontal bed wave theories.

scholarly journals On step approximations for water-wave problems

1994 ◽  
Vol 278 ◽  
pp. 229-249 ◽  
Author(s):  
D. V. Evans ◽  
C. M. Linton
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Water Waves ◽  
Water Wave ◽  
Matrix Theory ◽  
Bottom Topography ◽  
Surface Boundary ◽  
Scattering Problems ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition

The scattering of water waves by a varying bottom topography is considered using two-dimensional linear water-wave theory. A new approach is adopted in which the problem is first transformed into a uniform strip resulting in a variable free-surface boundary condition. This is then approximated by a finite number of sections on which the free-surface boundary condition is assumed to be constant. A transition matrix theory is developed which is used to relate the wave amplitudes at ±∞. The method is checked against examples for which the solution is known, or which can be computed by alternative means. Results show that the method provides a simple accurate technique for scattering problems of this type.

Coupled Dynamic Analysis of a Moored Spar Platform in Time Domain

2010 ◽  
Author(s):  
M. D. Yang ◽  
B. Teng
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Dynamic Analysis ◽  
Time Domain ◽  
Surface Boundary ◽  
Spar Platform ◽  
Mooring Lines ◽  
Coupled Dynamic Analysis ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition

A time-domain simulation method is developed for the coupled dynamic analysis of a spar platform with mooring lines. For the hydrodynamic loads, a time domain second order method is developed. In this approach, Taylor series expansions are applied to the body surface boundary condition and the free surface boundary condition, and Stokes perturbation procedure is then used to establish corresponding boundary value problems with time-independent boundaries. A higher order boundary element method is developed to calculate the velocity potential of the resulting flow field at each time step. The free-surface boundary condition is satisfied to the second order by 4th order Adams-Bashforth-Moultn method. An artificial damping layer is adopted on the free surface to avoid the wave reflection. For the mooring-line dynamics, a geometrically nonlinear finite element method using isoparametric cable element based on the total Lagrangian formulation is developed. In the coupled dynamic analysis, the motion equation for the hull and dynamic equations for mooring lines are solved simultaneously using Newmark method. Numerical results including motions and tensions in the mooring lines are presented.

scholarly journals Free-Surface Effects on Interaction of Multiple Ships Moving at Different Speeds

2019 ◽  
Vol 63 (4) ◽  
pp. 251-267 ◽  
Author(s):  
Zhi-Ming Yuan ◽  
Liang Li ◽  
Ronald W. Yeung
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Present Article ◽  
Hydrodynamic Interaction ◽  
Surface Effects ◽  
Superposition Method ◽  
Surface Boundary ◽  
Gravitational Acceleration ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition

Ships often have to pass each other in proximity in harbor areas and waterways in dense shipping-traffic environment. Hydrodynamic interaction occurs when a ship is overtaking (or being overtaken) or encountering other ships. Such an interactive effect could be magnified in confined waterways, e.g., shallow and narrow rivers. Since Yeung published his initial work on ship interaction in shallow water, progress on unsteady interaction among multiple ships has been slow, though steady, over the following decades. With some exceptions, nearly all the published studies on ship-to-ship problem neglected free-surface effects, and a rigid-wall condition has often been applied on the water surface as the boundary condition. When the speed of the ships is low, this assumption is reasonably accurate as the hydrodynamic interaction is mainly induced by near-field disturbances. However, in many maneuvering operations, the encountering or overtaking speeds are actually moderately high (Froude number Fn > 0.2, where <inline-graphic xlink:href="josr10180089inf1.tif"/>, U is ship speed, g is the gravitational acceleration, and L is the ship length), especially when the lateral separation between ships is the order of ship length. Here, the far-field effects arising from ship waves can be important. The hydrodynamic interaction model must take into account the surface-wave effects. Classical potential-flow formulation is only able to deal with the boundary value problem when there is only one speed involved in the free-surface boundary condition. For multiple ships traveling with different speeds, it is not possible to express the free-surface boundary condition by a single velocity potential. Instead, a superposition method can be applied to account for the velocity field induced by each vessel with its own and unique speed. The main objective of the present article is to propose a rational superposition method to handle the unsteady free-surface boundary condition containing two or more speed terms, and validate its feasibility in predicting the hydrodynamic behavior in ship encountering. The methodology used in the present article is a three-dimensional boundary-element method based on a Rankine-type (infinite-space) source function, initially introduced by Bai and Yeung. The numerical simulations are conducted by using an in-house‐developed multibody hydrodynamic interaction program “MHydro.” Waves generated and forces (or moments) are calculated when ships are encountering or passing each other. Published model-test results are used to validate our calculations, and very good agreement has been observed. The numerical results show that free-surface effects need to be taken into account for Fn > 0.2.

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