有限深水中骑行波的显式Hamilton描述

小尺度波(扰动波)迭加在大尺度波(未受扰动波)上形成的波动一般称之为“骑行波”。研究了有限可变深度的理想不可压缩流体中的骑行波的显式Hamilton表示,考虑了自由面上流体与空气之间的表面张力。采用自由面高度和自由面上速度势构成的Hamilton正则变量表示骑行波的动能密度,并在未受扰动波的自由面上作一阶展开。运用复变函数论方法处理了二维流动。先用保角变换将物理平面上的流动区域交换到复势平面上的无限长带形区域,然后在复势平面上用Fourier变换解出Laplace方程,最后经Fourier逆变换求出了扰动波速度势所满足的积分方程。作为特例考虑了平坦底部的流动,导出了动能密度的显式表达式。这里给出的积分方程可以替代相当难解的Hamilton正则方程。通过求解积分方程可得出Lagrange密度的显式表达式。本文提出的方法为研究骑行波的Hamilton描述以及波的相互作用问题提供了新的途径,有助于了解海面的小尺度波的精细结构。

水波与双重不同竖直刚性薄板相互作用的理论研究

基于势流理论和线性水波理论,应用匹配特征函数展开法和最小二乘法,对正向波与双重不同竖直刚性薄板在有限均匀深水中的相互作用进行了理论研究,并给出了解析解.分析了两板吃水比、后板吃水、两板间距等结构因素对反射系数和水平波浪力的影响规律.

Scattering of Surface Water Waves Involving Semi-infinite Floating Elastic Plates on Water of Finite Depth

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Exciting Forces for a Wave Energy Device Consisting of a Pair of Coaxial Cylinders in Water of Finite Depth

Two coaxial vertical cylinders-one is a riding hollow cylinder and the other a solid cylinder of greater radius at some distance above an impermeable horizontal bottom,were considered.This problem of diffraction by these two cylinders,which were considered as idealization of a buoy and a circular plate,can be considered as a wave energy device.The wave energy that is created and transferred by this device can be appropriately used in many applications in lieu of conventional energy.Method of separation of variables was used to obtain the analytical expressions for the diffracted potentials in four clearly identified regions.By applying the appropriate matching conditions along the three virtual boundaries between the regions,a system of linear equations was obtained,which was solved for the unknown coefficients.The potentials allowed us to obtain the exciting forces acting on both cylinders.Sets of exciting forces were obtained for different radii of the cylinders and for different gaps between the cylinders.It was observed that changes in radius and the gap had significant effect on the forces.It was found that mostly the exciting forces were significant only at lower frequencies.The exciting forces almost vanished at higher frequencies.The problem was also investigated for the base case of no plate arrangement,i.e.,the case having only the floating cylinder tethered to the sea-bed.Comparison of forces for both arrangements was carried out.In order to take care of the radiation of the cylinders due to surge motion,the corresponding added mass and the damping coefficients for both cylinders were also computed.All the results were depicted graphically and compared with available results.

Influence of Wave Breaking on Wave Statistics for Finite-Depth Random Wave Trains

The influence of wave breaking on wave statistics for finite-depth random wave trains is investigated experimentally. This paper is to investigate the influence of wave breaking and water depth on the wave statistics for random waves on water of finite depth. Greater attention is paid to changes in wave statistics due to wave breaking in random wave trains. The results show skewness of surface elevations is independent of wave breaking and kurtosis is suppressed by wave breaking. Finally, the exceedance probabilities for wave heights are also investigated.

Oblique Wave-free Potentials for Water Waves in Constant Finite Depth

In this paper, a method to construct oblique wave-free potentials in the linearised theory of water waves for water with uniform finite depth is presented in a systematic manner. The water has either a free surface or an ice-cover modelled as a thin elastic plate. For the case of free surface, the effect of surface tension may be neglected or taken into account. Here, the wave-free potentials are singular solutions of the modified Helmholtz equation, having singularity at a point in the fluid region and they satisfy the conditions at the upper surface and the bottom of water region and decay rapidly away from the point of singularity. These are useful in obtaining solutions to oblique water wave problems involving bodies with circular cross-sections such as long horizontal cylinders submerged or half-immersed in water of uniform fmite depth with a free surface or an ice-cover modelled as a floating elastic plate. Finally, the forms of the upper surface related to the wave-free potentials constructed here are depicted graphically in a number of figures to visualize the wave motion. The results for non-oblique wave-free potentials and the upper surface wave-free potentials are obtained. The wave-free potentials constructed here will be useful in the mathematical study of water wave problems involving infinitely long horizontal cylinders, either half-immersed or completely immersed in water.

Effect of Bottom Undulation on the Waves Generated Due to Rolling of a Plate

In the present paper, the effect of a small bottom tmdulation of the sea bed in the form of periodic bed form on the surface waves generated due to a rolling oscillation of a vertical barrier either partially immersed or completely submerged in water of non uniform finite depth is investigated. A simplified perturbation technique involving a non dimensional parameter characterizing the smallness of the bottom deformation is applied to reduce the given boundary value problem to two independent boundary value problems upto first order. The first boundary value problem corresponds to the problem of water wave generation due to rolling oscillation of a vertical barrier either partially immersed or completely submerged in water of uniform finite depth. This is a well known problem whose solution is available in the literature. From the second boundary value problem, the first order correction to the wave amplitude at infinity is evaluated in terms of the shape function characterizing the bottom undulation, by employing Green＇s integral theorem. For a patch of sinusoidal ripples at the sea bottom, the first order correction to the wave amplitude at infinity for both the configuration of the barrier is then evaluated numerically and illustrated graphically for various values of the wave number. It is observed that resonant interaction of the wave generated, with the sinusoidal bottom undulation occurs when the ratio of twice the wavelength of the sinusoidal ripple to the wave length of waves generated, approaches unity. Also it is found that the resonance increases as the length of the barrier increases.