Probability distribution of surface slope for nonlinear random sea waves and calculation of whitecap coverage

Based on the nonlinear model of two-dimensional random sea waves, a statistical distribution of wave surface slope exact to the third order is derived by using the expansion of the characteristic function and direct calculations of each order moment. Based on the distribution of wave surface slope derived in this paper, a whitecap coverage is proposed by using the limit surface slope as a criterion of wave breaking. The whitecap coverage expressed by the model depends on three parameters which can be determined in principle by the linear wave spectrum and three kinds of wave-wave interaction.     

Analysis of single and tandem cylinder data using an orthogonal Volterra model approach

The development of a definitive predictive model that accurately accounts for the nonlinear hydrodynamics and structural response behavior observed in arrays of closely spaced risers on deep water structures will require a more detailed understanding of this fluid–structure interaction. Through the analysis and interpretation of data from model basin tests on single and paired tandem cylinder configurations this study is directed at uncovering the nature of some aspects of this nonlinear response behavior using an orthogonal third-order Volterra technique that can delineate between linear, quadratic and cubic nonlinear frequency dependent behavior. As part of the analysis procedure the data was organized in input–output pairs that would provide logical groupings of the measured quantities. The data pairs presented in this study include wave excitation and inline cylinder displacement, wave excitation and transverse cylinder displacement, wave excitation and inline reaction force, and, upstream cylinder and downstream cylinder response. This information is presented in terms of spectral and coherence plots. The single cylinder data is presented as a means to contrast the behavior of the tandem cylinders. Both configurations were analyzed at two different pretensions adding another dimension to this investigation. It is shown that although a primary variable such as displacement may be more easily measured, pretension and force measurements provide an important key to our understanding of this difficult problem.     

Statistical Distribution of Depth-Integrated Local Horizontal Momentum for Second-Order Random Ocean Waves in Finite Water Depth

Based on the second-order random wave solutions of water wave equations in tinite water depth, statistical distributions of the depth-integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all detemained by the water depth and the wavenumber spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.     

On vertical velocity fluctuations and internal tides in an upwelling region off the west coast of India

Hourly fluctuations of vertical velocity in relation to components of flow and wind and temperature oscillations at a morring site in the shelf waters off the west coast of India are discussed. The vertical velocities were computed from a time series of vertical temperature profiles assuming that horizontal advection of temperature is negligible. The computed values at a depth of 40 m during the 72-h period of observation were of the order of 10⁻¹ to 10⁻²cm s⁻¹, with a mean value of −2·77 × 10⁻² cm s⁻¹ indicating a net upward movement of water. The computed vertical velocity showed fluctuations of about 2–3 h, in addition to weaker signals of about 12 h. Based on the spectral estimates, we speculate that these fluctuations of 2–3 h in the vertical velocity may be caused by the fluctuations in the along-shore wind. The oscillations of isotherms found in the temperaturedepth time series and the spectral estimates of temperature and cross-shore flow component showed a periodicity of about 12 h, which indicated the presence of semi-diurnal internal waves. The fact that these internal wave troughs were associated with the measured onshore flow suggested that the waves were propagating offshore. The computed stability parameters showed little evidence of instability or mixing. It was found that the isotherm troughs in the temperaturedepth time series at about 12-h period coincided with high vertical shear in the cross-shore direction and low values of Brunt Vaisälä frequency.     

Water Wave Refraction and Diffraction over Frictional Topography

- This paper considers the effects of wave energy dissipation induced by sea-bottom friction on the computational results of water wave refraction and diffraction with the parabolic equation method. The presented results show that the friction factor formula adopted in this paper is of higher numerical accuracy than that introduced by Dalrymphe (1984), and it can be used to compute wave propagation over large open areas.     

Wave characteristics past a flexible fishnet

The scattering of surface waves by a flexible fishnet is studied analytically. The fishnet is modelled as a porous flexible barrier displaced solely by hydrodynamic force like a catenary. The objective is to investigate how a flexible permeable barrier affects the passing waves in the way they are transmitted and reflected, as observed by the fact that the water inside a fishfarm surrounded by fishnets is significantly calmer than that outside. The boundary value problems are solved by defining the reflection coefficient in terms of velocity potential and then the full solutions are obtained by suitable application of the eigenfunction expansion method and the least squares approximation method. The variations of the reflection coefficient, hydrodynamic pressure, barrier deformation and surface wave elevation are determined with respect to the barrier length, porosity and stiffness. It is observed that as the fishnet gets more flexible, its deformation increases and the reflection coefficient decreases, whereas as the fishnet gets more porous, more water can pass through it and thus the reflection coefficient, barrier deformation and the hydrodynamic force are reduced. The flexibility of the barrier behaves like its porosity by allowing more wave energy to act on it through its deformation and hence reduce the reflection and hydrodynamic force of the incident waves acting on the barrier.     

Experimental study on the performance of the multiple-layer breakwater

Based on the idea of disturbing the water motion in the upright direction, a new kind of multiple-layer breakwater is proposed in this article, which mainly consists of several horizontal plates. The breakwater's performance of dissipating waves has been investigated in detail in the regular wave tests. The factors identified with the characteristics of the breakwater are discussed, such as the relative width, the wave steepness and the models geometrical parameters (the width and the gap). The comparison and analysis of the transmission and reflection coefficients with respect to different factors are presented. The model test results indicate that the multiple-layer breakwater has the good characteristic of dissipating waves. Further more, only in a little extent can it reflect the waves. The multiple-layer breakwater proposed in the paper is very significative to promote the open type breakwater to be the permanent wave attenuator in the application.     

一个新的非恒定型不规则波缓坡方程

缓坡方程由Ｂｅｒｋｈｏｆ所推导并在规则波折射绕射问题的研究上有着广泛的应用。然而对于不规则波折射绕射问题研究，缓坡方程还处于发展研究阶段，本文采用Ｐａｄｅ近似并仿Ｋｕｂｏ方法对缓坡波动方程进行了推导，得到了一个含有时间高阶导数项的不规则波缓坡方程，随即采用ＷＫＢ方法对这个不规则波的缓坡方程进行了简化，推导出一个较为实用的含有一阶时间导数的不规则波缓坡的波动方程。通过数值手段对所推导的不规则波缓坡方程进行了数值模拟，其结果与物模实验较为一致