The Nonlinear Wave Force on a Circular Cylinder in Shallow Water

Based on the 1st order cnoidal wave theory, the nonlinear wave diffraction around a circular cylinder in shallow water is studied in this paper. The equation of the wave surface around the cylinder is formulated and by using this formula the wave surface elevation on the cylinder surface can be obtained. In this paper, the formula for calculating the cnoidal wave force on a circular cylinder is also derived. For the wave conditions which are often encountered in practical engineering designs, the ratios of the nonlinear wave forces to the linear wave forces are calculated, and the results are plotted in this paper for design purposes. In order to verify the theoretical results, model tests are conducted. After comparing the test results with the theoretical ones, it is concluded that, in shallow water, for the case of T g / d~(1/2) > 8-10 and H / d > 0.3, the cnoidal wave theory should be used to calculate the wave action on a cylindrical pier.     

Low-frequency damping of a moored semisubmersible obtained from simulated extinction tests and mean wave drift forces

Low-frequency damping of a moored semisubmersible drilling platform was obtained from numerical extinction tests simulated in still water and in regular waves and from mean wave drift forces calculated at zero forward speed. The influence of drag forces was represented by the modified Morison equation. The platform as used for the 18th ITTC Comparative Mooring Study was analyzed in irregular beam waves. The computed time series of sway as well as the corresponding sway response spectrum compared favourably with model test measurements, demonstrating that this procedure to determine low-frequency damping can be effective.     

Gravity torques for surface waves

The effects of the gravity torques acting on the angular momentum of surface gravity waves are calculated theoretically. For short crested waves the gravity torque is caused by the force of gravity on the orbiting fluid particles acting down the slopes of the crests and troughs and in the direction parallel to the crests and troughs. The gravity torque tries to rotate the angular momentum vectors, and thus the waves themselves, counterclockwise in the horizontal plane, as viewed from above, in both hemispheres. The amount of rotation per unit time is computed to be significant assuming reasonable values for the along-crest and trough slopes for waves in a storm area. The gravity torque has a frequency which is double the frequency of the waves. For long crested waves the gravity torque acts in the vertical plane of the orbit and tries to decelerate the particles when they rise and accelerate them when they fall. By disrupting the horizontal cyclostrophic balance of forces on the fluid particles (centrifugal force versus pressure force) the gravity torque accounts qualitatively for the three characteristics of breaking waves: that they break at the surface, that they break at the crest, and that the crest breaks in the direction of wave propagation.     

A comparison of several wave spectra for the random wave diffraction by a semi-infinite breakwater

A comparison of the diffraction of multidirectional random waves using several selected wave spectrum models is presented in this paper. Six wave spectrum models, Bretschneider, Pierson–Moskowitz, ISSC, ITTC, Mitsuyasu, and JONSWAP spectrum, are considered. A discrete form for each of the given spectrum models is used to specify the incident wave conditions. Analytical solutions based on both the Fresnel integrals and polynomial approximations of the Fresnel integrals and numerical solutions of a boundary integral approach have been used to obtain the two-dimensional wave diffraction by a semi-infinite breakwater at uniform water depth. The diffraction of random waves is based on the cumulative superposition of linear diffraction solution. The results of predicted random wave diffraction for each of the given spectrum models are compared with those of the published physical model presented by Briggs et al. [1995. Wave diffraction around breakwater. Journal of Waterway, Port, Coastal and Ocean Engineering—ASCE 121(1), 23–35]. Reasonable agreement is obtained in all cases. The effect of the directional spreading function is also examined from the results of the random wave diffraction. Based on these comparisons, the present model for the analysis of various wave spectra is found to be an accurate and efficient tool for predicting the random wave field around a semi-infinite breakwater or inside a harbor of arbitrary geometry in practical applications.     

受陆岸影响浅水区台风风浪的计算方案

在我国港口工程技术规范的波浪成长理论基础上，考虑到台风波浪的基本特点、等效水深的概念、浅水区波浪的折射、不规则波的能量分布特性、受陆岸和岛屿影响角度范围内的有效能量风区长度等因素，提出了受陆岸、岛屿影响浅水区（包括海湾区）台风风浪的计算方案。本方案只需台风中心位置、中心气压和计算点于各方位的风区长度（受陆岸影响部分）等资料，便可快速地得到计算点的波浪要素。经实测资料验证，效果良好。     

Refraction-Diffraction Mathematical Model for Waves With Lateral Energy Transmission Mechanism and Its Verification

To solve problems concerning wave elements and wave propagation, an effective way is the wave energy balance equation, which is widely applied in oceanography and ocean dynamics for its simple computation. The present papaer advances wave energy balance equations considering lateral energy transmission and energy loss as the governing equation for the study of wave refraction-diffraction. For the mathematical model, numerical simulation is made by means of difference method, and the result is verified with two examples.     

Numerical modelling of deformation of multi-directional random waves over a varying topography

Two numerical formulations of the breaking phenomenon were implemented in a numerical model for random wave propagation based on the elliptic formulation of the mild-slope equation. The randomness of the wave field was simulated based on a spectral component method, in which the 3-D spectrum is discretised in components of equal energy. One of the breaking process formulations is based on the concept of breaking each independent spectral component. The other is based on the distribution of the local amount of energy dissipated through the independent spectral components. The model based on the concept of breaking each independent spectral component produces the best estimates of the wave field, when the numerical results are compared with laboratory data.     

White-light promoted degradation of leucopterin and related pteridines dissolved in seawater, with evidence for involvement of complexation from major divalent cations of seawater

The photochemical instability of several related pteridines in seawater was investigated by aseptic incubation of solutions at 20–22°C under illumination from cool-white light of intensity 6 kerg cm⁻² sec⁻¹, and the chemical changes were spectrophotometrically monitored. All the pteridines showed markedly accelerated degradation from this illumination relative to their behaviour in total darkness.Pterin and lumazine were degraded very slowly with zero-order reaction kinetics, while the other pteridines photolysed rapidly (according to first-order kinetics) with decomposition rates increasing in the order dioxylumazine (2,4,6,7-tetrahydroxypteridine) < leucopterin < isoxanthopterin < xanthopterin < oxylumazine (2,4,6-trihydroxypteridine). Excepting leucopterin and dioxylumazine, the photolysis rates were attributable to the pH of seawater and not its salt content; this was also the case with oxylumazine which required the salt content of seawater for decomposition in darkness. Leucopterin and dioxylumazine (both 6,7-dihydroxylated pteridines) gave evidence of complexation with the major divalent cations (Ca²⁺, Mg²⁺) of seawater, by virtue of which their photolytic degradation rates were enhanced to magnitudes obtained in pH-10 buffer without seawater. It is proposed that such complexation produces structural forms of these pteridines analogous to their normal ionic forms at pH 10–12.The photolysis of the 6-hydroxylated pteridines (xanthopterin, oxylumazine) proceeded via intermediate formation of their corresponding 7-hydroxylated derivatives (leucopterin, dioxylumazine).