Combined refraction and diffraction models for sea waves over complicated topography and with currents in shallow water

-Combined refraction and diffraction models in the form of linear parabolic approximation are derived through smallparameter method. More strictly theoretical basis and more accuracy in the models than Lozano's (1980) are obtained. Some theoretical defects in Liu's model (1985) with consideration of current are not only found but also eliminated. More strict and accurate models are, therefore, presented in this paper.The calculation results and analysis in applying the models to actual wave field with consideration of bottom friction will be given in the following paper.

Ray path of head waves with irregular interfaces

Head waves are usually considered to be the refracted waves propagating along flat interfaces with an underlying higher velocity.However,the path that the rays travel along in media with irregular interfaces is not clear.Here we study the problem by simulation using a new approach of the spectral-element method with some overlapped elements（SEMO） that can accurately evaluate waves traveling along an irregular interface.Consequently,the head waves are separated from interface waves by a time window.Thus,their energy and arrival time changes can be analyzed independently.These analyses demonstrate that,contrary to the case for head waves propagating along a flat interface,there are two mechanisms for head waves traveling along an irregular interface：a refraction mechanism and transmission mechanism.That is,the head waves may be refracted waves propagating along the interface or transmitted waves induced by the waves propagating in the higher-velocity media.Such knowledge will be helpful in constructing a more accurate inversion method,such as head wave travel-time tomography,and in obtaining a more accurate model of subsurface structure which is very important for understanding the formation mechanism of some special areas,such as the Tibetan Plateau.

Influence of Energy Directional Spread on Wave Spectral Refraction

Pierson- Moskowitz Spectrum, JONSWAP Spectrum as well as Bretschneider- Mitsuyasu Spectrum are used in this paper for analyzing the influence of wave energy directional spread on refraction of wave spectrum due to both current and topography of sea bed. The author's calculation indicates that such kind influence on the characteristic value of wave height as well as the average direction of wave energy propagation can not be ignored.

RAPID AND NONDESTRUCTIVE MEASUREMENT SYSTEM FOR WELDING RESDlUAL STRESS BY ULTRASONIC METHOD

Traditional methods of residual stress measurement are generally destructive or semi-destructive, as well as expensive, time-consuming and complex to implement. With the new development of welded structure, traditional methods can not satisfy the need of full life task management. So the acoustical theory is introduced, since the ultrasonic technique provides a useful nondestructive tool in the evaluation of stresses. In this study an ultrasonic stress measurement experimental installation is established, which consists of a special transducer, a signal emission unit and a signal recipient processing unit. Longitudinal critically refracted wave is selected as the measurement wave mode. The supporting software is programmed by Labview software. The longitudinal residual stress and transverse residual stress of twin wire welded plate are measured by this installment, in which the measuring process is real-time, quick and nondestructive. The experiment results indicate that the system can satisfy the need of life evaluation for welded structure. The system is light and portable.

scattering and refracting of plane strain wave by a cylindrical inclusion in fluidsaturated soils

The problems involving scattering and refracting of plane strain wave by a cylinder in fluidsaturated soils are studied in this paper. The theoretical solutions for the amplitudes of scattering and refracting are derived on the basis of modified Biot′s theory for twophase medium in engineering, in which the compressibility of soil grains and the viscous coupling effect between the skeletal frame and the pore fluid are taken into account. Moreover, the amplitude equations of potential function are presented when the fluidsaturated soil cylindrical inclusion is degenerated into cylindrical cavity, rigid cylinder, single phase elastic cylinder and single phase fluid cylinder.

An Analytic-Numerical Solution of Wave Transformation

An analytic-numerical solution of wave transformation in shoaling water is presented in this paper. The analytical expression for wave heights along the wave rays is derived in consideration of the combined effect of water depth shoaling, the wave refraction and the sea bottom friction. The wave rays (orthogonals) are calculated by a fourth order Runge-Kutta algorithm and the wave crest lines are computed by an iteration procedure. The numerical results are compared with analytical solution for a special case of parallel- straight contour shore and field data, and comparisons show that the proposed mathematical model and computation method are very useful and convenient for engineering application.

An Analytical Solution for Wave Transformation Over Axi-Symmetric Topography

The present study considers wave scattering phenomena around a cylindrical island mounted on a general axisymmetric topography or a general submerged truncated axi-symmetric shoal based on the mild-slope equation. The method of separation of variables and Taylor series expansion are invoked to find the approximate solution to the variable water depth region which varies proportionally to an arbitrary power of radial distance. Validations against the solutions for the combined wave refraction and diffraction around a cylindrical island mounted on a paraboloidal shoal of Liu et al. in 2004 and the scattering and trapping of wave energy by a submerged truncated paraboloidal shoal of Lin and Liu in 2007 show excellent agreements as the power of radial distance being equal to two. For the solutions of wave refraction and diffraction around a cylindrical island mounted on a shoal with depth proportionally to an arbitrary power of radial distance, good agreements with Zhai et al.’s(2013) solutions are demonstrated. Since the robustness of the assumption of a general axi-symmetric geometry based on an arbitrary power variability of the radial distance, the present solution can be very conveniently employed to investigate the effects of bottom topography on wave scattering and trapping patterns.

RAY THEORY OF WATER WAVE REFRACTION ON COMPLEX TOPOGRAPHY

The caustic lines are formed as envelop lines of wave rays on the complex topo- graphy where conventional ray theory fails.By using the inner and outer scale method in the near region the caustic lines the singularities of the ray theory are dealt with.Using the conclusion that the phase of the ray in contact with the caustic line increases by π/2,the whole wave refraction problem is solvec except on caustic lines.

Theoretical study on lifetime of thermal-fixed volume holographic phase grating in photorefractive crystals

We review the dark decay of the electronic holographic phase grating before thermal fixing, and deduce the general analytic expression of the lifetime of thermal-fixed ionic holograms in the photorefractive crystal, by means of analogizing. Because the ions are optically inactive, the lifetime of thermal-fixed ionic holograms is only closely relate to the ionic decay rate which is determined by the conductivity of ionic species at a given temperature. We theoretically analyze and numerically simulate the influences on the lifetime of ionic grating from the crucial factors in the experiment and application. The results reveal that low temperature, low ion-concentration, and large grating spacing are advantages for extending the life of the thermal-fixed volume holographic phase grating in photorefractive crystal.