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.

Pulsed γ-ray properties of Crab pulsar in a retarded dipole with a current-induced magnetic field

Motivated by the Fermi observations of some γ-ray pulsars in which the phases of radio and γ-ray peaks are almost the same, we investigate the outer gap model in a retarded dipole with a current-induced magnetic field and apply it to explain pulsed γ-ray properties of the Crab pulsar. Our results show that the observed γ-ray energy-dependent light curves, which almost align with the radio light curve and phase averaged spectrum for the Crab pulsar, are reproduced well.

The Relationship between the Rise Width and the Full Width of γ-ray Burst Pulses and Its Implications

We investigate the relationship between the rise width and the full width of gamma-ray burst pulses. Theoretical analysis shows that either width is proportional to Г^-2△τθ,FWHMRc/c（Г the Lorentz factor of the bulk motion, △τθ,FWHM a local pulse＇s width, Rc the radius of fireballs and c the velocity of light）. We study the relationship for four samples of observed pulses. We find： （1） merely the curvature effect could reproduce the relationship between the rise and full widths with the same slope as derived from the model of Qin et al.; （2） gamma-ray burst pulses, selected from both the short and long GRBs, follow the same sequence in the rise width vs. full width diagram, with the shorter pulses at one end; （3） all GRBs may intrinsically result from local Gaussian pulses. These features place constraints on the physical mechanism（s） for producing long and short GRBs.

A geometric Model for the Spatial Correlation of an Acoustic Vector Field in Surface-generated Noise

Spatial correlation of sound pressure and particle velocity of the surface noise in horizontally stratified media was demonstrated, with directional noise sources uniformly distributed on the ocean surface. In the evaluation of particle velocity, plane wave approximation was applied to each incident ray. Due to the equivalence of the sound source correlation property and its directivity, solutions for the spatial correlation of the field were transformed into the integration of the coherent function generated by a single directional source. As a typical horizontally stratified media, surface noise in a perfect waveguide was investigated. Correlation coefficients given by normal mode and geometric models show satisfactory agreement. Also, the normalized covariance between sound pressure and the vertical component of particle velocity is proportional to acoustic absorption coefficient, while that of the surface noise in semi-infinitely homogeneous space is zero.

Variations in Wave Energy and Amplitudes along the Energy Dispersion Paths of Nonstationary Barotropic Rossby Waves

The variations in the wave energy and the amplitude along the energy dispersion paths of the barotropic Rossby waves in zonally symmetric basic flow are studied by solving the wave energy equation,which expresses that the wave energy variability is determined by the divergence of the group velocity and the energy budget from the basic flow.The results suggest that both the wave energy and the amplitude of a leading wave increase significantly in the propagating region that is located south of the jet axis and enclosed by a southern critical line and a northern turning latitude.The leading wave gains the barotropic energy from the basic flow by eddy activities.The amplitude continuously climbs up a peak at the turning latitude due to increasing wave energy and enlarging horizontal scale(shrinking total wavenumber).Both the wave energy and the amplitude eventually decrease when the trailing wave continuously approaches southward to the critical line.The trailing wave decays and its energy is continuously absorbed by the basic flow.Furthermore,both the wave energy and the amplitude oscillate with a limited range in the propagating region that is located near the jet axis and enclosed by two turning latitudes.Both the leading and trailing waves neither develop nor decay significantly.The jet works as a waveguide to allow the waves to propagate a long distance.

Trapping Mechanism for Long Waves over Circular Islands with Power Function Profiles

Long waves such as tsunamis can be trapped by islands due to wave refraction,and these trapped waves will cause huge damage even in the sheltered shoreline of the island.That all waves propagating into the topography and finally reaching the coastline are called perfect trapped modes,while any waves escaping from the topography are called leaky modes.Whether these long waves can be trapped is dependent on the depth profile of the island.This paper presents analytic solutions of the ray path for waves propagating into the circular island with power function profiles.Wave height distributions over the island are further investigated based on the principia that crowded rays correspond to large wave height and sparse rays correspond to small wave height.The trapped mechanism for water waves over the island is revealed based on their ray paths.Furthermore,the perfectly trapped criterion is derived,that is,when the slope gradient at the topography toe is greater than twice the ratio of the water depth to the radial distances,all wave rays propagating on the island will finally reach the coastline,and the waves are perfectly trapped.

Extension of e^N method to general three-dimensional boundary layers

In order to extend the eN method to general three-dimensional boundary layers, the conservation law of the imaginary parts for the wave parameters with a fixed wave vector is deduced. The compatibility relationship （CR） and the general theory of ray tracing （RT）, which have been extensively used in conservative systems, are applied to a general three-dimensional boundary layer belonging to non-conservative systems. Two kinds of eN methods, i.e., the eN-CR method and the eN-RT method, are established. Both the two kinds of methods can wavenumber and the amplitude of the be used to predict the evolutions of the spanwise disturbances in general three-dimensional boundary layers. The reliability of the proposed methods is verified and validated by performing a direct numerical simulation （DNS） in a hypersonic general three-dimensional boundary layer over an aircraft model. The results are also compared with those obtained by other eN methods, indicating that the proposed methods have great potential applications in improving the transition prediction accuracy in general three-dimensional boundary layers.

The Binary Black Hole Scenario for the BL Lacertae Object AO 0235+16

Recent analysis of the long term radio light curve of the extremely variableBL Lacertae object AO 0235+16 by Raiteri et al. have revealed the presence of recurrent outburstswith a period of ～ 5.7 +- 0.5 yr. Periodicity analysis of the optical light curve also showsevidence for a shorter period. Here we discuss whether such a behavior can be explained by a binaryblack hole model where the accretion disk of one of the supermassive black holes is precessing dueto the tidal effects of the companion. We estimate the mass of the accreting hole and analyzeconstraints on the secondary mass and the orbital parameters of the system. It is possible toprovide a viable interpretation of the available multiwavelength data.

Optical Flash of GRB 990123: Constraints on the Physical Parameters of the Reverse Shock

The optical flash accompanying GRB 990123 is believed to be powered by the reverse shock of a thin shell. With the best-fit physical parameters for GRB 990123 and the assumption that the parameters in the optical flash are the same as in the afterglow, we show that: 1) the shell is thick rather than thin, and we have provided the light curve for the thick shell case which coincides with the observation; 2) the theoretical peak flux of the optical flash accounts for only 3×10-4 of the observed. In order to remove this discrepancy, the physical parameters, the electron energy and magnetic ratios, εe and εB, should be 0.61 and 0.39, which are very different from their values for the late afterglow.

Studying the Fermi GeV light curve of Vela with the two-pole caustic model

An observation of the Vela pulsar with the Fermi Large Area Telescope has been recently reported and the GeV light curve shows two main peaks with a phase separation of ～0.43. We study the GeV light curve using the two-pole caustic model in which the peaks of the light curves of the pulsar result from caustic effects. The results show that the two-pole caustic model can reproduce the observed emission pattern of the two peaks and the bridge emission between them well, but overestimates the flux outside the two peaks. After taking account of the pair production effect on the azimuthal angle, we find that the resulting light curve is more consistent with the observation. We excluded the emissions from the field lines for which the distance from the null charge surface, where the pairs can be significantly produced, is larger than the radius of the light cylinder.

Complex ray method and its applications to underwater acoustics

In this paper, the principle of complex source point and various analytical methods of complex ray are summarized. Some possible applications of complex ray method to underwater acoustics are proposed, including complex ray analysis of directional acoustic fields, complex ray simulation of directivity of acoustic radiator arrays, complex ray transformation of acoustic fields from near zone to far zone, as well as theoretical prediction of sonar target strength by complex ray method.