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.

Group Velocity of Anisotropic Waves-Part Ⅱ: Conservative Properties

It has been argued in Part I that traditional expression of multidimensional group velocity used in meteorology is only applicable for isotropic waves. While for anisotropic waves, it cannot manifest propagation of waves group along the trajectory of a reference wave point, and varies with rotation of coordinates. The general mathematical expression of group velocity which may be used also for anisotropic waves has been derived in Part I. It will be proved that the mean wave energy, momentum and wave action density are all conserved as a wave group propagates at the general group velocity. Since general group velocity represents the movement of a reference point in either isotropic or anisotropic wave trains, it may be used to define wave rays. The variations of wave parameters along the rays in a slowly varying environment are represented by ray-tracing equations. Using the general group velocity, we may derive the anisotropic ray-tracing equations, which give the traditional ray-tracing equations for isotropic waves.

Vortex Rossby Waves in Asymmetric Basic Flow of Typhoons

Wave ray theory is employed to study features of propagation pathways（rays） of vortex Rossby waves in typhoons with asymmetric basic flow, where the tangential asymmetric basic flow is constructed by superimposing the wavenumber-1 perturbation flow on the symmetric basic flow, and the radial basic flow is derived from the non-divergence equation. Results show that, in a certain distance, the influences of the asymmetry in the basic flow on group velocities and slopes of rays of vortex Rossby waves are mainly concentrated near the radius of maximum wind（RMW）, whereas it decreases outside the RMW. The distributions of radial and tangential group velocities of the vortex Rossby waves in the asymmetric basic flow are closely related to the azimuth location of the maximum speed of the asymmetric basic flow, and the importance of radial and tangential basic flow on the group velocities would change with radius. In addition, the stronger asymmetry in the basic flow always corresponds to faster outward energy propagation of vortex Rossby waves. In short, the group velocities, and thereby the wave energy propagation and vortex Rossby wave ray slope in typhoons, would be changed by the asymmetry of the basic flow.

The Effect of Spatial Structure Character of Heat Source on the Ray Path and the Evolution of Wave Energy of Meridional Wave Train

This paper studies correlations between the spatial structure character of thermal forcing and deformation and the amplitude of rays of meridional wave train. It is shown that if thermal forcing appears a meridional linear variation the rays of quasi-stationary planetary wave may propagate along oblique lines and if the meridional variability of heat source has second order term the rays show distinct deformation as a great circular route. Additionally, the inhomogeneous distribution may cause lower frequency oscillations in mid- and low-latitudes. The combination of zonal and meridional wave numbers and distributive character of heat source may form an inverse mechanism of variational trend of generized wave energy, reflecting in some degree the physical process of transition between meridional and zonal flow patterns.

Three-dimensional display technologies in wave and ray optics: a review(Invited Paper)

Multiple three-dimensional （3D） display technologies are reviewed. The display mechanisms discussed in this paper are classified into two categories： holographic display in wave optics and light field display in ray optics, which present the 3D optical wave field in two different ways. Key technical characteristics of the optical systems and the depth cues of human visual system are analyzed. It is to be expected that these 3D display technologies will achieve practical applications with the increase of the optical system bandwidth.

INFLUENCES OF NONUNIFORM STRATIFICATION ON WAVE RAYS OF INTERNAL GRAVITY WAVE

In this paper the influences of nonuniform stratification on the propagating paths of internal inertial-gravity and pure gravity wave energy are discussed by using the WKB approximation method.The conditions for conservation of wave energy,generalized wave action and wave enstrophy are obtained.The necessary condition of instability for inter- nal gravity waves and the equation governing the refraction of wave rays are derived.Two types of critical levels are giv- en.Finally,the wave rays for different distributions of stratification are calculated by using the fourth-order Runge-Kutta method.

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.

A STUDY ON DEFORMATIONS OF RAY AND ITS RELEVANT FACTORS

In this paper,the effects of first and second meridional derivative(i.e.h_s~,d^2f/dy^2,″)of the Coriolis parameter,Westerly profile and topography structure on ray routes are qualitatively analysed by use of a sim- plified mathematical model.The analysis indicates that the second derivatives of the above relevant factors play an important role in the formation of great circle route.A profile of west wind similar to the real atmosphere may result in a“sine wave pattern”of ray.The effects of west wind shear,β factor and the slope of topography on the scale of radius of great circle,critical latitude of rays ard the amplitude of wave train of teleconnection aro also discussed.Additionally,the characters of critical velocity profile for meridionally trapped wave are men- tioned.