LINEAR AND NONLINEAR BAROTROPIC INSTABILITY

Based on a non-frictional and non-divergent nonlinear barotropic vorticity equation and its solutions oftravelling waves,the criteria for linear and nonlinear barotropic instability are gained respectively at an equilibriumpoint of the equation on a phase plane.The linear and nonlinear analytical solutions to instability waves arealso found.The computational results show that if their amplitudes are equal at the initial time,the amplitudeincrements of nonlinear instable barotropic wave are always less than those of linear instable barotropic wave.The nonlinear effects can slow down the exponential growth of linear instability.The time needed for makingthe amplitude double that of initial time by instabilities,is about 6h for linear instability and about 18h fornonlinear instability,the latter is in agreement with the observations in the real atmosphere.     

ENERGY,ENERGY FLUX AND LAGRANGIAN OF ROSSBY WAVE

The energy flux derived from the barotropic vorticity equation differs from that obtained directly from the momentum equation.We re-study this problem raised in the early 1960s.The results show that if the momentum equation is rewritten in such a way that it contains the same conditions as that for the barotropic vorticity equation,then the same form of average energy flux can be obtained for the waves with constant amplitudes.With this new momentum equation,the potential energy of Rossby wave is derived and Lagrangian of nonlinear barotropic vorticity equation can be approximately found with this potential energy.This provides a physical basis for studying the dynamics of nonlinear Rossby wave with the approach of calculus of variation.     

Coastal currents and eddies and their interaction with topography

The nonlinear interaction of vorticity driven coastal currents and eddies with topography is studied. The topography is either a semi-infinite escarpment perpendicular to the coast (such that topographic waves propagate toward the coast) or a semi-circular canyon or seamount attached to the coast. Assuming a piecewise constant potential vorticity distribution, the quasigeostrophic equations are solved using contour dynamics. Offshore propagating dipole eddies occur, whenever a coastal current or eddy interacts with escarpment and canyon topographies. The size and frequency at which dipoles form are found to depend on the vorticity of the current and amplitude of the topography. However, for a seamount, little eddy shedding is observed and the coastal current or eddy skirts around topography.     

The effects of zonal flow on nonlinear Rossby waves

In this paper, we using phase plane method have derived the stability criteria of linear and nonlinear Rossby waves under the conditions of semi-geostrophic approximation and have gotten the solutions and geostrophic vorticity of corresponding solitary Rossby waves. It is pointed out that the wave stability is connected with the distri-bution of zonal flow and when the zonal flow is different the solitary wave trough or ridge is formed.     

线性和非线性正压不稳定

本文从无摩擦的、无辐散的非线性正压涡度方程出发,利用行波解,在相平面上对方程的平衡点分别导得线性和非线性正压不稳定判据,与传统的不稳定判据作了比较分析。还求得了线性和非线性不稳定波的解析解,计算结果表明,若初始时刻两者波幅相等,则以后非线性不稳定波幅的增长值总小于线性不稳定波幅的增长值。非线性效应有使线性不稳定指数型增长减缓的作用。不稳定使得振幅比初始时刻增大一倍所需要的时间,对于线性不稳定大约是6h,对于非线性不稳定大约是18h,后者与实际大气中的观测事实是一致的。     

辐散风和瞬变的涡度通量对定常波的强迫

本文从理论分析、资料诊断和正压模式数值试验三个方面研究了瞬变的涡度通量的辐合与辐散风产生的涡度源之间的关系及它们在对流层上层定常波维持中的作用。结果表明， 瞬变涡度通量的辐合对辐散风产生的涡度源有抵消或耗散的趋势；定常波是在两种强迫力的共同作用下维持的。同时还研究了不同地区散度场对定常波的作用， 结果表明，中纬度东亚地区的辐合场对维持东亚大槽是重要的，并且这一辐合场与位于印度尼西亚地区的辐散场是维持西太平洋上副热带反气旋系统的主要强迫源。     

Sources of CAM3 vorticity bias during northern winter from diagnostic study of the vorticity equation

CAM3 (Community Atmosphere Model version 3) simulation bias is diagnosed using the vorticity equation. The study compares CAM3 output with ECMWF (European Centre for Medium-Range Weather Forecasts) 40?year reanalysis (ERA-40) data. A time mean vorticity bias equation is also formulated and the terms are grouped into categories: linear terms, nonlinear terms, transient contributions, and friction (calculated as a residual). Frontal cyclone storms have much weaker band passed kinetic energy and enstrophy in CAM3. The downstream end of the North Atlantic storm track (NAST) has large location error. While the vorticity equation terms have similar amplitude ranking in CAM3 and ERA-40 at upper levels, the ranking differs notably in the lower troposphere. The linear and friction terms dominate the vorticity bias equation. The transient terms contribute along the storm track, but the nonlinear terms are generally much smaller, with the primary exception being over the Iberian peninsula. Friction is much stronger in CAM3. As evidence, nearly all wavelengths (including the longest planetary waves) have smaller amplitude in CAM3 than in ERA-40 vorticity data. Negative near surface vorticity tendency bias on the European side of the Arctic is linked to the NAST track error (evident in the divergence term). CAM3 misses the Beaufort high in sea level pressure (SLP) due to low level warm temperature bias, too little vortex compression, and to too little horizontal advection of negative vorticity compared with ERA-40. Generally lower SLP values in CAM3 over the entire Arctic follow from lower level warm bias in CAM3.     

涡旋Rossby波传播的不同特征

用一个柱坐标系涡度正压方程的半谱模式，实施了4组试验，研究了不同初始扰动涡旋分布条件下，涡旋Rossby波的传播特征问题。结果指出：正值、负值相间的沿方向角二波分布的初始场，与只有正值涡旋的初始场相比，其后涡旋Rossby波的传播有明显的差别，即前者向内传播的涡量比后者衰减得快，而且前者是单峰传播，后者是双峰传播。     

Haurwitz solutions of the nonlinear shallow-water equations for small froude number

Summary In this note we find special solutions of the nonlinear shallow-water equations. From the first integrals of the potential vorticity and energy equations for steady flow we derive a single equation in the streamfunction. In the limiting case of very small Froude number, that equation has no solutions corresponding to gravity waves. Under a nonlinear transformation of dependent variable, it becomes a linear equation whose solutions are related to Haurwitz's solutions for nondivergent barotropic flow in spherical surfaces. The distinguishing feature of these solutions is that the streamlines coincide with contours of the free surface: thus, although the height of the free surface varies, the motions of the fluid are horizontal, and the flow is nondivergent.The solutions are easily modified to correspond to Rossby waves propagating eastward or westward without change of shape.The National Center for Atmospheric Research is sponsored by the National Science Foundation.This paper is dedicated to the memory of my scientific mentor and old friend, Bernhard Haurwitz.     

弱频散条件下大气运动的非线性演变过程

研究非线性过程对大气运动影响的一个常用方法是在一定条件下,将大气运动力学方程化为一些熟知的典型非线性演变方程,再利用数学中已有的结果进行讨论。Long、Redekopp等从地转涡度方程出发,证明了迭加在带状切变气流中的长的Rossby波的演变可以用著名的Kdv方程来描述。此