地形作用下的非线性Rossby波

本文利用一个受地形强迫作用的半地转正压模式讨论了非线性Rossby波的稳定度和解.结果发现,东西向地形和南北向地形对非线性Rossby波的稳定度和相速的影响很不相同.同时也发现,地形强迫下的非线性Rossby波可用著名的KdV方程描述.     

大气学科在与物理学科的交融中发展

2013年是北京大学物理学科的百年纪念,我们清楚地记得,在1952年国家进行院系调整时,清华大学气象系在谢义炳教授的倡议下,得到著名物理学家叶企孙、周培源的支持,融合到北京大学物理系[1],物理专业、气象专业共同组成北京大学物理系,1956年谢义炳教授任物理系副系主任。由于同在一个物理系,气象学科大大强化了数理基础。至今,大气学科融入北京大学物理学科已经61年,得到了迅速发展。     

Lam函数和非线性演化方程的多级准确解的不变性

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程 .并在Lam 方程和Lam 函数的基础上 ,应用Jacobi椭圆函数展开法求出了非线性演化方程的多级准确解 ,从而得到了多级准确解中存在的守恒形式 .     

大气中的非线性椭圆余弦波和孤立波

本文从非线性大气运动方程组出发,在力学的平衡点附近,用比较简洁的方法求得了非线性有限振幅的色散大气惯性波、重力内波、Rossby波均满足KdV方程,它的解为椭圆余弦波和孤立波。对有限振幅的Rossby波,建立了不同于Rossby公式的新的色散关系,它合有波的振幅因子。分析表明,对有限振幅的惯性波和重力内波,振幅大,宽度大的波传播越快;但对于Rossby孤立波,振幅大,宽度大的波传播越慢,极涡、阻塞切断系统可能属于这一类波。     

NONLINEAR CNOIDAL WAVES AND SOLITARY WAVES IN ATMOSPHERE

In this paper, starting with the equations describing the atmospheric motion and by arelatively simple method, we find that, nearby the mechanical equilibrium point, all thefinite amplitude nonlinear inertia waves, internal gravity waves and Rossby waves in thedispersive atmosphere satisfy the KdV (Korteweg-de Vries) equation, its solution being thecnoidal waves and solitary waves. For the finite amplitude Rossby waves, we find the newdispersive relation which is different from the Rossby formula and contains the amplitudeparameter. It is shown that the larger the amplitude and width, the faster are the wavesfor the finite amplitude inertia waves and internal gravity waves, and the slower are thewaves for the Rossby solitary waves, to which perhaps the polar vortex and the blocking orcut-off systems belong. This treatise gives the nonlinear waves a new way and inspires usto study the nonlinear adjustment process and evolution process and the turbulence structure.     

含变系数或强迫项的KdV方程的新解

Jacobi椭圆函数展开法被推广并用于求解另一种形式的KdV方程的新的精确解,所求解的这类KdV方程包括一种典型的变系数的KdV方程和具有强迫项（随机项）的KdV方程．用这种方法得到的新的类周期解在极限条件下可以退化为类孤立波解或类冲击波解．     

A Simple Fast Method in Finding Particular Solutions of Some Nonlinear PDE

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The periodic solutions for coupled integrable dispersionless equations

By using the Jacobi elliptic-function method,this paper obtains the periodic solutions for coupled integrable dispersionless equations. The periodic solutions include some kink and anti-kink solitons.     

非线性演化方程的显式行波解

本文系统归纳了重要的非线性演化方程的各类显式行波解.说明常微分方程中的同宿轨道和异宿轨道分别和非线性演化方程中的孤立波(或称脉冲波)和波前相对应.耗散系统也存在孤立波,二维(x,y)演化方程中的孤立波可以显示出模式(Pattern)结构.三维相空间的鞍点同宿轨道和鞍—焦点同宿轨道(称Silnikov同宿轨道)常和混沌相联系,     

ROSSBY WAVES WITH THE CHANGE OF β

In this paper, the change of the Rossby parameter β with latitude is considered and the parameter is introduced and the β-plane approximation is extended into which includes the parameter γ. Such approximation closes further to practice especially in the high latitude regions. We give emphasis to the research of the effect of the parameter γ on the Rossby waves. It is seen that the effect of the parameter γ is remarkable in the high latitude regions. It can produce the Rossby waves caused by the pure parameter γ. And the phase speed formula of Rossby waves with the change of β is generally given, which is degenerated into the well-known Rossby formula when γ_0=0. The researches also point out that when the change of β is regarded, even if the basic current a is a linear function of y the unstable modes can also take place. However, the parameter γ usually plays a stable part in the Rossby waves and it does affect the longitudinal scale and the structure of constant phase lines (trough-ridge li