切变纬向流中β效应与缓变地形Rossby波

正压流体中,从有外源的准地转位涡方程出发,采用摄动方法和时空伸长变换推导了具有β效应、缓变地形和外源的Rossby孤立波方程,得到Rossby波振幅满足带有缓变地形与外源强迫的非齐次mKdV-Burgers方程的结论.通过分析孤立Rossby波振幅的演变,指出了β效应、地形效应以及外源都是诱导Rossby孤立波产生的重要因素;说明了在缓变地形强迫效应和非线性作用相平衡的假定下,Rossby孤立波振幅的演变满足非齐次mKdV-Burgers方程;给出在切变基本气流下缓变地形和正压流体中Rossby波的相互作用关系.     

强迫耗散与β效应地形效应作用下的非线性Rossby波包

正压流体中,从有外源的准地转位涡方程出发采用摄动方法和时空伸长变换推导了具有β效应、地形效应和外源的强迫Rossby孤立波包方程,得到孤立Rossby波振幅的演变满足带有地形与外源强迫的非齐次非线性Schrödinger方程的结论. 通过分析孤立Rossby波包振幅的演变,指出了β效应、地形效应以及外源都是诱导Rossby孤立波产生的重要因素,说明了在地形强迫效应和非线性作用相平衡的假定下,Rossby孤立波包振幅的演变满足非齐次非线性Schrödinger 关键词： Rossby波包 β效应')" href="#">β效应 地形 Schrödinger方程     

层结流体中具有β效应与地形效应的强迫Rossby孤立波

层结流体中,从绝热位涡的扰动方程出发采用摄动方法和时空伸长变换推导了具有β效应和地形效应的强迫Rossby孤立波方程,得到孤立Rossby波振幅的演变满足带有地形强迫的非齐次mKdV方程的结论. 通过分析孤立Rossby波振幅的演变,即使基本气流没有切变,仍可能激发出Rossby孤立波.指出了科氏力效应、地形效应以及Vaisala-Brunt频率都是诱导Rossby孤立波产生的重要因素,说明了在地形强迫效应和非线性作用相平衡的假定下,Rossby孤立波振幅的演变满足非齐次的mKdV方程.讨论 关键词： 非齐次mKdV方程 β效应')" href="#">β效应 地形 Vaisala-Brunt 频率     

层结流体中在热外源和β效应地形效应作用下的非线性Rossby孤立波和非齐次Schrödinger方程

在层结流体中, 从带有地形、热外源耗散的下边界条件以及带有热外源的准地转位涡方程开始, 使用小参数展开方法和多尺度时空伸长变换推导出了具有热外源、β效应和地形效应的强迫Rossby孤立波方程, 得到孤立Rossby振幅满足的带有地形与热外源的非齐次非线性的Schrödinger方程. 通过分析Rossby孤立波振幅的变化, 指出了热外源、β效应和地形效应都是诱导Rossby孤立波产生的重要因素, 给出了切变基本流下地形、热外源和层结流体中Rossby的相互作用.     

缓变下垫面和耗散作用的非线性Rossby波

从准地转位涡方程出发,采用摄动方法和时空伸长变换推导了在缓变下垫面和耗散共同作用的Rossby代数孤立波方程,得到Rossby波振幅满足带有缓变下垫面的非齐次Benjamin-Davis-Ono-Burgers(BDOBurgers)方程的结论.指出地形效应和耗散是诱导非线性Rossby波产生的重要因素,说明了在缓变下垫面强迫效应和非线性作用相平衡的假定下,Rossby孤立波振幅的演变满足非齐次BDO-Burgers方程,给出在切变基本气流下缓变下垫面和正压流体中Rossby波的相互作用.     

缓变地形下Rossby波振幅演变满足的带有强迫项的KdV方程

运用非线性方法与摄动法,讨论了当地形随时间缓变时Rossby波振幅的演变问题.从均值流体准地转涡度方程推导,得到Rossby波振幅演变满足带有强迫项的KdV方程的结论,而地形随时间的缓慢变化诱导了该方程的强迫项. 关键词： 非线性Rossby波 带有强迫项的KdV方程 摄动法 缓变地形     

切变基本纬向流中β效应的赤道Rossby孤立波包

从描写赤道Rossby 波的正压大气位涡方程出发,采用多重尺度摄动方法推导出在切变基本纬向流中具有β效应的非线性赤道Rossby波包演变满足非线性Schrdinger方程,并得到单个包络孤立子波解,分析了基本切变流,β效应对非线性赤道Rossby波的影响. 关键词： 赤道Rossby波 β效应 非线性Schrö dinger方程 包络孤立子     

局地强迫激发的非线性长波扰动

利用扰动法导得了非线性强迫Boussinesq方程,利用数值解讨论了地形和外源等局地强迫激发的非线性长波扰动的一般性状和时间演变特征,并对移动性孤波与地形的相互作用进行了分析研究。     

耗散与局地地形激发的代数孤立长波（英）

利用包括地形外源和湍流耗散的准地转涡度方程导出了包含强迫项和湍流耗散项的非齐次强迫BDO-Burgers方程，求出了小耗散存在情况下BDO-Burgers方程的近似解析解，讨论了代数孤立波的质量和能量的守恒关系，最后，对给定的弱切变基本气流和避地地形强迫，数据积分强迫BDO-Burgers方程，求得了不同参数下的数值解。     

局地外源激发的孤波的增强和演变

利用扰动法由准地转涡度方程导出了强迫mKdV方程，讨论了强迫mKdV孤波的质量和能量的时间演变，并通过拟谱法求得了强迫mKdV方程的数值解。计算结果显示，局地外源强迫激发的mKdV孤波与失谐参数α和外源强度有密切关系。与强迫KdV方程相比，在强迫mKdV方程中，外源强迫可以激发出振幅更大的更不稳定的孤波。     

Dissipative Nonlinear Schrödinger Equation with External Forcing in Rotational Stratified Fluids and Its Solution

The dissipative nonlinear Schrödinger equation with a forcing item is derived by using of multiple scales analysis and perturbation method as a mathematical model of describing envelope solitary Rossby waves with dissipation effect and external forcing in rotational stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency and β effect are important factors in forming the envelope solitary Rossby waves. By employing Jacobi elliptic function expansion method and Hirota's direct method, the analytic solutions of dissipative nonlinear Schrödinger equation and forced nonlinear Schrödinger equation are derived, respectively. With the help of these solutions, the effects of dissipation and external forcing on the evolution of envelope solitary Rossby wave are also discussed in detail. The results show that dissipation causes slowly decrease of amplitude of envelope solitary Rossby waves and slowly increase of width, while it has no effect on the propagation speed and different types of external forcing can excite the same envelope solitary Rossby waves. It is notable that dissipation and different types of external forcing have certain influence on the carrier frequency of envelope solitary Rossby waves.     

Algebraic Rossby Solitary Waves Excited by Non-Stationary External Source

The paper deals with the effects of non-stationary external source forcing and dissipation on algebraic Rossby solitary waves.From quasi-geostrophic potential vorticity equation,basing on the multiple-scale method,an inhomogeneous Korteweg-de Vries-Benjamin-Ono-Burgers(KdV-B-O-Burgers) equation is obtained.This equation has not been previously derived for Rossby waves.By analysis and calculation,four conservation laws associated with the above equation are first obtained.With the help of pseudo-spectral method,the waterfall plots are obtained and the evolutional characters of algebraic Rossby solitary waves are studied.The results show that non-stationary external source and dissipation have great effect on the generation and evolution of algebraic solitary Rossby waves.     

Algebraic Rossby Solitary Waves Excited by Non-Stationary External Source

The paper deals with the effects of non-stationary external source forcing and dissipation on algebraic Rossby solitary waves. From quasi-geostrophic potential vorticity equation, basing on the multiple-scale method, an inhomogeneous Korteweg-de Vries-Benjamin-Ono-Burgers (KdV-B-O-Burgers) equation is obtained. This equation has not been previously derived for Rossby waves. By analysis and calculation, four conservation laws associated with the above equation are first obtained. With the help of pseudo-spectral method, the waterfall plots are obtained and the evolutional characters of algebraic Rossby solitary waves are studied. The results show that non-stationary external source and dissipation have great effect on the generation and evolution of algebraic solitary Rossby waves.     

耗散对孤波与局地地形相互作用的影响

利用扰动法，由包括耗散和地形的准地转位涡度方程导出了强迫mKdV-Burgers方程，求得了小耗散情形下mKdV-Burgers方程的近似分析解，分析了mKdV孤波质量和能量的时间演变特性。对给定的局地地形，利用拟谱法对强迫mKdV-Burgers方程进行了数值求解。结果显示，小耗散的存在使弧波的振幅和移速随时间缓慢地减小，孤波宽度则随时间缓慢增大；在耗散和地形强迫的非线性系统中，在孤波与地形的相互作用中，耗散的存在使孤波在强迫区附近振荡传播，这有利于大振幅扰动的形成。     

Generation of Solitary Rossby Waves by Unstable Topography

The effect of topography on generation of the solitary Rossby waves is researched.Here,the topography,as a forcing for waves generation,is taken as a function of longitude variable x and time variable t,which is called unstable topography.With the help of a perturbation expansion method,a forced mKdv equation governing the evolution of amplitude of the solitary Rossby waves is derived from quasi-geostrophic vorticity equation and is solved by the pseudospectral method.Basing on the waterfall plots,the generational features of the solitary Rossby waves under the influence of unstable topography and stable topography are compared and some conclusions are obtained.     

Forced solitary Rossby waves under the influence of slowly varying topography with time

By using a weakly nonlinear and perturbation method, the generalized inhomogeneous Korteweg-de Vries (KdV)-Burgers equation is derived, which governs the evolution of the amplitude of Rossby waves under the influence of dissipation and slowly varying topography with time. The analysis indicates that dissipation and slowly varying topography with time are important factors in causing variation in the mass and energy of solitary waves.     

Forced solitary Rossby waves under the influence of slowly varying topography with time

By using a weakly nonlinear and perturbation method, the generalized inhomogeneous Korteweg-de Vries (KdV)-Burgers equation is derived, which governs the evolution of the amplitude of Rossby waves under the influence of dissipation and slowly varying topography with time. The analysis indicates that dissipation and slowly varying topography with time are important factors in causing variation in the mass and energy of solitary waves.