非等谱广义耦合非线性Schrodinger方程的局部化孤立波

利用Hirota双线性方法求解了一个非等谱广义耦合非线性Schrodinger方程,得到它的Ⅳ一孤子解．其中单孤子可以描述一个任意大振幅且具有时间和空间双重局部性的孤立波,这种特征与所谓的“怪波”相一致．此外,借助于图像描述了二孤子的相互作用．     

完整Coriolis力作用下的非线性近惯性波

从包含有完整Coriolis力作用下的大气运动原始基本方程组出发,通过尺度分析,采用多重尺度法及摄动展开法,推导了中高纬大气非线性近惯性波振幅演化所满足的Korteweg-de Vries方程.从演化方程的结果可以看出Coriolis参数水平分量对非线性近惯性波的影响,主要体现为对频散效应的修正及与基本流的相互作用.从理论上解释了完整Coriolis力作用下的中高纬地区大气非线性近惯性波运动的物理机制.     

非等谱广义耦合非线性Schrdinger方程的局部化孤立波(英文)

利用Hirota双线性方法求解了一个非等谱广义耦合非线性Schr(o|¨)dinger方程,得到它的N-孤子解.其中单孤子可以描述一个任意大振幅且具有时间和空间双重局部性的孤立波,这种特征与所谓的"怪波"相一致.此外,借助于图像描述了二孤子的相互作用.     

轴对称模型的Hagen-Poiseuille流的运动不稳定性

本文讨论流体通过圆管的运动不稳定性问题。作为流体运动所受的干扰波,我们考虑了一个非线性轴对称模型。它对应的相关振幅函数满足扩散方程,且由于复杂的分子运动和流体粘性的相互作用,当流体的雷诺数增大时其扩散系数会出现负值。如负扩散现象出现,在流体运动中出现的湍流段内会引起流体的能量集中,并扮演减少阻尼的角色。     

等离子体中双流体模型的调制逼近北大核心CSCD

等离子体中的双流体模型描述了丰富的等离子体动力学行为,包括离子声波和等离子体波之间的相互作用.为了描述该双流体模型小振荡波包解包络的演化,利用多尺度分析方法将非线性Schrödinger(NLS)方程作为形式逼近方程导出,并通过对该双流体模型的真实解和逼近解之间的误差,在Sobolev空间中进行了一致能量估计,最终在时间尺度O(ε^(-2))上严格证明了NLS逼近的有效性.     

完整Coriolis力作用下带有外源强迫的非线性ZK方程

在正压流体中,从包含完整Coriolis参数的准地转位涡方程出发,在弱非线性长波近似下,采用多时空尺度和摄动方法,推导出大气非线性Rossby波振幅演变满足带有外源强迫的二维Zakharov-Kuznetsov(ZK)方程.然后利用Jacobi椭圆函数展开法,求解了ZK方程的椭圆正弦波解和孤立波解.分析结果表明,Coriolis参数的水平分量将影响二维Rossby波传播的频率特征,而外源不仅对二维Rossby波动的传播的频率有影响,对振幅也产生一个调制作用.     

非轴对称模型Hagen-Poiseuille流的不稳定性

本文讨论流体通过圆管的运动不稳定性问题.作为流体运动所受的扰动波,我们考虑一个三维非线性模型.它的相关振幅函数满足扩散方程,当流体的雷诺数增大时,由于复杂的分子扩散和流体粘性的相互作用.该方程的扩散系数会出现负值.在"负扩散"现象出现时.在流体运动中出现的"湍流段"内部会引起能量的集中和使流体的阻尼减少.文中所得结果对说明圆管流中出现湍流段的实验现象是有价值的.     

奇异半线性发展方程的局部Cauchy问题

本文在Ｂａｎａｃｈ空间Ｅ中讨论如下问题ｄｕｄｔ＋１ｔσＡｕ＝Ｊ（ｕ），０＜ｔＴ，ｌｉｍｔ→０＋ｕ（ｔ）＝０，其中ｕ：（０，Ｔ］Ｅ，Ａ是与ｔ无关的线性算子．（－Ａ）是Ｅ上Ｃ０半群｛Ｔ（ｔ）｝ｔ０的无穷小生成元，常数σ１，Ｊ是一个非线性映射ＥＪ→Ｅ．它满足局部Ｌｉｐｓｃｈｉｔｚ条件．我们证明了当其Ｌｉｐｓｃｈｉｔｚ常数ｌ（ｒ）满足一定条件时．问题（Ｓ）有局部解，且在某函类中解唯一．设Ｊ（ｕ）＝｜ｕ｜γ－１ｕ＋ｆ（ｘ）（γ＞１），Ｅ＝Ｌｐ，ＥＪ＝Ｌｐγ时得到了与Ｗｅｉｓｌｅｒ［２］在非奇异情形类似的结果．     

关于可约布尔矩阵幂敛指数的一个Brualdi─Ross型上界

本文证明了可约布尔矩阵幂敛指数的一个Ｂｒｕａｌｄｉ－Ｒｏｓｓ型上界，并给出了幂敛指数达到此上界的矩阵的完全刻划．     

二维空间中具有积分型非线性Schrodinger方程组的初值问题

具有积分型非线性ｓｃｈｒｏｄｉｎｇｅｒ方程是在研究非线性Ｌａｎｇｍｕｉｒ波时考虑到离子惯性作用而导出的．本文讨论了二维空间中具有积分型非线性ｓｃｈｒｏｄｉｎｇｅｒ方程组的初值问题，用积分估计方法证明了整体解的存在唯一性．     

Nonlinearly Coupled KdV Equations Describing the Interaction of Equatorial and Midlatitude Rossby Waves

Amplitude equations governing the nonlinear resonant interaction of equatorial baroclinic and barotropic Rossby waves were derived by Majda and Biello and used as a model for long range interactions （teleconnections） between the tropical and midlatitude troposphere. An overview of that derivation is nonlinear wave theory, but not in atmospheric presented and geared to readers versed in sciences. In the course of the derivation, two other sets of asymptotic equations are presented： the long equatorial wave equations and the weakly nonlinear, long equatorial wave equations. A linear transformation recasts the amplitude equations as nonlinear and linearly coupled KdV equations governing the amplitude of two types of modes, each of which consists of a coupled tropical/midlatitude flow. In the limit of Rossby waves with equal dispersion, the transformed amplitude equations become two KdV equations coupled only through nonlinear fluxes. Four numerical integrations are presented which show （i） the interaction of two solitons, one from either mode, （ii） and （iii） the interaction of a soliton in the presence of different mean wind shears, and （iv） the interaction of two solitons mediated by the presence of a mean wind shear.     

两层流体中具有β变化和地形影响的Rossby波

本文研究了两层流体中具有变化的Rossby参数和地形Rossby波的问题.利用行波法和摄动的方法,获得了Rossby波振幅满足齐次KdV方程和齐次mKdV方程,推广了Rossby参数和地形对Rossby孤立波的影响.     

Evolution of Packets of Surface Gravity Waves over Strong Smooth Topography

Wave packets in a smoothly inhomogeneous medium are governed by a nonlinear Schrödinger (NLS) equation with variable coefficients. There are two spatial scales in the problem: the spatial scale of the inhomogeneities and the distance over which nonlinearity and dispersion affect the packet. Accordingly, there are two limits where the problem can be approached asymptotically: when the former scale is much larger than the latter, and vice versa. In this paper, we examine the limit where the spatial scale of (periodic or random) inhomogeneities is much smaller than that of nonlinearity/dispersion (i.e., the latter effects are much weaker than the former). In this case, the packet undergoes rapid oscillations of the geometric-optical type, and also evolves slowly due to nonlinearity and dispersion. We demonstrate that the latter evolution is governed by an NLS equation with constant (averaged) coefficients. The general theory is illustrated by the example of surface gravity waves in a channel of variable depth. In particular, it is shown that topography increases the critical frequency, for which the nonlinearity coefficient of the NLS equation changes sign (in such cases, no steady solutions exist, i.e., waves with frequencies lower than the critical one disperse and cannot form packets).     

On linear and nonlinear Rossby waves in an ocean

This paper deals with recent developments of linear and nonlinear Rossby waves in an ocean. Included are also linear Poincaré, Rossby, and Kelvin waves in an ocean. The dispersion diagrams for Poincaré, Kelvin and Rossby waves are presented. Special attention is given to the nonlinear Rossby waves on a β-plane ocean. Based on the perturbation analysis, it is shown that the nonlinear evolution equation for the wave amplitude satisfies a modified nonlinear Schrödinger equation. The solution of this equation represents solitary waves in a dispersive medium. In other words, the envelope of the amplitude of the waves has a soliton structure and these envelope solitons propagate with the group velocity of the Rossby waves. Finally, a nonlinear analytical model is presented for long Rossby waves in a meridional channel with weak shear. A new nonlinear wave equation for the amplitude of large Rossby waves is derived in a region where fluid flows over the recirculation core. It is shown that the governing amplitude equations for the inner and outer zones are both KdV type, where weak nonlinearity is balanced by weak dispersion. In the inner zone, the nonlinear amplitude equation has a new term proportional to the 3/2 power of the difference between the wave amplitude and the critical amplitude, and this term occurs to account for a nonlinearity due to the flow over the vortex core. The solution of the amplitude equations with the linear shear flow represents the solitary waves. The present study deals with the lowest mode (n=1) analysis. An extension of the higher modes (n?2) of this work will be made in a subsequent paper.     

Wave–Mean-Flow Interactions in a Forced Rossby Wave Packet Critical Layer

This paper describes the nonlinear critical layer evolution of a zonally localized Rossby wave packet forced in mid-latitudes and propagating horizontally on a beta plane in a zonal shear flow. The wave packet has an amplitude that varies slowly in the zonal direction. Numerical solutions of the governing nonlinear equations show that the wave–mean-flow interactions differ from those that would result with a monochromatic forcing. With the localized forcing, the net absorption of the disturbance at the critical layer continues for large time, because there is an outward flux of momentum in the zonal direction. Further insight into the mechanism for this and other aspects of the evolution of the critical layer is obtained through an approximate asymptotic analysis which is valid for large time.     

On the transition mode characterizing the triggering of a vibrator in the subsonic boundary layer on a plate

The problem of the development of two-dimensional linear perturbations in a boundary layer, generated by the triggering of a vibrator, is considered. Fourier transformations in the longitudinal coordinate and a Laplace transform in time are used to construct the solution. The inverse transforms are evaluated for large values of the characteristic time t and all values of the longitudinal coordinate x. Domains located downstream of the vibrator are studied in the first of which the perturbations will have the form of Tollmien-Schlichting waves that go over into a wave packet in the second domain. The identity in the structure of the wave packets, which are orthonormalized to the maximum amplitude for this packet for different frequencies of vibrator oscillation is noted.     

Rogue waves in baroclinic flows

We investigate an AB system, which can be used to describe marginally unstable baroclinic wave packets in a geophysical fluid. Using the generalized Darboux transformation, we obtain higher-order rogue wave solutions and analyze rogue wave propagation and interaction. We obtain bright rogue waves with one and two peaks. For the wave packet amplitude and the mean-flow correction resulting from the self-rectification of the nonlinear wave, the positions and values of the wave crests and troughs are expressed in terms of a parameter describing the state of the basic flow, in terms of a parameter responsible for the interaction of the wave packet and the mean flow, and in terms of the group velocity. We show that the interaction of the wave packet and mean flow and also the group velocity affect the propagation and interaction of the amplitude of the wave packet and the self-rectification of the nonlinear wave.     

正压大气模式下大地形和β变化的Rossby波

在正压大气模式下从准地转位涡方程出发,考虑地形和β随纬度变化下引进参数δ对Rossby波的共同作用,应用正交模方法得到在中高纬度具有大地形、Froude数以及参数δ的Rossby波相速度公式; 分析β变化下大地形和Froude数对Rossby波稳定度的影响,表明大地形、Froude数和参数δ对Rossby波的稳定性作用.     

Rossby Waves

An asymptotic solution of the linear shallow water equations for small Rossby number is constructed to describe Ross by waves. It leads to a dispersion or eiconal equation for the phase of the waves and a transport equation for their amplitude. It is shown how these equations can be solved by means of rays for both planetary and topographic Rossby waves. The method is illustrated by constructing the wave field produced by a time harmonic point source in fluid of uniform depth. This solution is a Green's function for the equations.     

The Effect of Meridional and Vertical Shear on the Interaction of Equatorial Baroclinic and Barotropic Rossby Waves

Simplified asymptotic equations describing the resonant nonlinear interaction of equatorial Rossby waves with barotropic Rossby waves with significant midlatitude projection in the presence of arbitrary vertically and meridionally sheared zonal mean winds are developed. The three mode equations presented here are an extension of the two mode equations derived by Majda and Biello [ 1 ] and arise in the physically relevant regime produced by seasonal heating when the vertical (baroclinic) mean shear has both symmetric and antisymmetric components; the dynamics of the equatorial baroclinic and both symmetric and antisymmetric barotropic waves is developed. The equations described here are novel in several respects and involve a linear dispersive wave system coupled through quadratic nonlinearities. Numerical simulations are used to explore the effect of antisymmetric baroclinic shear on the exchange of energy between equatorial baroclinic and barotropic waves; the main effect of moderate antisymmetric winds is to shift the barotropic waves meridionally. A purely meridionally antisymmetric mean shear yields highly asymmetric waves which often propagate across the equator. The two mode equations appropriate to Ref. [ 1 ] are shown to have analytic solitary wave solutions and some representative examples with their velocity fields are presented.