Coriolis力作用下的β效应与层结效应的Rossby孤立波

从包含完整Coriolis力的大气运动方程组出发,利用半地转近似导出了β效应、层结效应和地球旋转水平分量f_h共同作用下的非线性Rossby波满足KdV方程以及KdVmKdV方程.结果表明β效应、层结效应和地球旋转水平分量对Rossby的作用.     

近赤道完整Coriolis力作用下的非线性Rossby波

从既含有Coriolis力垂直分量又含有水平分量的位涡方程出发,采用不同的摄动方法推导了近赤道非线性Rossby波的演化方程,得到非线性Rossby波振幅演化满足非齐次Boussinesq方程或改进的Korteweg-de Vries方程.从演化方程可以看出Coriolis力水平分量对非线性Rossby波的影响,并且本文取特殊情况时包括了已有的一些结果.     

完整Coriolis力作用下的二维非线性Rossby波

本文在正压流体中,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地形强迫的非线性Zakharov-Kuznetsov(ZK)-Burgers方程.结果分析表明:地球旋转的水平分量、β效应、地形效应和耗散都是诱导二维Rossby波产生的重要因子.     

完整Coriolis力作用下的非线性Rossby波包

在正压流体中,从准地转正压涡度方程出发,运用时空伸长变换和摄动法推导了在完整Coriolis力作用下的非线性Rossby孤立波包振幅的演变满足非齐次非线性Schrodinger方程的结论.结果分析表明,完整Coriolis力中的水平分量对Rossby孤立波产生一定的影响,同时,β效应和地形效应也是诱导Rossby孤立波产生的重要因素.     

关于完整Coriolis力和地形作用下非线性Rossby波的研究

从含有完整Coriolis力的地转位涡方程出发,采用合理的赤道β平面近似,利用摄动法和时空伸长变换,推导了具有地形和耗散共同作用下的非线性Rossby波演变规律,其振幅满足非齐次Benjamin-Davis-Ono-Burgers(BDO-Burgers)方程.分析说明了地球旋转水平分量和下垫面对Rossby波演变的影响.当取特殊情况时,本文的结论可以退化为前人的结果.     

具有非线性地形的正压流体中孤立Rossby波的mKdV方程

正压流体中,采用摄动方法将准地转位涡方程推导出地形效应的mKdV方程,得到Rossby波振幅的演变满足地形效应的mKdV方程的结论,说明地形效应是诱导Rossby孤立波的重要因素.     

中层大气Rossby波与惯性重力波的非线性相互作用 （Ⅰ）相互作用方程

从包含Ｒｏｓｓｂｙ波和惯性重力波的大气运动方程组出发,采用弱非线性相互作用近似,推导出耗散大气中这两种尺度相差很大的波动之间的非线性相互作用方程．以此为基础,得到了描述窄角谱Ｒｏｓｓｂｙ波包和惯性重力波包的非线性时空演变规律的三波相互作用方程．数值分析表明,当一个Ｒｏｓｓｂｙ波包与两个惯性重力波包发生相互作用时,两个惯性重力波包之间进行快速的能量交换,同时与Ｒｏｓｓｂｙ波包之间进行缓慢的能量传输．从时间尺度上讲,惯性重力波可以看作Ｒｏｓｓｂｙ波包运动的背景噪声,因此上述非线性相互作用过程可以理解为大尺度Ｒｏｓｓｂｙ波包与背景噪声之间的能量交换过程．     

热带海洋和大气中地形Rossby波和Rossby波的耦合不稳定

当大尺度背景场存在赤道急流时, 由相应不均匀的温跃层(海洋)和高度场(大气)激发出的地形Rossby波和由β效应激发出的Rossby波, 在一定条件下, 通过相互作用后可产生一类新的不稳定, 称为地形Rossby波和Rossby波的耦合不稳定. 讨论了这类波系在ENSO发展中可能起的作用.     

中层大气Rossby波与惯性重力波的非线性相互作用 （Ⅰ）相互作用方程

从包含Ｒｏｓｓｂｙ波和惯性重力波的大气运动方程组出发,采用弱非线性相互作用近似,推导出耗散大气中这两种尺度相差很大的波动之间的非线性相互作用方程．以此为基础,得到了描述窄角谱Ｒｏｓｓｂｙ波包和惯性重力波包的非线性时空演变规律的三波相互作用方程．数值分析表明,当一个Ｒｏｓｓｂｙ波包与两个惯性重力波包发生相互作用时,两个惯性重力波包之间进行快速的能量交换,同时与Ｒｏｓｓｂｙ波包之间进行缓慢的能量传输．从时间尺度上讲,惯性重力波可以看作Ｒｏｓｓｂｙ波包运动的背景噪声,因此上述非线性相互作用过程可以理解为大尺度Ｒｏｓｓｂｙ波包与背景噪声之间的能量交换过程．     

Rossby波的螺旋斑图

应用描写大气大尺度运动的准地转方程组,求得了大气Rossby波的三维定常流场以及相应的位温场、涡度场和散度场,其中的三维流场构成了物理空间的一个非线性自治动力系统. 研究表明,Rossby波具有     

Shear flow instability of rotating hydromagnetic fluids

Abstract

The effect of an axial magnetic field on the linear stability of shear flows in rotating systems is examined by extending Busse's analysis of the nonmagnetic case to fluids of high magnetic diffusivity in the presence of a magnetic field. The shear is caused by differential rotation which creates slight deviations from a state of rigid rotation, corresponding to a small Rossby number. It is found that the Rossby number for the onset of instability is larger when a magnetic field is present than when it is absent.     

The generation of baroclinic Rossby waves by stationary and and translating currents part 1. Stationary current forcing

Abstract

This paper investigates the generation of linear, baroclinic Rossby waves by an imposed current distribution, in a reduced gravity ocean, both with and without an eastern coast. A zonal current is impulsively applied and maintained along the northern edge of the domain of solution. Using Green's function techniques, analytical solutions are found, and these are evaluated for small times. Numerical solutions are obtained for larger times. The upper layer depth field consists of a transient response, due to the sudden application of the current. Maintenance of the current causes a response which is singular along the line of imposed non-zero h _y. The interior field decays with time (this is shown asymptotically). The parameters used are appropriate for the mid-latitude North Pacific, and the results are relevant to sudden transport changes in the North Pacific Current.     

On the exact shape of the horizontal profile of a topographically rectified tidal flow

Abstract

Starting from the nonlinear shallow water equations of a homogeneous rotating fluid we derive the equation describing the evolution of vorticity by a fluctuating bottom topography of small amplitude, using a multiple scale expansion in a small parameter, which is the topographic length scale relative to the tidal wave length. The exact response functions of residual vorticity for a sinusoidal bottom topography are compared with those obtained by a primitive perturbation series and by harmonic truncation, showing the former to be invalid for small topographic length scales and the latter to be only a fair approximation for vorticity produced by planetary vortex stretching. In deriving the exact shape of the horizontal residual velocity profile at a step-like break in the bottom topography, it is shown that the Lagrangian profile only exists in a strip having the width of the amplitude of the tidal excursion at both sides of the break, and that it vanishes outside that interval. Moreover, in the limit of small amplitude topography at least, it vanishes altogether for the generation mechanism by means of planetary vortex stretching. The Eulerian profile is shown to extend over twice the interval of the Lagrangian profile both for production by vortex stretching and by differential bottom friction. These finite intervals over which the residual velocity profiles exist for a step-like topography are not reproduced by harmonic truncation of the basic equation. This method gives exponentially decaying profiles, indicating spurious horizontal diffusion of vorticity. In terms of orders of magnitude, the method of harmonic truncation is reliable for residual velocity produced by vortex stretching but it overestimates the residual velocity produced by differential bottom friction by a factor 2.     

切变基本纬向流中非线性赤道Rossby长波

为了解决观测和理论研究中的一些问题以及更好地了解热带大气动力学 ,有必要进一步研究基本气流的变化对大气中赤道Rossby波动的影响 .本文研究分析基本气流对赤道Rossby长波的影响 ,利用一个简单赤道 β平面浅水模式和摄动法 ,研究纬向基本气流切变中非线性赤道Rossby波 ,推导出在切变基本纬向流中赤道Rossby长波振幅演变所满足的非线性KdV方程并得到其孤立波解 .分析表明 ,孤立波存在的必要条件是基本气流有切变 ,而且基流切变不能太强 ,否则将产生正压不稳定 .     

Dispersive effects of zonally varying topography on quasigeostrophic Rossby waves

Abstract

Dispersion of linear quasigeostrophic plane waves in a stratified ocean with bottom topography is discussed. Particular emphasis is given to cases for which zonal gradients in the sea floor height are important. As such, the relative importance of the topographic and planetary β-effects is strongly dependent on wave vector orientation. The magnitude of the topographic slopes considered is chosen such that these two effects (topographic and planetary β) are of comparable importance. In the interest of simplicity, stratification is taken to be independent of depth. The eigenvalue problem which must be solved to find the free modes of oscillation has already been treated in the literature (in fact, Charney and Flierl (1981) have treated the effects of a more realistic stratification). The aim of this note is to more fully expose, primarily by example, several dispersive properties of these free wave modes which have been largely overlooked.     

切变基本纬向流中非线性赤道Rossby长波

为了解决观测和理论研究中的一些问题以及更好地了解热带大气动力学 ,有必要进一步研究基本气流的变化对大气中赤道Rossby波动的影响 .本文研究分析基本气流对赤道Rossby长波的影响 ,利用一个简单赤道 β平面浅水模式和摄动法 ,研究纬向基本气流切变中非线性赤道Rossby波 ,推导出在切变基本纬向流中赤道Rossby长波振幅演变所满足的非线性KdV方程并得到其孤立波解 .分析表明 ,孤立波存在的必要条件是基本气流有切变 ,而且基流切变不能太强 ,否则将产生正压不稳定 .     

Influence of Pacific on Southern Indian Ocean Rossby Waves

The sea-surface height anomalies derived from Simple Ocean Data Assimilation (SODA) during 1958–2001, Topex/Poseidon satellite during 1993–2001 and the SODA heat content anomalies (125 m depth) during 1958–2001 are filtered into annual and biennial Rossby wave components using a two-dimensional Finite Impulse Response filter. The filtered Rossby wave components (both annual and biennial) in the southern Pacific and Indian Oceans have considerable strength and variability. The propagation of annual and biennial Rossby waves in the Indonesian through-flow region [12.5°S–7.5°S] of the Indian Ocean is in phase with the southern Pacific Ocean waves. So it is speculated that the Pacific Ocean influences the Indian Ocean, especially through the region 17.5°S to 7.5°S and thus the southern Pacific Rossby waves could be an unexplored contributor to the Indian Ocean Rossby waves. We also carried out Fast Fourier Transform (FFT) and wavelet analysis on the tide gauge sea-level data along the Australian coast to support our claim. Filtered annual and biennial components of SODA heat content anomalies (125 m depth) also support these findings.     

Effect of pressure gradients and line-tying on the magnetic stability of coronal loops

Abstract

In this paper we study the stability of an idealised magnetostatic coronal loop, incorporating both the effect of line-tying, due to the dense photosphere, and of pressure gradients. The stability equations may be solved analytically for our particular equilibrium. From the marginally stable case, the critical conditions separating instability from stability are derived. It is found that stretching or twisting a loop eventually makes it kink unstable.