A new model for algebraic Rossby solitary waves in rotation fluid and its solution

A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space.Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves,the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves,the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon.

(2+1)-dimensional dissipation nonlinear Schrdinger equatio for envelope Rossby solitary waves and chirp effect

In the past few decades, the （1 ＋ 1）-dimensional nonlinear Schr6dinger （NLS） equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the （1＋1）-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new （2＋1）-dimensional multiscale transform, we derive the （2＋1）-dimensional dissipation nonlinear Schrodinger equation （DNLS） to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of （2＋ 1）-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the （2＋ 1）-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.

Oscillatory Rossby Solitary Waves in the Atmosphere

The linear Rossby wave frequency expression is expanded at higher accuracy based on the scale difference characteristics of atmospheric long waves in the x and y directions. That the nature of the waves represented by the expansion is identical to that of the original ones is demonstrated both in phase velocity C and wave energy dispersion speed C., followed by the derivation of the nonlinear expression describing atmospheric long wave behaviors with the associated approximate analytic solution obtained. Then, for the first time atmospheric' oscillatory Rossby solitary wave with its dispersion relation is obtained by numerical calculation with the aid of physical parameters of the real atmosphere. The solitary wave is found to be very close to such longwave systems as blocking highs and cut-off depressions in the actual atmosphere.

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.

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 vortieity equation and is solved by the pseudo-spectral 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.

NONLINEAR SCHRODINGER EQUATION IN THE ROTATIONAL BAROTROPIC ATMOSPHERE AND ATMOSPHERIC BLOCKING

In this paper,the WKB method is used to obtain the nonlinear Schrdinger equation satisfied by nonlinear Rossby wave in the rotational barotropic atmosphere.It is found that the nonlinear Schrdinger equation has an envelope solitary wave solution under the condition 1≤m≤2(m the zonal wavenumber),and the phase speed of envelope solitary Rossby wave in the atmosphere is related to the square of its amplitude linearly,that is,the larger the amplitude of envelope solitary Rossby wave,the smaller its propagation speed.Farthermore, the blocking high and cut-off low pressures which are consistent with the observations of blocking in the atmo- sphere are obtained by calculating envelope solitary Rossby wave,and the blocking structures persist more than five days,the results demonstrate that the envelope solitary Rossby wave is a possible mechanism about the formation,maintenance and breakout of blocking in the atmosphere.