A THEORY OF BLOCKING FORMATION IN THE ATMOSPHERE

In this paper, a new theory of blocking formation was proposed. The nonlinear Schrdinger equation satisfied by nonlear barotropic Rossby waves for the weak shear zonal flow was obtained by using the WKB method. It was pointed out that when the Rossby wavenumbers sarisfied the relation: k/3相似文献   

NONLINEAR GRAVITY INERTIAL WAVE OF TWO DIMENSIONS AND DISCUSSION OF THE POSSIBILITY OF SOLITARY WAVE''''S EXISTENCE

In this paper we discuss the problem of a nonlinear gravity inertial wave of twodimensions and the possibility of solitary wave's existence. First of all, the existingcondition and analytic solution expression of shallow water waves are obtained by theapplication of the qualitative method of O. D. Es. We find that when the problem is de-generated, some physical values produce the nonlinear solitary wave, while other physi-cal values will be unbounded, so we consider that the nonlinear solitary wave for thesystem does not exist. Then we introduce concepts of the generalized energy (i. e. pseu-do-energy): when the pseudo-energy produces the tiny change at acting on a special ex-ternal effect, there will be solitary waves in this system. Finally, we obtain the repre-sentative of the nonlinear solitary wave which is different from KdV equation.     

Nonlinear Rossby Waves and Their Interactions (Ⅰ) ——Collision of Envelope Solitary Rossby Waves

By using the multiple-scale perturbation method a set of equations which describes two interacting nonlinear Rossby waves in the barotropic atmosphere is derived. The equations are used to study the collision of two envelope solitary Rossby waves. It is found that for a range of parameters, the collision interactions are envelope soliton-like in that the properties of the two envelope solitary waves change very little. For other parameters, new "inelastic" effects are observed, including speed changes, fission of envelope solitary waves and energy dispersion. It is also found that despite of the complexity of the interacting process, the energy of each wave is conserved.     

Jumping solitary waves in an autonomous reaction-diffusion system with subcritical wave instability

We describe a new type of solitary waves, which propagate in such a manner that the pulse periodically disappears from its original position and reemerges at a fixed distance. We find such jumping waves as solutions to a reaction-diffusion system with a subcritical short-wavelength instability. We demonstrate closely related solitary wave solutions in the quintic complex Ginzburg-Landau equation. We study the characteristics of and interactions between these solitary waves and the dynamics of related wave trains and standing waves.     

PERIODIC, SOLITARY AND DISCONTINUOUS PERIODIC SOLUTION OF NONLINEAR WAVES IN THE ATMOSPHERE AND THEIR EXISTENCE (Ⅱ)——ON THE POSSIBILITY OF TAYLOR EXPANSION, M CRITERION AND NONLINEAR WAVE SPEED FORMULAS

In this part, the nonlinear wave speed formulas are discussed. Because the nonlinear wave speed formulas are relative to wave form, we introduce a non-dimensional quantity M, which describes the nonlinear wave pattern and qualitatively determines the nonlinear degree. It is called M criterion. The wave speed formulas of the nonlinear Rossby wave and the nonlinear inertial gravity wave are also discussed. The wave speed of the former decreases with the growth of the amplitude but that of the latter is on the opposite. Furthermore we have also discussed the problems which must be taken note of in applying the Taylor expansion as we solve the approximate solution of nonlinear waves.     

A nonlinear RDF model for waves propagating in shallow water

In this paper, a composite explicit nonlinear dispersion relation is presented with reference to Stokes 2nd order dispersion relation and the empirical relation of Hedges. The explicit dispersion relation has such advantages that it can smoothly match the Stokes relation in deep and intermediate water and Hedgs's relation in shallow water. As an explicit formula, it separates the nonlinear term from the linear dispersion relation. Therefore it is convenient to obtain the numerical solution of nonlinear dispersion relation. The present formula is combined with the modified mild-slope equation including nonlinear effect to make a Refraction-Diffraction (RDF) model for wave propagating in shallow water. This nonlinear model is verified over a complicated topography with two submerged elliptical shoals resting on a slope beach. The computation results compared with those obtained from linear model show that at present the nonlinear RDF model can predict the nonlinear characteristics and the combined refracti     

On nonlinear waves in an elastic solid

We describe the nonlinear dispersive dissipative evolution of strain waves in a solid in the limiting condition B∼O(R/L), where B is the characteristic amplitude of the wave, L its wavelength and R the radius of a solid rod. We also provide conditions on dissipation and dispersion for the propagation of either shocks or solitary waves of permanent form.     

线性变位极谱法研究: XIII. 统一的配位吸附波理论

本文讨论包括吸附、扩散、电极反应速率等多种因素同时发生作用时配位吸附波的理论,提出的统一方程式包括可逆、不可逆和准可逆过程常规示波极谱、一次导数和二次导数极谱波方程式。利用铅(II)-8-羟基喹啉体系进行验证,理论与实验结果相符。     

Traveling wave patterns in nonlinear reaction–diffusion equations

In this paper we study a reaction–diffusion model equation with general nonlinear diffusion and arbitrary kinetic orders in the reaction terms, which appears in the applied biochemical modeling. We carry both analytical and numerical studies of the model equation to show the existence of monotone and oscillatory waves. Our numerical computations are illustrated for a particular case of the equation by using different methods which lead to accurate wave profiles and confirm the analytical results.     

ON NONLINEAR GRAVITY TRAVELLING WAVE

In this paper, a two--layer model with dispersive and dissipative effects but without Co-?iolis effect is investigated. It is proved that in the model, under certain parameter condi-tions, there exists monotone travelling wave as well as oscillation travelling wave in additionto the nonlinear periodic solution and solitary wave. The conditions for their existence areprovided. It is particularly pointed out that the pattern of the oscillation travelling wave issimilar to that of the pressure upwelling wave of a squall line which passes certain region.     

A SCHEME FOR EVALUATING THE MEAN MERIDIONAL CIRCULATION OF THE ATMOSPHERE

Based on the continuity of the atmosphere, a new scheme is developed to diagnose the atmospheric mean meridional circulations. ECMWF analyses four times per day of January 1982 were retrieved to evaluate the global mean meridional circulation. Investigations and calculations show that this new scheme produced more reasonable results in comparison with the traditional scheme. The existence of the double Hadley cell in the winter hemisphere is confirmed as well.     

Nonlinear EHD Stability of the Interfacial Waves of Two Superposed Dielectric Fluids

The slow modulation of the interfacial capillary–gravity waves of two superposed dielectric fluids with uniform depths and solid horizontal boundaries, under the influence of a normal electric field and in the absence of surface charges at their interface, is investigated by using the multiple-time scales method. It is found that the complex amplitude of quasi-monochromatic traveling waves can be described by a nonlinear Schrödinger equation in a frame of reference moving with the group velocity. The stability characteristics of a uniform wave train are examined analytically and numerically on the basis of the nonlinear Schrödinger equation, and some limiting cases are recovered. Three cases appear, depending on whether the depth of the lower fluid is equal to, greater than, or less than the depth of the upper fluid. The effect of the normal electric field is determined for the three stability regions of the pure hydrodynamic case. It is found that the normal electric field has a destabilizing influence in the first stability region and a stabilizing effect in the second and third stability regions. Moreover, one new unstable region or two new stable and unstable regions appear, all of which increase when the electric field increases. On the other hand, the complex amplitude of quasi-monochromatic standing waves near the cutoff wavenumber is governed by a similar type of nonlinear Schrödinger equation in which the roles of time and space are interchanged. This equation makes it possible to estimate the nonlinear effect on the cutoff wavenumber.     

A quasicontinuum approximation for solitons in an atomic chain

An accurate approximation is derived for solitary wave motion in a one-dimensional oscillator chain. Analysis shows that waves exist, travelling faster than sound, whenever the repulsive wall of the potential is anharmonic. The waves carry considerable momentum and potential energy but relatively little kinetic energy.     

2D general nonlinear parabolic equation for unstable wave package envelope in structural macrokinetics

We reduce the mathematical model for a chemical reaction in a moving medium to the general nonlinear parabolic equation (GNPE) for the complex amplitude of envelope wave to analyse weakly nonlinear interactions in supercritical regions. We use the method of many scales, wave packages, modification of Mandelshtam method and take into account the group velocity of envelope wave that is typical for nonlinear dispersive medium. GNPE describes the long-term system behaviour after stability loss and its coefficients are explicitly expressed through parameters of the initial nonlinear partial differential equations. It is taking into account the location of wave packet centre out of harmonics with maximum increment.     

Iterative solution of Bloch-type equations: stability conditions and chaotic behavior

Two different form of nonperturbative Bloch-type equations are studied: one for the wave operator of the N-electron Schr?dinger equation, another one for obtaining first-order density matrix P in one-electron theories (Hartree–Fock or Kohn–Sham). In both cases, we investigate the possibility of an iterative solution of the nonlinear Bloch equation. To have a closer view on convergence features, we determine the stability matrix of the iterative procedures and determine the Ljapunov exponents from its eigenvalues. For some of the cases when not every exponents are negative, chaotic solutions can be identified, which should of course be carefully avoided in practical iterations.     

一种研究聚合物非等温结晶动力学的方法

作者基于多年对聚合物结晶动力学方面研究的工作积累,联合Avrami方程和Ozawa方程,提出了一种研究聚合物非等温结晶动力学的新方法.该方法既克服了使用Ozawa方程所获得的数据点过少,常常出现非线性,不能获得可靠的动力学参数的缺点,又克服了使用经Jeziorny修正的Avrami方程所获得的表观Avrami指数无法准确预测非等温过程成核生长机理的缺点.该方法已成功用于多种聚合物体系,被国内外学者引用数百次,已成为研究聚合物非等温结晶动力学一种有效方法.     

A nonlinear RDF model for waves propagating in shallow water

In this paper, a composite explicit nonlinear dispersion relation is presented with reference to Stokes 2nd order dispersion relation and the empirical relation of Hedges. The explicit dispersion relation has such advantages that it can smoothly match the Stokes relation in deep and intermediate water and Hedgs’s relation in shallow water. As an explicit formula, it separates the nonlinear term from the linear dispersion relation. Therefore it is convenient to obtain the numerical solution of nonlinear dispersion relation. The present formula is combined with the modified mild-slope equation including nonlinear effect to make a Refraction-Diffraction (RDF) model for wave propagating in shallow water. This nonlinear model is verified over a complicated topography with two submerged elliptical shoals resting on a slope beach. The computation results compared with those obtained from linear model show that at present the nonlinear RDF model can predict the nonlinear characteristics and the combined refraction and diffraction of shallow-water waves.     

Thermal waves scattering by a subsurface sphere in a semi-infinite exponentially graded material using non-Fourier's model

In this study, the multiple scattering of thermal waves and temperature distribution resulting from a subsurface sphere in a semi-infinite exponentially graded material are investigated, and the analytical expression of the temperature at the surface of the graded material is obtained. Non-Fourier heat conduction equation is applied to solve the temperature at the surface, and the image method is used to satisfy the semi-infinite boundary condition of graded material. The thermal wave fields are expressed using wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary condition of the sphere. According to the wave equation of heat conduction, a general solution of scattered thermal waves is presented for the first time. The temperature distribution and phase difference at the surface of the semi-infinite material with different parameters are graphically presented. Analyses show that the hyperbolic heat conduction equation cannot be regarded as a continuation of the parabolic heat conduction equation at very short time scale. The effects of the incident wave number, the structural and physical parameters on the distribution of temperature and phase difference in the semi-infinite material are also examined.