Hamiltonian description of barotropic Rossby waves

A transformation into the normal canonical variables is found in the beta-plane approximation for barotropic Rossby waves of an arbitrary amplitude. This transformation is used to derive a matrix of three-wave interaction and to find an expression for the fourth-order term in the interaction Hamiltonian, which describes the modulation instability of Rossby waves. An increment of this instability has been calculated and estimated numerically.     

Complex waves in a two-layer circular shielding waveguide

Certain dispersion properties of natural complex waves are considered in a two-layer circular shielded waveguide. The results of a solution of the dispersion equation on an electronic computer are presented for the case of complex waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 1, pp. 112–116, January, 1972.     

Guided elastic waves in a pre-stressed compressible interlayer

The propagation of guided elastic waves in a pre-stressed elastic compressible layer embedded in a different compressible material is examined. The waves propagate parallel to the planar layer interfaces as a superposed dynamic stress state on the statically pre-stressed layer and host material. The underlying stress condition in the two materials is characterized by equibiaxial in-plane deformations with common principal axes of strain, one of the axes being perpendicular to the layering. Both materials have arbitrary strain energy functions. The dispersion equation is derived in explicit form. Analysis of the dispersion equation reveals the propagation characteristics and their dependence on frequency, material parameters and stress parameters. Combinations of these parameters are also defined for which guided waves cannot propagate.     

Dispersion and attenuation of gravity waves in ice: a two-layer viscous fluid model with experimental data validation

A theoretical model describing the propagation of gravity waves on ice-covered waters is developed. The ice–water system is approximated as a two-layer viscous and immiscible Newtonian fluid. The model is validated against existing viscous models by using laboratory and in situ collected wave data.     

Hydromagnetic surface waves in a moving compressible plasma column

Summary The dispersive characteristic of hydromagnetic surface waves along a plasma-plasma interface when one of the fluids has a relative motion has been studied as a function of the compressibility factors ₁/V ₁, wheres ₁ andV ₁ are the acoustic and Alfvén wave speed in one of the media. Both slow and fast magnetosonic surface waves for each symmetric and asymmetric modes can exist. The nature and existence of these modes depend on the values ofs ₁/V ₁ and ϑ, the angle of wave propagation. The phase velocity of the slow wave increases whereas for the fast wave it decreases with increase in the angle ϑ. The authors of this paper have agreed to not receive the proofs for correction.     

Random sound waves in a weakly stratified atmosphere

The influence of random mass density and velocity fields on the frequencies and amplitudes of the sound waves that propagate along a constant gravity field is examined in the limit of weak random fields, small amplitude oscillations and a weakly stratified medium. Using a perturbative method, we derive dispersion relations from which we conclude that the effect of a space-dependent random mass density field is to attenuate sound waves. Frequencies of these waves are higher than in the case of a coherent medium. A time-dependent random mass density field increases frequencies and amplifies the sounds waves. On the other hand, a space-dependent random flow reduces the wave frequencies and attenuates the sound waves. The time-dependent random flow raises the frequencies of the sound waves and amplifies their amplitudes. In the limit of the gravity-free medium the above results are in an agreement with the former findings.     

Quasi-solitons of magnetostatic waves in a two-layer structure under single-mode excitation

We investigate the quasi-solitons of the envelope of forward body magnetostatic waves in a structure that consists of two magnetically coupled films separated by a nonmagnetic interlayer under the initial excitation of a pulse in one of them. We have found that as the pulse propagates, its energy is transferred from one film to the other through intermode coupling; as a result, “pulsating” quasi-solitons of the coupled modes of the two films emerge. We show that the amplitude of each of the mode pulses at the exit from the waveguide can be regulated over a wide range by varying the magnetizing field.     

Synchronization of spiral waves in a two-layer coupled inhomogeneous excitable system

We studied synchronization behaviours of spiral waves in a two-layer coupled inhomogeneous excitable system. It was found that phase synchronization can be observed under weak coupling strength. By increasing the coupling strength, the synchronization is broken down. With the further increase of the coupling strength, complete synchronization and phase synchronization occur again. We also found that the inhomogeneity in excitable systems is helpful to the synchronization.     

Modulation instability of magnetostatic waves in a magnetically coupled two-layer structure

Modulation instability of direct bulk magnetostatic waves in structures consisting of two magnetically coupled planar films separated by a nonmagnetic layer is studied. It is found that, depending on the type of excitation of the waveguide modes, mode coupling can either change the characteristics of the modulation wave instability or ensure their stability with respect to the corresponding perturbations by affecting the dispersion properties of the structure.     

双层耦合Lengel-Epstein模型中的超点阵斑图

用双层耦合的Lengel-Epstein模型, 研究了两个子系统的图灵模对斑图的影响,发现其波数比在斑图的形成和选择过程中起着重要作用.当波数比为1时,双层系统未能发生耦合,只能出现条纹和六边形斑图;当波数比处于1-√17 的范围时,两子系统发生耦合,图灵模之间发生共振相互作用,得到种类丰富的超点阵斑图,包括暗点、点-棒和复杂超六边、Ⅰ-型和Ⅱ-型白眼、类蜂窝和环状超六边等斑图;当波数比大于√17 , 系统选择的斑图类型不再变化,均为环状超六边斑图.数值模拟得到的条纹、六边形、超六边点阵、Ⅱ-型白眼斑图和类蜂窝斑图均已在介质阻挡放电系统实验中观察到. 另外,还得到了超点阵斑图的波数随两个扩散系数乘积D_uD_v的变化曲线,发现其随的D_uD_v增大而减小. 关键词： 耦合系统 超点阵 波数比 数值模拟     

Fisher renormalization in a compressible spherical model

The Fisher-renormalized Ising exponents are being shown to correspond rather to a compressible spherical model of Berlin and Kac, than to the compressible Ising model of Baker and Essam.     

Benney's long waves equations: Hamiltonian form alism

The connection between the Lie algebra of Hamilton plane vector fields and Benney's momentum equations is shown.     

Harmonics of Tollmien — Schlichting waves in a compressible boundary layer

The harmonics of Tollmien—Schlichting waves in a compressible boundary layer of a plate are computed with the aid of nonlinear parabolized stability equations. At the (downstream) growth of the second harmonic amplitude up to the values of the order of the basic harmonic amplitude, the amplification rate of the latter is shown to increase abruptly. A similar rapid deviation from the results of the linear theory characterizes the onset of the boundary-layer transition to turbulent state. Computations are carried out for the Mach numbers M = 0.01 and 2. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 05-01-00079a).