Generation of vortices by gravity waves on a water surface

The generation of a vortex motion on a water surface by gravity waves at frequencies of 3 and 4 Hz and wavelengths of 17 and 9.7 cm, respectively, has been studied experimentally. It has been shown that the results can be described by a model of the formation of a vorticity by nonlinear waves. It has been shown for the first time that the vorticity amplitude on a water surface depends on the phase difference between the waves propagating at an angle of 90° with respect to each other and with a period of 360°. A quadratic dependence of the surface vorticity amplitude on the angular amplitude of the waves has been observed. Transfer of the energy of the vortex motion from the pumping region to a larger scale has been discovered.     

Solitary wave for a nonintegrable discrete nonlinear Schr?dinger equation in nonlinear optical waveguide arrays

We study a nonintegrable discrete nonlinear Schr?dinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term.     

On the possibility of initiating a corona discharge at the crests of nonlinear waves on the surface of a charged thin layer of a viscous conducting liquid

An analytic expression for the electrostatic field strength at the free surface of a thin layer of a uniformly charged viscous incompressible liquid is obtained in second-order asymptotic calculations in the amplitude of a periodic capillary-gravity wave propagating over the liquid surface. It is shown that a corona discharge at the crests of the waves can be initiated at subcritical values of the field strength (in the sense of possible realization of the Tonks-Frenkel instability). The electrostatic field strength at the crests of nonlinear waves increases with the wavenumber and the wave amplitude.     

Nonlinear periodic waves on the charged surface of a viscous finite-conductivity fluid

The profile of a periodic capillary-gravitational wave propagating over the surface of a viscous finite-conductivity fluid is found in a second-order approximation in initial deformation amplitude. When the finiteness of the rate with which the potential of the fluid smoothes out as capillary-gravitational waves travel over its free surface is taken into account, the intensity of nonlinear interaction between the waves changes. This intensity is found to depend on the electric charge surface density, conductivity of the fluid, and wavenumbers. The finiteness of the potential smoothing rate influences the nonlinear interaction between the waves nonmonotonically.     

Non-dispersive traveling waves in inclined shallow water channels

Existence of traveling waves propagating without internal reflection in inclined water channels of arbitrary slope is demonstrated. It is shown that traveling non-monochromatic waves exist in both linear and nonlinear shallow water theories in the case of a uniformly inclined channel with a parabolic cross-section. The properties of these waves are studied. It is shown that linear traveling waves should have a sign-variable shape. The amplitude of linear traveling waves in a channel satisfies the same Green's law, which is usually derived from the energy flux conservation for smoothly inhomogeneous media. Amplitudes of nonlinear traveling waves deviate from the linear Green's law, and the behavior of positive and negative amplitudes are different. Negative amplitude grows faster than positive amplitude in shallow water. The phase of nonlinear waves (travel time) is described well by the linear WKB approach. It is shown that nonlinear traveling waves of any amplitude always break near the shoreline if the boundary condition of the full absorption is applied.     

Propagation and interaction of nonlinear waves in a liquid with gas bubbles

The propagation and interaction of nonlinear solitonlike waves in a liquid with gas bubbles are considered using the Nakoryakov-Pokusaev-Shreiber two-wave equation. It is shown that these waves exist within the “opacity” window for linear waves. The interaction of such waves propagating in opposite directions may lead to their splitting into secondary localized waves.     

非线性兰姆波在阶梯板中传播的有限元仿真

在非线性兰姆波检测中,累积二次谐波是重要的检测信号.该文利用有限元法仿真了非线性兰姆波在阶梯板中的产生和传播过程,通过二维离散傅里叶变换分析了兰姆波的传播模态和各个模态通过波导横截面的能流大小,给出了各个模态在阶梯板中的反射、透射系数,总结了其随阶梯板厚度的变化规律.研究发现,随着台阶增高,散射效应使得兰姆波更难入射波...     

Formation of an energy cascade in a system of vortices on the surface of water

The formation of an energy cascade in a system of vortices generated by perpendicular standing waves with a frequency of 6 Hz on the water surface has been experimentally studied. It has been found that peaks appear on the energy distribution over wave vectors E(k) after switching on pumping. These peaks are transformed with time because of the energy redistribution over scales. The stationary distribution E(k) established 300 s after switching on pumping can be described by a power-law function of the wave vector E(k) ～ k^1.75. It has been shown that waves with frequencies of about 18, 15, 12, 9, and 3 Hz appear on the surface of water owing to the nonlinear interaction at the excitation of a 6-Hz wave. It is assumed that the energy cascade of the turbulent motion in the wave vector range of 0.3–5 cm^?1 is formed by the nonlinear interaction between vortices generated by all waves propagating on the surface and direct energy fluxes toward high wave vectors dominate.     

一维非线性声波传播特性

针对一维非线性声波的传播问题进行了有限元仿真和实验研究. 首先推导了一维非线性声波方程的有限元形式, 含有高阶矩阵的非线性项导致声波具有波形畸变、谐波滋生、基频信号能量向高次谐波传递等非线性特性. 编制有限元程序对一维非线性声波进行了计算并对仿真得到的畸变非线性声波信号进行处理, 分析其传播性质和物理意义. 为验证有限元计算结果, 开展了水中的非线性声波传播的实验研究, 得到了不同输入信号幅度激励下和不同传播距离的畸变非线性声波信号. 然后对基波和二次谐波的传播性质进行详细讨论, 分析了二次谐波幅度与传播距离和输入信号幅度的变化关系及其意义, 拟合出二次谐波幅度随传播距离变化的方程并阐述了拟合方程的物理意义. 结果表明, 数值仿真信号及其频谱均与实验结果有较好的一致性, 证实计算方法和结果的正确性, 并提出了具有一定物理意义的二次谐波随传播距离变化的简单数学关系. 最后还对固体中的非线性声波传播性质进行了初步探讨. 本研究工作可为流体介质中的非线性声传播问题提供理论和实验依据.     

Nonlinear TE-polarized quasi-surface waves in a symmetric optical waveguide with a nonlinear core

A theory of nonlinear polarized symmetric quasi-surface waves in a symmetric planar structure with a nonlinear core and linear coatings has been proposed. The nonlinearity of the core is caused by exciton-photon interaction and optical exciton-biexciton conversion. The dispersion laws for propagating waves have been obtained and studied.     

Decaying solitary waves propagating in one-dimensional damped granular chain

We numerically investigate the nonlinear waves propagating in a one-dimensional particle chain when the damping effect is taken into account. It is found that decaying solitary waves exist, in which the amplitude of the wave decreases exponentially as time increases. Meanwhile, the velocity of the solitary wave also slows down as time goes. This result implies that the damping coefficient is an important parameter in such a nonlinear system. Theoretical analysis has also been done by the reductive perturbation method. The result indicates that the nonlinear waves propagating in such a system can be described by the damped KdV equation.     

Nichtlineare Wechselwirkung elektromagnetischer Wellen im Plasma mit konstantem Magnetfeld

The nonlinear interaction of waves in anisotropic plasmas is considered. Solving the hydrodynamics equations with a n-th order perturbation procedure, an equation for the nonlinear electric field is derived. The n-th order current produced by interaction of waves with lower order is represented by means of a nonlinear tensor of conductivity, which is calculated for n = 2. It is shown, that a miced plasma wave with combination frequencies is excited as the result of interaction of two transverse (ordinary) waves propagating perpendicular to the magnetic field.     

Steady-state vectorial self-diffraction on a non-local photorefractive grating in a crystal of symmetry \overline{4}3m at symmetrical transmitting geometry

The steady-state two-wave interaction in a cubic crystal of the symmetry group 3m with the non-local photorefractive response in the absence of an external electric field is considered for the case of arbitrary interaction orientation with respect to the crystallographic coordinate system and for arbitrary intensities and polarization states of incident light waves. The self-diffraction problem is described on the basis of four coupled-wave equations in terms of the complex scalar amplitudes of components of the light waves with orthogonal linear polarization. The derived conservation laws are valid for the non-linear dependency of the photorefractive-grating amplitude on the modulation coefficient of the interference light pattern. It follows from these laws that the two non-unidirectional energy fluxes can form the total energy exchange between the two interacting light waves. A set of independent conservation laws allows us to decouple the coupled-wave equations and to obtain their analytical solution, at least, in the form of quadrature formulae. For example, such a solution is derived for the case of linearly polarized incident light waves and for the linearized dependency of the photorefractive-grating amplitude on the modulation coefficient. The explicit analytical expressions for the scalar amplitudes are obtained for the transversal electro-optic configuration of interaction. The possibility of polarization-state transformation of light waves without energy exchange between them is shown. Received: 30 July 2002 / Published online: 11 December 2002 RID="*" ID="*"Corresponding author. Fax: +7-3822/414321, E-mail: litvinov@ed.rk.tusur.ru     

Nonlinear electrostatic waves in a magnetized plasma

The modulational interaction of finite-amplitude high-frequency electrostatic waves propagating at an arbitrary angle to an external magnetic field with slow plasma motion is considered. A set of nonlinear evolution equations describing the interaction is obtained. New types of solitary waves propagating at near sonic speeds are found.     

Propagation of waves in a multicomponent plasma having charged dust particles

Propagation of both low and high frequency waves in a plasma consisting of electrons, ions, positrons and charged dust particles have been theoretically studied. The characteristics of dust acoustic wave propagating through the plasma has been analysed and the dispersion relation deduced is a generalization of that obtained by previous authors. It is found that nonlinear localization of high frequency electromagnetic field in such a plasma generates magnetic field. This magnetic field is seen to depend on the temperatures of electrons and positrons and also on their equilibrium density ratio. It is suggested that the present model would be applicable to find the magnetic field generation in space plasma.     

Surface waves in a crystal with switching Kerr nonlinearity

In this paper, we explore transverse electric surface waves propagating along the crystal with jump change of Kerr nonlinearity in dependence on field amplitude. The dielectric permittivity in the proposed model of nonlinearity is characterized by abruptly changing unperturbed dielectric constant and Kerr nonlinearity coefficient from one value to another when field amplitude exceeds the threshold value of the switching field. This allows to find exact solutions of model equations in different cases of nonlinearity signs, and to obtain the dependence of wave characteristics, including total power flux, on effective refractive index in explicit form. Such solutions describe two new types of nonlinear surface waves with specific structure depending on electric field amplitude. We derive the conditions of surface domain formation. It is found that the largest percentage of radiation is concentrated within the domain.     

Stochastic heating of plasma at electron cyclotron resonance

It is shown theoretically and experimentally that stochastic heating of plasma electrons is highly efficient. Calculations have shown that over the course of 100 periods of an external microwave field the kinetic energy of the particles reaches values of around 1.0 MeV and the average energy reaches values of the order of 0.3 MeV in the field of two oppositely propagating characteristic (eigen) waves of a cylindrical waveguide, with amplitudes 24 kV/cm in a 1 kG stationary magnetic field. Stochastic instability develops as a result of overlapping of non-linear cyclotron resonances. The experimental results agree with the theory: When these waves are excited by a 0.9 MW external source, above a threshold of 0.45 MW one obtains x rays with a photon energy corresponding to a maximum electron energy of the order of 1 MeV over about 800 periods of the external microwave field. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 11, 806–811 (10 June 1999)     

Self-localized nonlinear surface magnetic polaritons in a ferromagnetic medium

The properties of electromagnetic waves propagating in a semibounded, nonlinear, ferromagnetic medium are investigated. It is shown that under certain conditions the interaction between the spin and electromagnetic waves results in the localization of volume polaritons near the surface. Self-localization of surface polaritons due to the nonlinear properties of the medium occurs thereby. The nonlinear Schrödinger equation for nonlinear surface and volume polaritons is derived, and the conditions under which solitons of these waves exist are determined. The wave intensity required to observe the predicted effects is estimated.     

Effect of the anisotropy of a conducting layer on the dispersion law of electromagnetic waves in layered metal-dielectric structures

The dispersion laws of electromagnetic waves in layered periodic metal-dielectric structures with anisotropic metal layers have been theoretically analyzed. It has been found that the anisotropy of metal layers is responsible for the appearance of additional allowed energy bands for photons. It has been shown that these bands correspond to plasma (Langmuir) waves propagating in anisotropic metal layers of the structure. Conditions under which the directions of group and phase velocities of Langmuir waves coincide or are opposite have been determined. It has been shown that the penetration of the electromagnetic field of Langmuir waves into dielectric layers is exponentially weak and this field is primarily concentrated in metal layers, where it oscillates in the direction perpendicular to the plane of the layers.     

Nonlinear analysis of a wave motion on the surface of a jet moving in a dielectric medium placed in a longitudinal electric field

The possibility of degenerate internal nonlinear resonance interaction between capillary waves with arbitrary symmetry (arbitrary azimuthal numbers) on the surface of a charged cylindrical jet of an ideal incompressible conducting liquid is demonstrated. The jet moves in an ideal incompressible dielectric medium collinearly with an external uniform electrostatic field. It is shown, in particular, that six different resonance situations take place for axisymmetric waves in which primary waves and waves due to the nonlinearity of the equations of hydrodynamics exchange energy.