Order parameter description of walk-off effect on pattern selection in degenerate optical parametric oscillators

Degenerate optical parametric oscillators can exhibit both uniformly translating fronts and nonuniformly translating envelope fronts under the walk-off effect. The nonlinear dynamics near threshold is shown to be described by a real convective Swift-Hohenberg equation, which provides the main characteristics of the walk-off effect on pattern selection. The predictions of the selected wave vector and the absolute instability threshold are in very good quantitative agreement with numerical solutions found from the equations describing the optical parametric oscillator.     

Three-dimensional absolute and convective instabilities in mixed convection of a viscoelastic fluid through a porous medium

By using the mathematical formalism of absolute and convective instabilities we study the nature of unstable three-dimensional disturbances of viscoelastic flow convection in a porous medium with horizontal through-flow and vertical temperature gradient. Temporal stability analysis reveals that among three-dimensional (3D) modes the pure down-stream transverse rolls are favored for the onset of convection. In addition, by considering a spatiotemporal stability approach we found that all unstable 3D modes are convectively unstable except the transverse rolls which may experience a transition to absolute instability. The combined influence of through-flow and elastic parameters on the absolute instability threshold, wave number and frequency is then determined, and results are compared to those of a Newtonian fluid.     

Convective and absolute instabilities in the subcritical Ginzburg-Landau equation

We study the nature of the instability of the homogeneous steady states of the subcritical real Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by the destabilizing cubic nonlinearities, is confirmed by the numerical analysis of the evolution of its perturbations. It is also shown that the dynamics of these perturbations is such that finite size effects may suppress the transition from convective to absolute instability. Finally, we analyze the instability of the subcritical middle branch of steady states, and show, analytically and numerically, that this branch may be convectively unstable for sufficiently high values of the group velocity. Received 17 December 1998     

Three dimensional convective instability in nematic liquid crystal under an ac field

Using a light scattering technique, fluctuations in nematic MBBA under an a.c. field are investigated near a three dimensional convective instability point. It is found that the instability is accompanied by a critical slowing down of the thermally excited twist fluctuation and the appearance of the macroscopic undamped oscillation. A distribution of the molecular orientation is also proposed.     

Absolute and convective instabilities of a viscous film flowing down a vertical fiber

The stability of a viscous film flowing down a vertical fiber under the action of gravity is analyzed both experimentally and theoretically. At large or small film thicknesses, the instability is convective, whereas an absolute instability mode is observed in an intermediate range of film thicknesses for fibers of small enough radius. The onset of the experimental irregular wavy regime corresponds precisely to the theoretical prediction of the threshold of the convective instability.     

W波段回旋行波管绝对不稳定性的分析

 绝对不稳定性是制约回旋行波管性能的主要因素之一。通过回旋行波管色散方程,详细分析了W波段基波回旋行波管绝对不稳定性的形成和特征,提出了采用多段损耗波导来抑制绝对不稳定性的方法。分析表明,绝对不稳定性的起振存在一定阈值,起振电流对电子注参数和电路参数极其敏感,确定起振电流是稳定器件工作的前提条件。通过PIC模拟,给出了采用无损耗波导结构,且工作电流为25 A和10 A条件下的放大器频谱图和功率图,结果表明绝对不稳定性的出现与否主要由工作电流是否超过起振的阈值电流决定,损耗波导是抑制绝对不稳定性的有效手段。     

Single-particle Cherenkov effect in a bounded spatial region

The problem of the development of a beam instability in a bounded spatial region due to the single-particle Cherenkov effect is studied in the linear approximation. The threshold conditions for the onset of the convective and absolute instabilities of different longitudinal modes and their growth rates are determined with allowance for reflections from the boundaries of the system.     

Threshold fields for stimulated Brillouin scattering in spatially limited plasma

Brillouin scattering in an infinite medium is anisotropic, in this case the threshold of absolute instability is caused by attenuation of scattered waves. If the collision attenuation mechanism prevails, the minimum threshold value is observed during backward scattering. For a scattering region limited in the longitudinal direction (parallel to the direction of pumping wave propagation), the backward scattering threshold will be greater than for an infinite medium due to convective loss associated with energy removal by scattered waves. In this paper, the scattering of a wide wave beam in plasma is considered, whose dimension in the transverse direction to the pumping wave propagation substantially exceeds the dimension in the longitudinal direction. It was revealed that in this case, during angle scattering the instability threshold can be less than the threshold for backward scattering due to the increased time of radiation removal from the interaction region. This effect was not taken into account previously. In turn, the decrease of the threshold leads to increasing the radiation loss, which is important in plasma heating problems. The results can also be used for plasma diagnostics.     

基于损耗介质加载波导的回旋行波管放大器的互作用分析

损耗介质波导对提高回旋行波管放大器的稳定性等性能具有积极的作用.本文基于损耗介质波导中工作模式的场表达式,推导出电子回旋脉塞互作用线性理论.通过系统的数值计算发现损耗介质波导与光滑金属圆波导中的工作模式从场型分布和色散关系上都具有一一对应关系;通过Laplace变换,利用互作用线性理论计算工作模式的起振场型和阈值,并研究互作用系统磁场、电流和介质层对放大特性的影响.这些研究成果对促进损耗介质在回旋行波管放大器中的运用和高稳定性回旋行波管放大器的发展具有积极的作用.     

高超声速边界层中由粗糙元引起强制转捩的机理

由大粗糙元引起的高超声速边界层强制转捩在航天技术中有实际应用, 因而近年来受到人们的广泛关注.虽然目前导致该转捩过程的内在机理尚不完全清楚, 但有一点是明确的, 即粗糙元的尾迹流场中存在强对流不稳定性.文章的出发点是研究这种对流不稳定模态是如何触发转捩的.首先通过CFD方法, 计算出高超声速边界层中粗糙元的尾迹流场, 并对其进行二维稳定性分析.结果发现, 在传统不稳定Tollmien-Schlichting(T-S)模态出现的临界Reynolds数之前, 存在高增长率的无黏不稳定模态, 表现为对称的余弦模态和反对称的正弦模态.然后对该不稳定模态在粗糙元尾迹流中的演化进行了模拟, 验证了二维稳定性分析的结果, 并考察了非平行性效应的影响.最后通过直接数值模拟, 研究由这些不稳定模态触发转捩的全过程.结果表明, 对流不稳定模态确实是导致边界层转捩的关键机制.该转捩过程的特点是, 局部湍斑首先在不稳定模态特征函数的峰值附近出现, 然后向全流场扩散.就文章研究的工况而言, 余弦和正弦模态的相互作用对转捩的影响并不明显, 且后者在转捩过程中起主导作用.      

Absolute instability of a liquid jet in a coflowing stream

Cylindrical liquid jets are inherently unstable and eventually break into drops due to the Rayleigh-Plateau instability, characterized by the growth of disturbances that are either convective or absolute in nature. Convective instabilities grow in amplitude as they are swept along by the flow, while absolute instabilities are disturbances that grow at a fixed spatial location. Liquid jets are nearly always convectively unstable. Here we show that two-phase jets can breakup due to an absolute instability that depends on the capillary number of the outer liquid, provided the Weber number of the inner liquid is >O(1). We verify our experimental observations with a linear stability analysis.     

Experimental study of the instability of a film flowing down a vertical fiber

The wavy dynamics of a viscous film flowing axisymmetrically on a vertical fiber is characterized experimentally. The study of the initial response of the flow to natural noise shows a well-defined transition between a convective and an absolute instability [1]. In the convective case, disturbances of controlled frequencies have been applied at inlet. The flow responds to inlet excitation at frequencies lower than a well-defined cut-off frequency. A good agreement has been found with the linear stability analysis and with the solution to a two-equation model [2] in the nonlinear regime.     

Parametric decay instabilities of the fast wave in the lower hybridfrequency regime

Three possible delay instabilities of the fast wave in the lower hybrid frequency regime are presented. It has been considered that a fast wave may decay into a high-frequency, lower hybrid wave and a low-frequency wave, either the ion-Bernstein wave, ion-acoustic wave, or kinetic Alfven wave. Explicit expressions for growth rates, homogeneous thresholds, and convective thresholds have been given. Applications have been pointed out in tokamak plasma during current drive experiments and magnetospheric plasmas. For example, for PLT tokamak parameters, the convective threshold for the decay instability of the fast wave into lower hybrid and ion acoustic wave is ~180 W/cm²     

Low-frequency potential structures in a nonuniform dusty magnetoplasma

The linear and nonlinear properties of a modified convective cell (MCC) in a nonuniform dusty magnetoplasma with a perpendicular plasma flow are investigated. It is shown that the free energy of the equilibrium plasma flow can drive the MCC at nonthermal levels. By choosing some specific profiles for the sheared plasma flow and the dust number density, we analyze the eigenvalue equation for deducing the growth rate and the threshold of a convective mode instability which arises due to its interaction with the shear plasma flows. Our analytical results show that a Rayleigh-type instability sets in provided that the characteristic width of the flow does not exceed a certain value. On the other hand, the nonlinear equation, which governs the dynamics of the nonlinearly interacting convective modes, admits stationary solutions in the form of a vortex chain associated with zonal flows, as well as tripolar and global vortices. The relevance of our investigation to a laboratory experiment is discussed.     

Modification of pattern formation in doubly resonant second-harmonic generation by competing parametric oscillation

We analyze pattern formation in doubly resonant intracavity second-harmonic generation in the presence of competing nondegenerate parametric downconversion. We show that for positive cavity detuning of the fundamental frequency the threshold for parametric oscillation is lower than that of transverse, pattern forming instabilities. The parametric oscillation strongly modifies the pattern dynamics found previously in a simplified analysis that neglects parametric instability [Phys. Rev. E 56, 4803 (1997)]. Stationary and dynamic patterns in the presence of parametric oscillation are found numerically.     

Secondary transverse instabilities in optical parametric oscillators

We investigate the effect of coupling between diffraction and walk-off on secondary instabilities in nondegenerate optical parametric oscillators. We show that traveling waves that propagate in the walk-off direction, which are generated at the onset of absolute instability, experience Eckhaus and zigzag phase instabilities. Each of these secondary instabilities splits into absolute and convective instabilities that modify the Eckhaus and zigzag instability boundaries. As a consequence, the stability domain of modulated traveling waves is enlarged and may coexist with uniform steady states. The predictions are consistent with the numerical solutions of the optical parametric oscillator model.     

Stabilization of solitons generated by a supersonic flow of Bose-Einstein condensate past an obstacle

The stability of dark solitons generated by supersonic flow of a Bose-Einstein condensate past an obstacle is investigated. It is shown that in the reference frame attached to the obstacle a transition occurs at some critical value of the flow velocity from absolute instability of dark solitons to their convective instability. This leads to the decay of disturbances of solitons at a fixed distance from the obstacle and the formation of effectively stable dark solitons. This phenomenon explains the surprising stability of the flow picture that has been observed in numerical simulations.     

Fingering instability in forward smolder combustion

We use numerical strategies to examine the linear and nonlinear stability of forward smolder waves in the framework of a simplified thermal–diffusive model, with the hydrodynamic effects completely filtered out. The configuration consists of a horizontal thin solid fuel, over which air blows in the same direction as the smolder front propagation. It is found that, in the absence of convective heat losses, the whole one-dimensional adiabatic solution branch is linearly stable; in contrast, when the convective heat loss effect is taken into account, fingering instability emerges provided the incoming air flow rate is within a narrow range near the one-dimensional extinction limit, a manifestation that is reminiscent of the familiar cellular instability occurring in the context of low-Lewis-number diffusion flames. Accordingly, the fingering instability herein identified in forward smolder combustion is purely thermal–diffusive in nature. Furthermore, a heuristic analysis by drawing an analogy with premixed flame suggests that the occurrence of such fingering instability is the joint consequence of the Lewis number effects and convective heat losses. It is proposed that a Hele–Shaw-type combustion channel may be adopted to experimentally reveal the fingering patterns predicted by current numerical simulations.