Nonlinear Rayleigh–Taylor instability of two superposed magnetic fluids under parallel rotation and a normal magnetic field

The Rayleigh–Taylor instability (RTI) of a ferrofluid has been the subject of recent research, because of its implications on the stability of stellar and planetary interiors. This paper analyzes the effects of rotation and magnetic field on nonlinear RTI of two superposed ferrofluids. It is considered that the system is subjected to uniform parallel rotation and normal magnetic field. Surface tension acts at the interface. The method of multiple scales is utilized to obtain the solutions and dispersion relations are obtained for the nonlinear problem of RTI of magnetic fluids. Finally the stability of the problem is discussed.     

Flames in narrow circular tubes

We examine an axi-symmetric deflagration located in a tube with thermally active walls. It is noted that the flame-in-tube configuration defines a classical edge-flame, a flame in a shear flow for which there is a water-shed solution for a critical value of the Damköhler number (D), ignition front solutions for larger values of D, and failure wave solutions for smaller values. We examine semi-infinite tubes with a heat flux imposed at the tube wall ends, to simulate experiments reported in the 30th Symposium. We identify parameters for which stable solutions are obtained at certain flow rates, but unstable solutions are generated at higher flow rates, followed by stable solutions at still higher flow rates. These solutions are consistent with the experimental record. Instability leads either to regular oscillations or to a violent process characterized by quenching and re-ignition.     

On intrinsic oscillation in radiation-affected diffusion flames

A linear stability analysis is conducted to study the onset of near-limit flame oscillation with radiative heat loss in 1-D chambered planar flames using multi-scale activation-energy asymptotics. The oscillatory instability near the radiation-induced extinction limit at large Damköhler numbers is identified, in additional to the one near the kinetic limit at small Damköhler numbers. It is shown that radiative loss assumes a similar role as varying the thermal diffusivity of the reactants. Thus, flame oscillation near the radiative limit is still thermal-diffusive in nature although it may develop under unity Lewis numbers. The unstable range of Damköhler numbers near the radiative limit shows quite similar parametric dependence on the Lewis numbers of reactants, Le_F and Le_O, the stoichiometry, ?, and the radiative loss as that near the kinetic limit. They both increase monotonically with Le_O and ? and increase then decrease with Le_F. Increasing radiative loss extends the parameter range under which flame oscillations may develop. However, they show different dependence on the temperature difference between the supplying reactants. Unless radiative loss approaches its maximum value the system can sustain, flame oscillation near the radiative limit is only possible within a limited range of ΔT, whereas it is promoted monotonically with decreasing ΔT near the kinetic limit. Furthermore, while radiative loss shows small effect on the nondimensional oscillation frequency, the dimensional frequency of flame oscillations near the radiative limit can be substantially smaller than that near the kinetic limit.     

非磁化等离子体和磁化等离子体的电磁辐射特性研究

本文研究非磁化和磁化双MAXWELL分布等离子体的电磁不稳定性色散方程和电磁辐射增长率.结果表明,非磁化等离子体不能辐射出电磁波,而磁化等离子体能够辐射出电磁波.并分析讨论了磁化等离子体在不同参数下的电磁辐射增长率随辐射频率、等离子体密度和温度的变化.     

Nonlinear analysis of the deformation and breakup of viscous microjets using the method of lines

We present a numerical model for predicting the instability and breakup of viscous microjets of Newtonian fluid. We adopt a one‐dimensional slender‐jet approximation and obtain the equations of motion in the form of a pair of coupled nonlinear partial differential equations (PDEs). We solve these equations using the method of lines, wherein the PDEs are transformed to a system of ordinary differential equations for the nodal values of the jet variables on a uniform staggered grid. We use the model to predict the instability and satellite formation in infinite microthreads of fluid and continuous microjets that emanate from an orifice. For the microthread analysis, we take into account arbitrary initial perturbations of the free‐surface and jet velocity, as well as Marangoni instability that is due to an arbitrary variation in the surface tension. For the continuous nozzle‐driven jet analysis, we take into account arbitrary time‐dependent perturbations of the free‐surface, velocity and/or surface tension as boundary conditions at the nozzle orifice. We validate the model using established computational data, as well as axisymmetric, volume of fluid (VOF) computational fluid dynamic (CFD) simulations. The key advantages of the model are its ease of implementation and speed of computation, which is several orders of magnitude faster than the VOF CFD simulations. The model enables rapid parametric analysis of jet breakup and satellite formation as a function of jet dimensions, modulation parameters, and fluid rheology. Copyright © 2010 John Wiley & Sons, Ltd.     

A simple proof of the linear instability of rotating liquid drops

We give a simplified proof of the linear instability of equilibrium figures of rotating liquid based on energy estimates.      

Unstable plasma characteristics in mirror field electron cyclotron resonance microwave ion source

Electron cyclotron plasma reactor are prone to instabilities in specific input power [3–7] region (150–450 watts). In this region power absorption by gas molecules in the cavity is very poor and enhanced input power gets reflected substantially without increasing ion density. There are abrupt changes in plasma characteristics when input power was decreased from maximum to minimum, it was observed that reflected power changed from <2% to ∼50%. Minimum two jumps in reflected power were noticed in this specific power region and these appear to be highly sensitive to three stub tuner position in the waveguide for this particular input power zone. Unstable plasma region of this source is found to be dependent upon the magnetic field strength. Some changes in reflected power are also noticed with pressure, flow and bias and they are random in nature.     

Study of the membrane effect on turbulent mixing measurements in shock tubes

The effect of the thin membrane on the time evolution of the shock wave induced turbulent mixing between the two gases initially separated by it is investigated using two different sets of experiments. In the first set, in which a single-mode large-amplitude initial perturbation was studied, two gas combinations (air/SF and air/air) and two membrane thicknesses were used. The main conclusion of these experiments was that the tested membrane has a negligible effect on the evolution of the mixing zone, which evolves as predicted theoretically. In the second set, in which similar gas combinations and membrane thicknesses were used, small amplitude random-mode initial perturbation, caused by the membrane rupture, rather than the large amplitude single-mode initial perturbation used in the first set, was studied. The conclusions of these experiments were: (1) The membrane has a significant effect on the mixing zone during the initial stages of its growth. This has also been observed in the air/air experiment where theoretically no growth should exist. (2) The membrane effect on the late time evolution, where the mixing zone width has reached a relatively large-amplitude, was relatively small and in good agreement with full numerical simulations. The main conclusion from the present experiments is that the effect of the membrane is important only during the initial stages of the evolution (before the re-shock), when the perturbations have very small amplitudes, and is negligible when the perturbations reach relatively large amplitudes. Received 29 August 1998 / Accepted 25 December 1998     

Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's

We present a general result of transverse nonlinear instability of 1d solitary waves for Hamiltonian PDE's for both periodic or localized transverse perturbations. Our main structural assumption is that the linear part of the 1-d model and the transverse perturbation “have the same sign”. Our result applies to the generalized KP-I equation, the Nonlinear Schrödinger equation, the generalized Boussinesq system and the Zakharov–Kuznetsov equation and we hope that it may be useful in other contexts.     

Orbital Instability of Standing Waves for the Klein-Gordon-Zakharov System

O Introduction We consider the orbital instability of standing waves for the Klein-Gordon-Zakharov system with different propagation speeds in three space dimensions