Weak Nonlinearity of Ablative Rayleigh--Taylor Instability

The weakly nonlinear regime of single mode ablative Rayleigh-Taylor instability is studied, with consideration of preheat effect and the width of the ablation front. The Rayleigh-Taylor linear growth rate agrees well with the direct numerical simulation. For the density perturbation, the amplitude distribution of the fundamental mode has one peak value whereas those of the second and third harmonics have two and three peak values, respectively. Harmonics generation versus wave number is also given and it is close to the result of direct numerical simulation.     

Compressible Rayleigh-Taylor Instability with Preheat in Inertial Confinement Fusion

The compressible Rayleigh-Taylor instability of accelerated ablation front is analysed in consideration of the preheat effects, and the corresponding eigen-problem is solved numerically using the fourth-order accurate two- point compact difference scheme. Both the growth rate and perturbation profiles are obtained, and the obtained growth rate is close to the results of direct numerical simulation. Our results show that the growth rate is more reduced and the cutoff wave length becomes longer as preheat increases.     

Numerical Simulation of Anisotropic Preheating Ablative Rayleigh-Taylor Instability

The linear growth rate of the anisotropic preheating ablative Rayleigh-Taylor instability （ARTI） is studied by numerical simulations. The preheating model κ （T）=κSH [1＋f（T）] is applied, where f（T） is the preheating function interpreting the preheating tongue effect in the cold plasma ahead of the ablative front. An arbitrary coefficient D is introduced in the energy equation to study the influence of transverse thermal conductivity on the growth of the ARTI. We find that enhancing diffusion in a plane transverse to the mean longitudinal flow can strongly reduce the growth of the instability. Numerical simulations exhibit a significant stabilization of the ablation front by improving the transverse thermal conduction. Our results are in general agreement with the theory analysis and numerical simulations by Masse [Phys. Rev. Lett. 98 （2007） 245001].     

Phase Effect on Mode Coupling in Kelvin-Helmholtz Instability forTwo-Dimensional Incompressible Fluid

This paper studies the phase effect in mode coupling of Kelvin-Helmholtzinstability in two-dimensional incompressible fluid. It is found that thereis an important growth phenomenon of every mode in the mode couplingprocess. The growth changes periodically with phase difference and in thecondition of our simulation the period is about 0.7π. The periodcharacteristic is apparent in all stage of the mode coupling process,especially in the relatively later stage.     

Lie Symmetry and Nonlinear Instability in Computation of KdV Solitons

The soliton calculation method put forward by Zabusky and Kruskal has played an important role in the development of soliton theory, however numerous numerical results show that even though the parameters satisfy the linear stability condition, nonlinear instability will also occur. We notice an exception in the numerical calculation of soliton, gain the linear stability condition of the second order Leap-frog scheme constructed by Zabusky and Kruskal, and then draw the perturbed equation with the finite difference method. Also, we solve the symmetry group of the KdV equation with the knowledge of the invariance of Lie symmetry group and then discuss whether the perturbed equation and the conservation law keep the corresponding symmetry. The conservation law of KdV equation satisfies the scaling transformation, while the perturbed equation does not satisfy the Galilean invariance condition and the scaling invariance condition. It is demonstrated that the numerical simulation destroy some physical characteristics of the original KdV equation. The nonlinear instability in the calculation of solitons is related to the breaking of symmetry.     

Flat Solitary Waves due to a Submerged Body Moving in a Stratified Fluid

A theoretical model for interaction of a submerged moving body with the conjugate flow in a three-layer fluid is proposed to depict the internal flat solitary wave, which is observed in experiments conducted by the present authors. A set of coupled nonlinear algebraic equations is derived for the interracial displacements. The numerical results indicate that （a） the conjugate flow due to a two-dimensional body moving at the bottom possesses an apparent behaviour with two convex interfaces, （b） the solution satisfying the existence criterion is always unique near the relatively stable state of system. Theoretical analysis is qualitatively consistent with the experimental results obtained.     

Electrostatic Instabilities at High Frequency in a Plasma Shock Front

New electrostatic instabilities in the plasma shock front are reported. These instabilities are driven by the electro- static field which is caused by charge separation and the parameter gradients in a plasma shock front. The linear analysis to the high frequency branch of electrostatic instabilities has been carried out and the dispersion relations are obtained numerically. There are unstable disturbing waves in both the parallel and perpendicular directions of shock propagation. The real frequencies of both unstable waves are similar to the electron electrostatic wave, and the unstable growth rate in the parallel direction is much greater than the one in the perpendicular direction. The dependence of growth rates on the electric field and parameter gradients is also presented.     

A Weakly Nonlinear Model for Kelvin-Helmholtz Instability in Incompressible Fluids

A weakly nonlinear model is proposed for the Kelvin-Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling.     

Magneto-Hydrodynamic High-n Ballooning Mode Instability of an Analytic Axi-Symmetric Toroidal Equilibrium with Arbitrary Aspect Ratio

An exact ballooning mode eigen-equation is derived to study stability of axi-symmetric toroidal plasma with arbitrary aspect ratio, including the tokamak, the finite aspect ratio and the spherical torus plasmas. For comparison with the widely used （ s-α） model, an analytic exact equilibrium configuration with circular magnetic surfaces is analysed in detail. It is indicated that the （s - α） model needs to be improved for more realistic configurations.     

Instabilities developed in stratified flows over pronounced obstacles

In the present work we study numerical and experimentally the flow of a two-layer stratified fluid over a topographic obstacle. The problem reflects a wide number of oceanographic and meteorological situations, where the stratification plays an important role. We identify the different instabilities developed by studying the pycnocline deformation due to a pronounced obstacle. The numerical simulations were made using the model caffa3D.MB which works with a numerical model of Navier-Stokes equations with finite volume elements in curvilinear meshes. The experimental results are contrasted with numerical simulations. Linear stability analysis predictions are checked with particle image velocimetry (PIV) measurements.     

Wavelet Cross-Spectrum Analysis of Multi-Scale Disturbance Instability and Transition on Sharp Cone Hypersonic Boundary Layer

Experimental measurement of hypersonic boundary layer stability and transition on a sharp cone with a half angle of 5° is carried out at free-coming stream Mach number 6 in a hypersonic wind tunnel. Mean andfluctuation surface-thermal-flux characteristics of the hypersonic boundary layer flow are measured by Pt-thin-film thermocouple temperature sensors installed at 28 stations on the cone surface along longitudinal direction. At hypersonic speeds, the dominant flow instabilities demonstrate that the growth rate of the second mode tends to exceed that of the low-frequency mode. Wavelet-based cross-spectrum technique is introduced to obtain the multi-scale cross-spectral characteristics of the fluctuating signals in thefrequency range of the second mode. Nonlinear interactions both of the second mode disturbance and the first mode disturbance are demonstrated to be dominant instabilities in the initial stage of laminar-turbulence transition for hypersonic shear flow.     

Magnetorotational instability in nonmagnetized plasma

It is shown that the magnetorotational instability (MRI) can be driven in nonmagnetized plasma. In this case, in contrast to the case of strongly magnetized plasma, radial derivative of plasma rotation frequency should be positive for such a driving. The characteristic wave lengths of MRI in nonmagnetized plasma are of the same order of magnitude as those for the Weibel instability.     

Water Surface Wave in a Trough with Periodical Topographic Bottom

We present the theoretical and experimental results of water surface wave in a trough with periodical topographic bottom under parametric excitation. There are 19 steps of the same size periodically inserted into the trough. It is found that waveforms observed in the experiment are consistent with theoretical ones. Moreover, some complex and interesting phenomena arise in the experiment due to nonlinearity.[第一段]     

Anisotropic emission in laser-produced aluminum plasma in ambient nitrogen

We report on the dynamical expansion of pulsed laser ablation of aluminum in ambient pressure of nitrogen using images of the expanding plasma. The plasma follows shock model at pressures of 0.1 Torr and drag model at 70 Torr, respectively, with incident laser energy of 265 mJ. The plasma expansion shows unstable boundaries at 70 Torr and is attributed to Rayleigh-Taylor instability. The growth time of Rayleigh-Taylor instability is estimated between 0.09 and 4 μs when the pressure is varied from 1 to 70 Torr. The pressure gradients at the plasma-gas interface gives rise to self-generated magnetic field and is estimated to be 26 kG at 1 Torr ambient pressure using the image of the expanding plasma near the focal spot. The varying degree of polarization of Al III transition 4s ²S_1/2-4p ²P°_3/2 at 569.6 nm gives rise to anisotropic emission and is attributed to the self-generated magnetic field that results in the splitting of the energy levels and subsequent recombination of plasma leading to the population imbalance.     

Role of Viscosity Stratification and Insoluble Surfactant in Instability of Two-Layer Channel Flow

We study, for the case of the two layer plane Poiseuille flow, the effect of viscosity stratification and interracial surfactant on the flow instability. Considering a normal mode of the streamwise wave number α, both the linear and energy analyses are presented. The expressions of perturbation energy supplied at the interface are derived. The result demonstrates that the jumps of horizontal velocity and tangential stress of the perturbed flow across the interface could be induced by the presence of viscosity stratification and surfactant. This is expected to be responsible for the Yih and Marangoni instability.     

Short Wavelength Ion Temperature Gradient Driven Instability in Noncircular Flux Surface Plasmas with Finite Aspect Ratio

By employing the local equilibrium of shaped tokamak plasmas, a gyrokinetic model with integral eigenmode equations is developed to investigate effects of the finite aspect ratio and noncircular flux surface on short wavelength ion temperature gradient （SWITG） driven modes. It is found that when nonadiabatic electron and trapped particle effects are not considered, the SWITG mode can be stabilized by finite aspect ratio A, elongation and triangularity δ, and can be destabilized by the Shafranov shift gradient θRo/θr.     

On the general form of the Benjamin-Bona-Mahony equation in fluid mechanics

In the study of many problems of mechanical and physical sciences, various versions of the Benjamin-Bona-Mahony (BBM) equation or the regularized-long-wave equation have been proposed. In this paper, we obtain the solitary-wave solutions to the general form of the BBM equation, which fully cover the variety of the BBM solitary waves previously reported. This work has been supported by the China Talent Fund, by the Cheung Kong Scholars Programme of China, by the Cheung-Kong-Scholar Research Concerted Fund of Beijing University of Aeronautics and Astronautics, and by the Doctoral Education Fund in Basic Sciences of Beijing University of Aeronautics and Astronautics.     

First Observation of Neoclassical Tearing Modes in the HL-2A Tokamak

The m/n = 2/1 neoclassical tearing modes are first observed in HL-2A low density, low beta plasma with central electron cyclotron resonance heating. The neoclassical tearing modes （NTMs） are triggered by a sawtooth crash with m/n = 1/1 precursors, which are toroidal coupled with a small scale m/n = 2/1 mode. The time history of the island width is compared with the prediction of the NTM theory, showing a good agreement between theory and experiment.     

The Rossby wave extra invariant in the physical space

It was found out in 1991 that the Fourier space dynamics of Rossby waves possesses an extra positive-definite quadratic invariant, in addition to the energy and enstrophy. This invariant is similar to the adiabatic invariants in the theory of dynamical systems. For many years, it was unclear if this invariant—known only in the Fourier representation—is physically meaningful at all, and if it is, in what sense it is conserved. Does the extra conservation hold only for a class of solutions satisfying certain constraints (like the conservation in the Kadomtsev-Petviashvili equation)? The extra invariant is especially important because this invariant (provided it is meaningful) has been connected to the formation of zonal jets (like Jupiter’s stripes).In the present paper, we find an explicit expression of the extra invariant in the physical (or coordinate) space and show that the invariant is indeed physically meaningful for any fluid flow. In particular, no constraints are needed. The explicit form also enables us to note several properties of the extra invariant.     

Wide- and narrow-band saturated fluorescence measurements of hydroxyl concentration in premixed flames from 1 bar to 10 bar

We have studied the use of wide-band detection in conjunction with saturation of a rovibronic transition of OH within itsA ^{2 +}–X ²(0,0) band. For wide-band detection, in which fluorescence is detected from the entire excited rotational manifold, the fluorescence yield is sensitive to collisions in two ways. First, it is sensitive to the ratio of rate coefficients describing rotational energy transfer and electronic quenching; this ratio determines the number of neighboring rotational levels that are populated during the laser pulse. Second, the fluorescence yield can vary with the total collisional rate coefficient; only after a sufficient number of collisions, corresponding to 2.5 ns in an atmospheric flame, does the rotational manifold reach steady state. We also compare measurements employing wide-band (detecting theR ₁ andR ₂ branches) and narrow-band (detecting a single transition) saturated fluorescence of OH. Over a wide range of conditions — obtained by varying the equivalence ratio, temperature, N₂ dilution, and pressure — the wide- and narrow-band fluorescence techniques compare well. Given this good agreement, wide-band saturated fluorescence could be especially useful for analyzing atmospheric flames with XeCl-excimer lasers; one can potentially obtain 2—D images of OH which have a high signal-to-noise ratio and a reduced sensitivity to laser irradiance and quenching.