Linear instability and adiabaticity of a dark state during conversion of two species of fermionic atoms to stable molecules

In the present paper, we investigate the linear instability and adiabaticity of a dark state during conversion of two species of fermionic atoms to stable molecules through the stimulated Raman adiabatic passage aided by Feshbach resonance. We analytically obtain the regions for the appearance of linear instability. Moreover, taking 40K and 6Li atom molecule conversion systems as examples, we give the unstable regions numerically. We also attempt to obtain the adiabatic criterion for this nonlinear system with classical adiabatic dynamics and study the adibaticity of the dark state with the adiabatic condition.

Onset of Linear Instability in a Complex Plasma with Cairns Distributed Electrons

A rigorous theoretical investigation of linear dust ion acoustic (DIA) solitary waves in an unmagnetized complex plasma consisting of ion and ion beam fluids, nonthermal electrons that are Cairns distributed and immobile dust particles were undertaken. It was found out that, for large beam speeds, three stable modes propagated as solitary waves in the beam plasma. These were the “Fast”, “Slow” and “Ion-acoustic” modes. For two stream instability to occur between ion and ion beam, it is shown that or when .

Linear Analysis of Longshore Currents Instability over Mild Slopes

Longshore current instability is important to nearshore hydrodynamic and sediment transport. This paper investigates the longshore current instability growth model based experimental data with different velocity profiles of slopes1:100 and 1:40 by adopting a linear shear instability model with the bottom friction effects. The results show that:(1)Only backshear mode exists in the instability of longshore current for slope 1:40 and frontshear and backshear modes may exist slope 1:100.(2) The peaks of linear instability growth mode for slope 1:100 correspond to three cases: the dominant peak is formed by the joint action of both frontshear and backshear, or by backshear alone without the existence of the smaller peak or formed by either the frontshear or backshear.(3) Bottom friction can decrease the corresponding unstable growth rate but it cannot change the unstable fluctuation period. The results of fluctuation period, wavelength and spatial variation obtained by the analysis of linear shear instability are in good agreement with experimental results.

A CFD-Aided Galerkin Method for Global Linear Instability Analysis

Global linear instability analysis is a powerful tool for the complex flow diagnosis.However,the methods used in the past would generally suffer from some dis-advantages,either the excessive computational resources for the low-order methods or the tedious mathematical derivations for the high-order methods.The present work proposed a CFD-aided Galerkin methodology which combines the merits from both the low-order and high-order methods,where the expansion on proper basis func-tions is preserved to ensure a small matrix size,while the differentials,incompressibility constraints and boundary conditions are realized by applying the low-order linearized Navier-Stokes equation solvers on the basis functions on a fine grid.Several test cases have shown that the new method can get satisfactory results for one-dimensional,two-dimensional and three-dimensional flow problems and also for the problems with complex geometries and boundary conditions.

Linear Growth of Rayleigh-Taylor Instability of Two Finite-Thickness Fluid Layers

The linear growth of Ftayleigh-Taylor instability （FtTI） of two superimposed finite-thickness fluids in a gravita- tional field is investigated analytically. Coupling evolution equations for perturbation on the upper, middle and lower interfaces of the two stratified fluids are derived. The growth rate of the RTI and the evolution of the amplitudes of perturbation on the three interfaces are obtained by solving the coupling equations. It is found that the finite-thickness fluids reduce the growth rate of perturbation on the middle interface. However, the finite-thickness effect plays an important role in perturbation growth even for the thin layers which will cause more severe RTI growth. Finally, the dependence of the interface position under different initial conditions are discussed in some detail.

Baroclinic Instability in the Generalized Phillips' Model Part Ⅱ:Three-layer Model

The nonlinear stability of the three-layer generalized Phillips model, for which the velocity in each layeris constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol'd'svariational principle and a prior estimate method. The nonlinear stability criteria are established. For comparison, the linear instability criteria are also obtained by using normal mode method. and the influences ofthe free parameter, β parameter and curvature in vertical profile of the horizontal velocity on the linear instability are discussed by use of the growth rate curves. The comparison between the nonlinear stability criterion and the linear one is made. It is shown that insome cases the two criteria are exactly the same in form, but in other cases, they are different. This phenomenon, which reveals the nonlinear property of the linear instability features. is explained by the explosiveresonant interaction (ERI). When there exists the ERI, i.e., the nonlinear mechanisms play a leading role inthe dynamical system. the nonlinear stability criterion is different from the linear one, on the other hand.when there does not exist the ERI. the nonlinear stability criterion is the same as the linear one in form.

Instability in Three-Dimensional Magnetohydrodynamic Flows of an Electrically Conducting Fluid

The three-dimensional instability of an electrically conducting fluid between two parallel plates affected by an imposed transversal magnetic field is numerically investigated by a Chebyshev collocation method. The QZ method is utilized to obtain neutral curves of the linear instability. The details of instability are analyzed by solving the generalized Orr-Sommerfeld equation. The critical Reynolds number Rec, the stream-wise and span-wise critical wave numbers αc and βc are obtained for a wide range of Hartmann number Ha. The effects of Lorentz force and span-wise perturbation on three-dimensional instability are investigated. The results show that magnetic field would suppress the instability and critical Reynolds number tends to be larger than that for two-dimensional instability.

Linear global stability of a confined plume

A linear stability analysis is performed for a plume flow inside a cylinder of aspect ratio 1. The configu- ration is identical to that used by Lopez and Marques （2013） for their direct numerical simulation study, It is found that the first bifurcation, which leads to a periodic axisymmetric flow state, is accurately pre- dicted by linear analysis： both the critical Rayleigh number and the global frequency are consistent with the reported DNS results. It is further shown that pressure feedback drives the global mode, rather than absolute instability.

An experimental study of the spatial structures of the instabilities of longshore currents on plane beaches

A laboratory experiment on alongshore currents is conducted for two plane beaches with slopes 1：40 and 1：i00 to investigate the instability of alongshore currents. The dye release experiment is also performed synchronously in surf zone. Complicated and strongly unstable motions of alongshore currents are observed in the experiment. To examine the spatial and temporal variations of the shear instabilities of longshore clearly, dye batches are released in surf zone. The deformation of the dye patch is observed efficiently and effectively with charge coupled device （CCD） system. Some essential characteristics of the shear instability are validated from the results of image analyses of the temporal variation of the dye patch. The influences of alongshore currents, Stokes drift, large-scale vorticity and the shear instabilities on the transport of dye are analyzed using the collected images. The spatial structure of the instabilities of longshore currents is studied by analyzing collected images of the dye patch. And the phase velocity of the meandering movements is obtained through measuring the movement distances of the oscillations of dye patch in alongshore direction with time. The results suggest that the propagation speed of the shear instability is approximately 5070 7570 of maximum of mean alongshore currents for irregular and regular waves. The calculated propagation speed using a linear instability analysis theory is compared with the experimental results. The comparison shows agreements between them.

Three dimensional simulations of penetrative convection in a porous medium with internal heat sources

The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.

FLOQUET STABILITY ANALYSIS OF TWO-LAYER FLOWS IN VERTICAL PIPE WITH PERIODIC FLUCTUATION

Based on linear stability theory, parametric resonance phenomenon of a liquidgas cylindrical flow in a vertical pipe with periodic fluctuation was discussed with the help of Floquet theory and Chebyshev spectral collocation method. The effects of different physical parameters were investigated on the properties of parametric resonance and the stability characteristics of flow field.

PDRK:A General Kinetic Dispersion Relation Solver for Magnetized Plasma

A general,fast,and effective approach is developed for numerical calculation of kinetic plasma linear dispersion relations.The plasma dispersion function is approximated by J-pole expansion.Subsequently,the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system.Numerical solutions for the least damped or fastest growing modes using an 8-pole expansion are generally accurate;more strongly damped modes are less accurate,but are less likely to be of physical interest.In contrast to conventional approaches,such as Newton＇s iterative method,this approach can give either all the solutions in the system or a few solutions around the initial guess.It is also free from convergence problems.The approach is demonstrated for electrostatic dispersion equations with one-dimensional and twodimensional wavevectors,and for electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with relative parallel velocity flows between species.

LINEAR AND NONLINEAR BAROTROPIC INSTABILITY

Based on a non-frictional and non-divergent nonlinear barotropic vorticity equation and its solutions of travelling waves,the criteria for linear and nonlinear barotropic instability are gained respectively at an equilibrium point of the equation on a phase plane.The linear and nonlinear analytical solutions to instability waves are also found.The computational results show that if their amplitudes are equal at the initial time,the amplitude increments of nonlinear instable barotropic wave are always less than those of linear instable barotropic wave. The nonlinear effects can slow down the exponential growth of linear instability.The time needed for making the amplitude double that of initial time by instabilities,is about 6h for linear instability and about 18h for nonlinear instability,the latter is in agreement with the observations in the real atmosphere.

Linear stability analysis of interactions between mixing layer and boundary layer flows

The linear instabilities of incompressible confluent mixing layer and boundary layer were analyzed.The mixing layers include wake,shear layer and their combination.The mean velocity profile of confluent flow is taken as a superposition of a hyperbolic and exponential function to model a mixing layer and the Blasius similarity solution for a flat plate boundary layer.The stability equation of confluent flow was solved by using the global numerical method.The unstable modes associated with both the mixing and boundary layers were identified.They are the boundary layer mode,mixing layer mode 1（nearly symmetrical mode）and mode 2（nearly anti-symmetrical mode）.The interactions between the mixing layer stability and the boundary layer stability were examined.As the mixing layer approaches the boundary layer,the neutral curves of the boundary layer mode move to the upper left,the resulting critical Reynolds number decreases,and the growth rate of the most unstable mode increases.The wall tends to stabilize the mixing layer modes at low frequency.In addition,the mode switching behavior of the relative level of the spatial growth rate between the mixing layer mode 1 and mode 2 with the velocity ratio is found to occur at low frequency.

Instability analysis and drag coefficient prediction on a swept RAE2822 wing with constant lift coefficient

Swept wing is widely used in civil aircraft,whose airfoil is chosen,designed and optimized to increase the cruise speed and decrease the drag coefficient.The parameters of swept wing,such as sweep angle and angle of attack,are determined according to the cruise lift coefficient requirement,and the drag coefficient is expected to be predicted accurately,which involves the instability characteristics and transition position of the flow.The pressure coefficient of the RAE2822 wing with given constant lift coefficient is obtained by solving the three-dimensional Navier-Stokes equation numerically,and then the mean flow is calculated by solving the boundary layer（BL） equation with spectral method.The cross-flow instability characteristic of boundary layer of swept wing in the windward and leeward is analyzed by linear stability theory（LST）,and the transition position is predicted by eNmethod.The drag coefficient is numerically predicted by introducing a laminar/turbulent indicator.A simple approach to calculate the lift coefficient of swept wing is proposed.It is found that there is a quantitative relationship between the angle of attack and sweep angle when the lift coefficient keeps constant;when the angle of attack is small,the flow on the leeward of the wing is stable.when the angle of attack is larger than 3°,the flow becomes unstable quickly;with the increase of sweep angle or angle of attack the disturbance on the windward becomes more unstable,leading to the moving forward of the transition position to the leading edge of the wing;the drag coefficient has two significant jumping growth due to the successive occurrence of transition in the windward and the leeward;the optimal range of sweep angle for civil aircraft is suggested.

Three-dimensional simulation for problem of penetrative convection near the maximum density

The problem of penetrative convection with the cubic and fifth-order equations of state proposed by Merker, Waas and Grigull is studied. Both linear instability and nonlinear stability analyses are performed to assess the suitability of linear theory to predict destabilisation of the convection. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three-dimensional simulation. The results show that the linear threshold accurately predicts the onset of instability in the basic steady state solution.

稀薄气体效应对高超声速边界层稳定性的影响

临近空间高超声速飞行器在跨越大气层飞行时可能经历从连续到稀薄流域.本文基于Navier-Stokes(NS)方程和NS改进模型研究了稀薄气体效应对高超声速边界层稳定性的影响.首先在传统线性稳定性理论(linear stability theory,LST)中引入壁面滑移条件和非线性输运模型,发展了适用于稀薄剪切流的拓展稳定性分析方法.然后重点分析了马赫数10、飞行高度55 km的尖平板绕流,研究了稀薄气体效应(包括壁面滑移效应和剪切非平衡效应)对边界层稳定性的影响机理.结果表明,对于基本流,稀薄气体效应使得边界层变薄,边界层剖面的广义拐点向壁面靠近.对于稳定性,稀薄气体效应通过影响基本流使第二模态更稳定,而通过修正稳定性方程使第二模态更不稳定,综合效应使得第二模态更稳定.然而,对于第一模态,稀薄气体效应始终起不稳定效果.这些结果从宏观角度揭示了近连续流域高超声速平板边界层的稳定性特征.