Analysis on the Moist Potential Vorticity and Conditional Symmetric Instability of a Rainstorm

[Objective] The research aimed to analyze the moist potential vorticity (MPV) and conditional symmetric instability (CSI) of a rainstorm in Guangxi in the prior flood season. [Method] Based on the conventional observation data, precipitation data from the automatic station and 1°×1° six-hourly reanalyzed data from NCEP, MPV and CSI in a rainstorm process which occurred in the prior flood season in Guangxi were analyzed. The characteristics of MPV component and role of CSI before and after the rainstorm occurrence were discussed. [Result] The dense belt of isoline in the southeast of MPV1 positive-value area (MPV2 negative-value area) at 925 hPa, the underneath of sloping MPV1 positive-value column (MPV2 negative-value column) on the profile map and the underneath of dense belt of θe isoline had the good corresponding relationships with the falling zone of strong precipitation. After the system developed strongly, the enhancements of gradient and intensity of MPV1 and MPV2 predicted the rainstorm increase. In the beginning period of strong precipitation occurrence, the convective instability at 850-650 hPa co-existed with CSI. The convective instability and vertical movement played the main role. In the middle and latter periods of strong precipitation, the high-altitude weak cold air further invaded southward. It triggered the release of unstable energy, and compelled that the original sloping θe dense belt became steep. It was favorable for the development of sloping vorticity, and the atmosphere gradually turned into the neutral state of convection. CSI and ramp motion played the major role. Then, the rainstorm continued. [Conclusion] The research provided the theory basis for the application of MPV and CSI into the local routine business.

Study on Moist Potential Vorticity and Symmetric Instabilityduring a Heavy Rain Event Occurred inthe Jiang-Huai Valleys

In the light of the theory on moist potential vorticity (MPV) investigation was undertaken of the 700 hPa vertical (horizontal) component MP1 (MPV2) for the heavy rain event occurring in July 5–6, 1991. Results show that the distribution features of the two components were closely related to the development of a mesoscale cyclone as a rainstorm-causing weather system in the lower troposphere in such a way that the ambient atmosphere of which MPV1 > 0 and MPV2 < 0 with |MPV1| ≥ |MPV2| favored the genesis of conditional symmetric instability (CSI) and that, as indicated by calculations, a CSI sector was really existent in the lower troposphere during the heavy rain happening and contributed greatly to its development.

Effect of spin on the instability of THz plasma waves in field-effect transistors under non-ideal boundary conditions

Terahertz(THz) radiation can be generated due to the instability of THz plasma waves in field-effect transistors(FETs). In this work, we discuss the instability of THz plasma waves in the channel of FETs with spin and quantum effects under non-ideal boundary conditions. We obtain a linear dispersion relation by using the hydrodynamic equation, Maxwell equation and spin equation. The influence of source capacitance, drain capacitance, spin effects, quantum effects and channel width on the instability of THz plasma waves under the non-ideal boundary conditions is investigated in great detail. The results of numerical simulation show that the THz plasma wave is unstable when the drain capacitance is smaller than the source capacitance;the oscillation frequency with asymmetric boundary conditions is smaller than that under non-ideal boundary conditions;the instability gain of THz plasma waves becomes lower under non-ideal boundary conditions. This finding provides a new idea for finding efficient THz radiation sources and opens up a new mechanism for the development of THz technology.

Sufficient conditions of Rayleigh-Taylor stability and instability in equatorial ionosphere

Rayleigh-Taylor （R-T） instability is known as the fundamental mechanism of equatorial plasma bubbles （EPBs）. However, the sufficient conditions of R-T instability and stability have not yet been derived. In the present paper, the sufficient conditions of R-T stability and instability are preliminarily^derived. Linear equations for small perturbation are first obtained from the electron/ion continuity equations, momentum equations, and the current continuity equation in the equatorial ionosphere. The linear equations can be casted as an eigenvalue equation using a normal mode method. The eigenvalue equation is a variable coefficient linear equation that can be solved using a variational approach. With this approach, the sufficient conditions can be obtained as follows： if the minimum systematic eigenvalue is greater than one, the ionosphere is R-T unstable; while if the maximum systematic eigenvalue is less than one, the ionosphere is R-T stable. An approximate numerical method for obtaining the systematic eigenvalues is introduced, and the R-T stable/unstable areas are calculated. Numerical experiments axe designed to validate the sufficient conditions. The results agree with the derived suf- ficient conditions.

The instability conditions of a gas trapped in weak weakly interacting Fermi magnetic field

In this paper the analytical expression of free energy expressed by small parameter r of a weakly interacting Fermi gas trapped in weak magnetic field is derived by using ＇the maximum approximation＇ method and the ensemble theory. Based on the derived expression, the exact instability conditions of a weakly interacting Fermi gas trapped in weak magnetic field at both high and low temperatures are given. From the instability conditions we get the following two results. （1） At the whole low-temperature extent, whether the interactions are repulsive or attractive with （αn-k 4εF/3） （n and εF denote the particle-number density and the Fermi energy respectively, α = 4πah^2/m, and a is s-wave scattering length） positive, there is a lower-limit magnetic field of instability; in addition, there is an upper-limit magnetic field for the system of attractive interactions with （αn ＋ 4εF/3） negative. （2） At the whole high-temperature extent, the system with repulsive interactions is always stable, but for the system with attractive interactions, the greater the scattering length of attractive interactions ｜α｜ is, the stronger the magnetic field is and the larger the particle-number density is, the bigger the possibility of instability in the system will be.

Proton Cyclotron Instability Threshold Condition of Suprathermal Protons by Kappa Distribution

Observation has clearly shown that natural space plasmas generally possess a pronounced non-Maxwellian high-energy tail distribution that can be well modeled by a kappa distribution. In this study we investigate the proton cyclotron wave instability driven by the temperature anisotropy （T⊥/TH 〉1） of suprathermal protons modeled with a typical kappa distribution in the magnetosheath. It is found that as in the case for a regular bi-Maxwellian, the supratherreal proton temperature anisotropy is subject to the threshold condition of this proton cyclotron instability and the instability threshold condition satisfies a general form T⊥/T｜｜ - 1 = S/β｜｜^α, with a very narrow range of the fitting parameters： 0.40 ≤ α ≤ 0.45, and a relatively sensitive variation 0.27 ≤ S ≤ 0.65, over 0.01 ≤β｜｜ 〈 10. Furthermore, the difference in threshold conditions between the kappa distribution and the bi-Maxwellian distribution is found to be small for a relatively strong growth but becomes relatively obvious for a weak wave growth. The results may provide a deeper insight into the physics of this instability threshold for the proton cyclotron waves.

Application of the Conditional Nonlinear Optimal Perturbations Method in a Theoretical Grassland Ecosystem

用曾等建议的一个简化非线性地理论的草地生态系统，我们与线性地稳定的草地(荒芜或潜伏的沙漠)说的 .The 结果表演能转与有限振幅非线性地不稳定的有条件的非线性的最佳的不安( CNOP )的途径学习敏感和草地生态系统的非线性的不稳定性到有限振幅的起始的不安 降水在之间的起始的 perturbations.When 二分叉指，大

A note for the mechanism of high-frequency oscillation instability resulted from absorbing boundary conditions

In this paper the explanation of the mechanism of high-frequency oscillation instability resulted from absorbing boundary conditions is further improved. And we analytically prove the proposition that for one dimensional discrete model of elastic wave motion, the module of reflection factor will be greater than 1 in high frequency band when artificial wave velocity is greater than 1.5 times the ratio of discrete space step to discrete time step. Based on the proof, the frequency band in which instability occurs is discussed in detail, showing such high-frequency waves are meaningless for the numerical simulation of wave motion.

Feasibility study of symmetric solution of molecular argon flow inside microscale nozzles

The computational cost of numerical methods in microscopic-scales such as molecular dynamics(MD) is a deterrent factor that limits simulations with a large number of particles. Hence, it is desirable to decrease the computational cost and run time of simulations, especially for problems with a symmetrical domain. However, in microscopic-scales, implementation of symmetric boundary conditions is not straightforward. Previously, the present authors have successfully used a symmetry boundary condition to solve molecular flows in constant-area channels. The results obtained with this approach agree well with the benchmark cases. Therefore, it has provided us with a sound ground to further explore feasibility of applying symmetric solutions of micro-fluid flows in other geometries such as variable-area ducts. Molecular flows are solved for the whole domain with and without the symmetric boundary condition. Good agreement has been reached between the results of the symmetric solution and the whole domain solution. To investigate robustness of the proposed method, simulations are conducted for different values of affecting parameters including an external force, a flow density, and a domain length. The results indicate that the symmetric solution is also applicable to variable-area ducts such as micro-nozzles.

Shock Induced Symmetric Compression in a Spherical Target

Shock induced symmetric compression has been studied in a spherical target. The shock induced interfacial radius will shrink and would reach a minimum point during implosion situation. However, after implosion the plasma tries to expand in blow off/explosion situation and as a result the interfacial radius will increase. Effects of plasma parameters like density and temperature have been studied numerically. It is seen that the density increases many times due to the mass conservation in imploding situation of a compressible shell like ICF. However, temperature will change rapidly due to change of inner density and so would be the pressure of compressible fluid following adiabatic law. Our analytical results agree qualitatively with those of simulation results in spherical geometry and also experimental observations conducted in cylindrical container.

Asymptotic Properties of Estimators for Ornstein-Uhlenbeck Processes with Small Symmetricα-Stable Motions

The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional least squares estimators(CLSEs)of all the parameters involved in the Ornstein–Uhlenbeck process are proposed.We establish the consistency and the asymptotic distributions of our estimators asεgoes to 0 and n goes to∞simultaneously.

对流风暴大气不稳定机制研究的若干问题

大气不稳定是强对流天气发生的必要条件之一,具有复杂性。首先简要回顾了气块假设,给出了该假设的应用局限性,比如气块在对流风暴中的强上升运动必然会导致环境大气气压和涡度的变化等;然后梳理了大气的静力不稳定、对称不稳定以及其他多种类型不稳定的概念,重点总结了条件不稳定、湿绝对不稳定和条件对称不稳定的判据及其与对流风暴发生发展的关系,同时澄清了一些错误认识。判别条件不稳定最有效的方法是对气块作有限虚拟位移、使用对流有效位能(CAPE)来判别。CAPE和对流抑制能量的计算对抬升气块的温湿状况较为敏感,并需要进行虚温订正;最优CAPE值较地表CAPE具有更好的代表性。在强垂直风切变、低CAPE环境中,由于旋转导致的动力扰动气压梯度的加速作用对强对流风暴的发展至关重要;对流不稳定不一定对应于条件不稳定。条件对称不稳定的方便判别方法是使用饱和湿地转位势涡度,文中进一步总结了该不稳定所致的中尺度雨带特征。

“21·11”极端暴雪过程多系统结构演变及热动力机制

利用多种实时观测资料和ERA5再分析资料,对造成2021年11月6—8日华北、东北极端暴雪过程多系统的结构特征及热动力机制进行分析。结果表明:此次过程先后由500 hPa高空横槽、河套西风槽及高空冷涡接力影响,其上空的高空急流不断加强并呈现“S”型弯曲,同时低空偏南风急流形成与加强,并在东北地区与高空急流耦合。此次过程阶段性特征明显,其影响系统的结构特征和水汽输送存在差异。回流冷锋形成的冷垫锋面较为浅薄,暖湿气流在其上倾斜上升。寒潮冷锋则较为陡立,上升气流随高度西倾。而锋面气旋结构较为深厚直立,使得气流呈垂直上升运动。随着斜压强迫的不断增强,850 hPa切变线由准东西向分布转为南北向分布,再演变为低涡切变结构。对应的水平涡度由弱转强,其上空正涡度垂直分布也逐渐加强,由弱倾斜上升运动逐步演变为较强垂直上升运动区,并在系统东侧形成次级环流下沉支。此次过程的发生发展与锋生作用密切相关,降雪落区和强度与锋区走向及锋生函数大小较为一致。假相当位温锋区在降雪3个阶段逐渐加强,垂直锋区和低层锋生函数由倾斜状态演变为近乎直立结构;湿位涡诊断表明,3个阶段降雪落区均发生在湿位涡正压项>0而斜压项<0配置的区域,条件性对称不稳定是此次过程的主要动力机制。

一类对称可微不变凸多目标规划的最优性

多目标规划与广义凸性是最优化理论的重要研究内容。主要利用Minch对称梯度,定义了一类对称可微G-B s-(p,r,ρ)不变凸函数,利用该函数建立了含有不等式约束的多目标规划问题,并证明了该函数凸性限制下的最优性充分条件,进一步拓宽了涉及B-(p,r)不变凸函数、G-ρ不变凸函数的文献中有关最优性条件的结论。

两个高阶正则拟微分算子积的对称性

研究了在Hilbert空间中两个一般的正则拟微分算式乘积的对称实现问题,刻画了由其确定对称算子的两点边界条件,得到两个高阶正则微分算子的乘积算子是对称算子的充分必要条件,所得结论包括了乘积算子的自共轭域的刻画这一结果作为其特殊情形.给出了乘积算子为对称算子的几个例子.

Radially Symmetrical Problems for Compressible Fluids with a High-Resolution Boundary Condition

Imposing appropriate numerical boundary conditions at the symmetrical center r=0 is vital when computing compressible fluids with radial symmetry.Extrapolation and other traditional techniques are often employed,but spurious numerical oscillations or wall-heating phenomena can occur.In this paper,we emphasize that because of the conservation property,the updating formula of the boundary cell average can coincide with the one for interior cell averages.To achieve second-order accuracy both in time and space,we associate obtaining the inner boundary value at r=0 with the resolution of the corresponding one-sided generalized Riemann problem(GRP).Acoustic approximation is applied in this process.It creates conditions to avoid the singularity of type 1/r and aids in obtaining the value of the singular quantity using L’Hospital’s rule.Several challenging scenarios are tested to demonstrate the effectiveness and robustness of our approach.

Analysis of high-frequency local coupling instability induced by multi- transmitting formula - P-SV wave simulation in a 2D waveguide

Local coupling instability will occur when the numerical scheme of absorbing boundary condition and that of the field wave equation allow energies to spontaneously enter into the computational domain. That is, the two schemes support common wave solutions with group velocity pointed into the computation domain. The key to eliminate local coupling instability is to avoid such wave solutions. For lumped-mass finite element simulation of P-SV wave motion in a 2D waveguide, an approach for stable implementation of high order multi-transmitting formula is provided. With a uniform rectangular mesh, it is proven and validated that high-freqaency local coupling instability can be eliminated by setting the ratio of the element size equal to or greater than x/2 times the ratio of the P wave velocity to the S wave velocity. These results can be valuable for dealing instability problems induced by other absorbing boundary conditions.

Evolution of Instability before and during a Torrential Rainstorm in North China

NCEP-NCAR reanalysis data were used to analyze the characteristics and evolution mechanism of convective and symmetric instability before and during a heavy rainfall event that occurred in Beijing on 21 July 2012.Approximately twelve hours before the rainstorm,the atmosphere was mainly dominated by convective instability in the lower level of 900-800 hPa.The strong southwesterly low-level jet conveyed the moist and warm airflow continuously to the area of torrential rain,maintaining and enhancing the unstable energy.When the precipitation occurred,unstable energy was released and the convective instability weakened.Meanwhile,due to the baroclinicity enhancement in the atmosphere,the symmetric instability strengthened,maintaining and promoting the subsequent torrential rain.Deriving the convective instability tendency equation demonstrated that the barotropic component of potential divergence and the advection term played a major role in enhancing the convective instability before the rainstorm.Analysis of the tendency equation of moist potential vorticity showed that the coupled term of vertical vorticity and the baroclinic component of potential divergence was the primary factor influencing the development of symmetric instability during the precipitation.Comparing the effects of these factors on convective instability and symmetric instability showed some correlation.

ON THE APPROXIMATE COMPUTATION OF EXTREME EIGENVALUES AND THE CONDITION NUMBER OF NONSINGULAR MATRICES

From the formulas of the conjugate gradient, a similarity between a symmetric positive definite (SPD) matrix A and a tridiagonal matrix B is obtained. The elements of the matrix B are determined by the parameters of the conjugate gradient. The computation of eigenvalues of A is then reduced to the case of the tridiagonal matrix B. The approximation of extreme eigenvalues of A can be obtained as a 'by-product' in the computation of the conjugate gradient if a computational cost of O(s) arithmetic operations is added, where s is the number of iterations This computational cost is negligible compared with the conjugate gradient. If the matrix A is not SPD, the approximation of the condition number of A can be obtained from the computation of the conjugate gradient on AT A. Numerical results show that this is a convenient and highly efficient method for computing extreme eigenvalues and the condition number of nonsingular matrices.