轴对称模型的Hagen-Poiseuille流的运动不稳定性

本文讨论流体通过圆管的运动不稳定性问题。作为流体运动所受的干扰波,我们考虑了一个非线性轴对称模型。它对应的相关振幅函数满足扩散方程,且由于复杂的分子运动和流体粘性的相互作用,当流体的雷诺数增大时其扩散系数会出现负值。如负扩散现象出现,在流体运动中出现的湍流段内会引起流体的能量集中,并扮演减少阻尼的角色。     

浅球薄壳轴对称极凹陷的非轴对称的动力不稳定性*

当壳厚-升高比ε2<<1时,由二次型载荷产生的轴对称极凹陷的浅球薄壳是动力不稳定的.微小的扰动足以使它变成非轴对称凹陷.在两种情形下,问题都可归结为特征值问题Tw_n=c_nw_n.其中T当ε2<<1时近似为一Sfrum-Liouville算子.本文用谱理论和Hilbert定理均可证明T至少存在一实的特征值;它意味着轴对称极凹陷是动力不稳定的.再进一步,本文还找出代表不稳定凹陷壳体的非轴对称变形的、属于一特征值的T的特征函数.     

狭吸积环中非轴对称动力学不稳定性的非线性演化

本文在孤子理论的框架下解释非轴对称动力学不稳定性的非线性演化.在长波不可压缩极限下,两维狭吸积环的色散关系与线性KdV方程的相同.我们认为:非线性动力学不稳定性数值模拟中的“行星状”解是KdV方程的孤子解.由于在动力学不稳定性的非线性演化中密度和熵的变化,吸积盘的涡度是不守恒量,这也使角动量在不稳定过程中重新分布.     

非轴对称的磁流体静力学平衡

本文用摄动展开的方法分析了一类磁流体静力学的平衡,其中基态是轴对称的,并具有强的环向磁场分量,扰动态是非轴对称的.这就在扰动态的环向动量守衡关系中,引进了环向的Lorentz力分量.可以组建两类太阳黑子模型,一类的半影纤维内磁场较强,另一类的磁场较弱.后者尽管早有观测报道,但一直缺乏理论的解释.     

基于网络流理论的非线性规划评价模型

针对既有的评价模型缺乏对评价结果保序性的讨论,以及难以有效处理缺失数据的问题,本文建立了一个新的评价模型用以解决以上问题。该模型建立在三个标准的基础上,这三个标准分别为“结果一致性”、“最小偏离性”和“最小差异性”,其为模型的建立提供了依据和理论基础;在已建立的非线性规划模型基础上,进行了模型的性质讨论,并将其归结为一类最小凸费用循环流的统一表述,这是解决模型的算法问题和揭示其蕴含的更为深刻的管理学意义的核心;最后,模型被用于一个示例分析和含有缺失数据的大规模数据集的实证分析,这些分析论证了该新模型的有效性。本文的模型提供了新的评价工具,扩展了运筹学和决策科学之间相互运用的案例,具有较好的保序性和处理缺失数据的能力,含有理论和实践的双重意义。     

圆柱振荡绕流的三维不稳定性研究

通过数值求解三维不可压缩Navier-Stokes方程,研究了振荡圆柱绕流的旋涡不稳定性.研究表明,在一定的参数范围内,由于旋涡不稳定性,振荡流动由二维演化成三维流动,并沿圆柱轴向形成交错排列的三维涡结构.数值计算合理地预测了三维涡结构的空间失稳波长,并与实验测试值相符很好.文中还进一步研究了圆柱的受力特性,通过求解Morison方程,计算了圆柱的阻力和惯性力特性,其计算结果与已有的实验数据相吻合.     

三阶非自治微分方程的不稳定性定理

本文运用构造李雅普诺夫函数的方法，给出了一类三阶非自治微分方程零解不稳定的充分条件．     

三阶非自治微分方程的不稳定性定理

本文运用构造李雅普诺夫函致的方法，给出了一类三阶非自治微分方程零解不稳定的充分条件。     

稳态轴对称非Kerr黑洞的热力学性质

本文讨论了具有质量多极矩的稳态轴对称非Kerr黑洞的热力学性质。这类黑洞的转动角速度为零,存在热辐射,且温度在视界上是常数。裸奇点的存在强烈影响黑洞两极点的Hawking温度,使其为零或发散。这表明,热力学定律禁止这类裸奇点的出现,甚至阻止这类黑洞的生成。     

在非轴对称非均匀媒质中光束的传播问题

本文导出光束在非轴对称非均匀媒质中传播的光线传输矩阵,为3×3阶,并给出在特定条件下的几种简化形式。为了进一步简化运算,接着引入相应的光线流图结构。分析了:传输空间折射率梯度对激光准直精度的影响,给出一系列公式;从而解决了当前存在的疑难。最后,对不均匀泵浦所引起的激光器光轴的变化,作了讨论。     

Local Instability in Curved Flow

Expressions are obtained for the rates of change of the vorticitycomponents about the tangent, principal normal, and binormalof inviscid flow of arbitrary configuration with curvature andtorsion of the particle paths, and non-uniform density. If a steady flow pattern exists the vorticity changes are exactlythose required to carry the fluid particles through it. A smallrotational displacement of a fluid element about each of thesedirections is then considered separately and if the additionalrate of change of vorticity has the same sign and order of magnitudeas the displacement the motion is unstable locally regardlessof the motion elsewhere. The equations depend on four quantities: the curvature, torsion,velocity and vorticity at the point where stability is beinginvestigated. These four quantities define a helical vortex,with the same stability properties, in which the flow is equivalent.There is therefore special merit in studying this case. It is found that a vortex with helical particle paths is unstablefor rotation of the fluid elements about directions which liebetween the vorticity vector and the direction of the axis ofthe motion, when the density is uniform. More generally, themotion is unstable for these disturbances if the stagnationpressure decreases radially outwards. A gradient of axial velocitycomponent always causes some local instability, and the mostlikely (fastest growing) disturbance is one in which rotationsoccur around a line everywhere bisecting the angle between thevorticity vector and the direction of the axis. The analysis shows that in two dimensional circular flow themost unstable disturbances are toroidal and in general curvedflow in two dimensions (without torsion) the most likely disturbancesare rotations around the tangent, i.e. longitudinal rolls. The criteria obtained for local instability do not agree witha Richardson-type criterion for local stability, but both showthe destabilizing effect of a radiating gradient of axial velocity.     

涡旋流动的空间不稳定性分析

本文研究无粘、不可压缩流体的涡旋流动的空间不稳定性,假定扰动波的波数k=k_r+ik_i是一复数,而它的频率ω为一给定的实数。这一假定意味着扰动沿涡旋流动的轴向随距离的增长而增长,但不随时间而增长。这种扰动的产生称之为空间不稳定性;与之相对应的是时间不稳定性,扰动波的波数k为一实数,而频率ω=ω_r+iω_i是一复数。本文的结果表明空间不稳定性分析是全面认识涡旋流动不稳定性的一种有用的工具。     

A New Mechanism For Linear and Nonlinear Hydrodynamic Instability

A certain class of three dimensional disturbances is studied which exhibit a strong resonance and consequently lead to the rapid development of relatively large amplitudes. For parallel flows a nonlinear theory is developed and results in evolution equations quite different from those usually found. It is believed that the selection mechanism explored here is relevant to a variety of nonlinear wave and instability problems.     

Long-Wave Instability in a Three-Layer Stratified Shear Flow

In inviscid fluid flows, instability can occur because of a resonance between two wave modes. For the case when the modes remain distinct at the critical point where the wave phase speeds coincide, then in the weakly nonlinear, long-wave limit, there is an expectation that the generic outcome is a model consisting of two coupled Korteweg–deVries equations. This situation is examined for a certain three-layer stratified shear flow.     

Long-Time Instability of the Couette Flow in Low Gevrey Spaces

We prove the instability of the Couette flow if the disturbances is less smooth than the Gevrey space of class 2. This shows that this is the critical regularity for this problem since it was proved in [5] that stability and inviscid damping hold for disturbances which are smoother than the Gevrey space of class 2. A big novelty is that this critical space is due to an instability mechanism which is completely nonlinear and is due to some energy cascade. © 2023 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.     

关于四阶变系数线性微分方程解的不稳定性

本文利用李雅普诺夫第二方法[1]给出了至少有一个特征根具有正实部的四阶变系数线性微分方程解的不稳定性的充分条件。     

A Necessary and Sufficient Instability Condition for Inviscid Shear Flow

We derive a condition that is necessary and sufficient for the instability of inviscid, two-dimensional, plane-parallel, shear flow with equilibrium velocity profiles that are monotonic, real analytic, functions of the cross-stream coordinate. The analysis, which is based upon the Nyquist method, includes a means for delineating the possible kinds of bifurcations that involve the presence of the continuous spectrum, including those that occur at nonzero wave number. Several examples are given.