一种非定常振荡流的稳定性分析

本文分析了一种非定常振荡的不稳定性问题。其特点是，应用偏微分方程特征理论以及Ｏ－Ｓ方程特征值的展开，求解扰动波的相函数而不是预先给定扰动波的波动形式。本文研究平面Ｐｏｉｓｅｔｔｉｌｌｅ流与其垂向振荡流的组合流动系统，对于连续振荡源导致的波包演化，该系统存在不稳定性。     

自由剪切流大尺度结构的二次稳定性*

本文用二次稳定性理论研究自由剪切湍流中周期性基本流空间增长扰动的稳定性。数值结果表明三维亚谐扰动对横向波数有很强的选择性,二维亚谐波的空间增长率最大。与之相反,基本模式的三维扰动在很大的波数范围内存在不稳定性,证明β=0时存在“转移”不稳定性;当KH波的幅值A≥0.06时出现分叉现象。     

剪切流动中短周期声重波的产生与发展

本文根据可压缩情况下的流体力学方程组,采用局域近似理论,建立了剪切流动中扰动的发展方程。本文还导出了剪切流动中声重波的色散关系,给出了参数空间中稳定与不稳定的分界图象,文中还给出了不稳定波增长率和振荡频率随切变强度和波长的分布,发现剪切不稳定性倾向于激发短周期的波动,其本征振荡周期的范围是1—6min按照色散关系和扰动的发展方程,本文讨论了白噪声形式的初始扰动在剪切流动中的演变过程。     

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。     

一类具扰动项的Hartree方程驻波的强不稳定性(英文)

本文研究一类具扰动项的Hartree方程.通过建立交叉不变流研究其解整体存在的最佳门槛.进而,研究其解的强不稳定性.     

可压缩Navier-Stokes方程平面Couette-Poiseuille流的线性不稳定性

主要研究可压缩流平面Couette-Poiseuille流的不稳定性.利用线性算子的扰动理论,得到当上板的速度小,且马赫数和雷诺数满足一定关系时,可压缩流平面Couette-Poiseuille流扰动问题是不稳定的.     

非轴对称模型Hagen-Poiseuille流的不稳定性

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扰动波,我们考虑一个三维非线性模型.它的相关振幅函数满足扩散方程,当流体的雷诺数增大时,由于复杂的分子扩散和流体粘性的相互作用.该方程的扩散系数会出现负值.在"负扩散"现象出现时.在流体运动中出现的"湍流段"内部会引起能量的集中和使流体的阻尼减少.文中所得结果对说明圆管流中出现湍流段的实验现象是有价值的.     

剪切流中表面重力波的四阶Zakharov方程及其应用

当二维剪切流沿垂向线性变化时,剪切流中的二维重力波仍满足无旋条件.本文首先推导了线性剪切流中二维表面重力波的三阶和四阶Zakharov方程,它也适用于无剪切流的三维重力表面波场.用Zakharov方程研究了剪切流中波列的第一类不稳定性问题,给出了不稳定判别式,详细讨论了剪切流对不稳定区域和增长率的影响,得到了由于流的存在而出现的新的不稳定区.     

脉冲波作用下的高超音速非定常流动模拟及影响研究

采用高阶精度有限差分方法模拟了快声波脉冲扰动作用下的高超音速非定常流场,分析了脉冲波与高超音速流场的相互干扰,并应用Fourier频谱分析研究扰动波在边界层的发展．结果表明:来流脉冲扰动波与激波及边界层强烈相互作用,弓形激波明显向内弯曲,激波后扰动波被显著放大;来流扰动波与弓形激波干扰形成的边界层外的扰动波和近壁面内形成的边界层扰动波存在明显分界．钝锥头部参数扰动幅值要远大于其他位置参数扰动幅值．在边界层内的发展阶段,一些扰动模态持续增长,一些扰动模态被过滤掉,不再增长,甚至衰减,而也有一些扰动模态先衰减再增长．总的来说,在钝锥头部低频扰动模态为主导模态,随着扰动从流场上游向下游发展,总扰动模态中的低频模态成份和高频模态成份所占的比例开始转变,高频模态成分显著地增大．     

明渠层流失稳与沙纹成因机理研究

动床水流中,泥沙起动之后,往往要出现沙纹,沙纹成因各家的解释不一。白玉川,罗纪生的观点是:沙纹的尺度较小,主要是由于明渠层流不稳定性波或床面近壁流层中小尺度拟序结构发展演化所致。当床面边界附近扰动波或拟序结构以及水流自身所产生的床面底部切应力大于Shields切应力后,床面即产生响应,形成沙纹;如果扰动所产生的扰动切应力频率接近床面泥沙固有频率,则产生与泥沙颗粒的共振,这种现象也称之为“泥沙的检波性质”,此时床面发生最大响应,沙纹发展速度也最快。     

Instability of Three Dimensional Waves in Shear Flows

The instability of a shear flow is greatly affected by the presence of one or more preexisting waves. This problem is considered for an oblique wave on a parallel shear flow with a free surface. The analysis uses a mean flow first harmonic theory.     

一种计算超声速流中由湍流剪切层脉动引起的激波振荡频率的方法

在超声速或高超声速绕流中,一种很严重的脉动压力环境是由激波边界层相互作用引起的激波振荡.这种高强度的振荡激波可能诱发结构共振.因这一现象非常复杂,已发表的文章都采用经验或半经验方法.本文首次从基本流体动力学方程出发,给出了由湍流剪切层引起的激波振荡频率的理论解,得到了振荡频率随气流Mach数M_∞和压缩折转角θ的变化规律,计算结果与实验值是相符的.本文为激波振荡导致的气动弹性问题提供了一种有价值的理论方法.     

Homogenization of dynamic laminates

This paper addresses the study of the homogenization problem associated with propagation of long wave disturbances in materials whose properties exhibit not only spacial but also temporal inhomogeneities (called dynamic materials). The study was initiated by Lurie in his pioneering work of 1997. Homogenization theory is employed to replace an equation with oscillating coefficients by a homogenized equation. Two typical examples of periodic homogenization are considered: the wave equation and Maxwell's system coefficients oscillating rapidly not only in space but also in time. Conditions that generate applicability of the homogenization procedure to dynamic materials composites are developed. In particular, we examine a cell problem for periodic composites as well as the laminate formulae. The effective tensors of rank-one laminates for one-dimensional wave equation and the full Maxwell's system are computed explicitly. We also note some dramatic differences between the hyperbolic and the elliptic cases.     

Flow Past a Swept Wing with a Compliant Surface: Stabilizing the Attachment-Line Boundary Layer

Many aquatic species such as dolphins and whales have fins, which can be modeled as swept wings. Some of these fins, such as the dorsal fin of a dolphin, are semi-rigid and therefore can be modeled as a rigid swept wing with a compliant surface. An understanding of the hydrodynamics of the flow past swept compliant surfaces is of great interest for understanding potential drag reduction mechanisms, especially since swept wings are widely used in hydrodynamic and aerodynamic design. In this paper, the flow past a swept wing with a compliant surface is modeled by an attachment-line boundary layer flow, which is an exact similarity solution of the Navier–Stokes equations, flowing past a compliant surface modeled as an elastic plate. The hydrodynamic stability of the coupled problem is studied using a new numerical framework based on exterior algebra. The basic instability of the attachment line boundary layer on a rigid surface is a traveling wave instability that propagates along the attachment line, and numerical results show that the compliance results in a substantial reduction in the instability region. Moreover, the results show that, although the flow-field is three-dimensional, the qualitative nature of the instability suppression is very similar to the qualitative reduction of instability of the two-dimensional Tollmien–Schlichting modes in the classical boundary-layer flow past a compliant surface.     

Finite-amplitude Rotational Waves in Viscous Shear Flows

Growing finite-amplitude initially spanwise-independent two-dimensional rotational waves and their nonlinear interaction with unidirectional viscous shear flows of various strengths are considered. Both primary and secondary instabilities are studied, but only secondary instabilities are permitted to vary in the spanwise direction. A generalized Lagrangian-mean formulation is employed to describe wave-mean interactions, and a separate theory is constructed to account for the back effect of the developing mean flow on the wave field. Viscosity is seen to significantly complicate calculation of the back effect. The primary instability is seen to act as a platform for, and catalyst to, secondary instabilities. The analysis leads to an eigenvalue problem for the initial growth of the secondary instability, this being a generalization of the eigenvalue problem constructed by Craik for inviscid neutral waves. Two inviscid secondary instability mechanisms to longitudinal vortex form are observed: the first has as its basis the Craik–Leibovich type 2 mechanism. The second, which is as yet unproven, requires that both the wave and flow field distort in concert at all levels of shear. Both mechanisms excite exponential growth on a convective rather than diffusive scale in the presence of neutral waves, but growing waves alter that growth rate.     

Deterministic representation of chaos with application to turbulence

Chaos and unpredictability in some classical dynamic systems are eliminated by referring the governing equation to a specially selected rapidly oscillating (non-inertial) frame of reference in which the stabilization effect is caused by inertia forces. The resulting motion is found as a sum of smooth and non-smooth (rapidly oscillating) parts. The solution is stable and reproducible in the sense that small changes in initial conditions lead to small changes in both smooth and non-smooth components. In this interpretation, conceptually the closure problem in turbulence is reduced to the problem of finding such a frame of reference where the high Reynolds number instability is eliminated. The usefulness of the approach is illustrated by examples.     

Analytical Solutions of the Internal Gravity Wave Equation in a Stratified Medium with Shear Flows

Computational Mathematics and Mathematical Physics - The problem of constructing internal gravity wave fields generated by an oscillating localized point source of disturbances in a stratified...     

Viscous potential flow analysis of magnetohydrodynamic interfacial stability through porous media

In the view of viscous potential flow theory, the hydromagnetic stability of the interface between two infinitely conducting, incompressible plasmas, streaming parallel to the interface and subjected to a constant magnetic field parallel to the streaming direction will be considered. The plasmas are flowing through porous media between two rigid planes and surface tension is taken into account. A general dispersion relation is obtained analytically and solved numerically. For Kelvin-Helmholtz instability problem, the stability criterion is given by a critical value of the relative velocity. On the other hand, a comparison between inviscid and viscous potential flow solutions has been made and it has noticed that viscosity plays a dual role, destabilizing for Rayleigh-Taylor problem and stabilizing for Kelvin-Helmholtz. For Rayleigh-Taylor instability, a new dispersion relation has been obtained in terms of a critical wave number. It has been found that magnetic field, surface tension, and rigid planes have stabilizing effects, whereas critical wave number and porous media have destabilizing effects.