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.     

Nonlinear Dynamics of Pipes with Pulsatile Flow

The dynamic behaviour of pipes conveying flowing fluid can be significantly influenced by the periodically changing flow. The fluid is considered to be incompressible, frictionless and its velocity relative to the pipe is harmonic function of time of which magnitude does not depend on spatial coordinates. The pipe is modelled as an inextensible continuum. The investigations were performed using three bifurcation parameters: the frequency, the perturbation amplitude and the mean flow velocity. In super‐critical case the nonlinear dynamics was shown in bifurcation diagrams.     

Nonlinear Wave Packets in Flows with Critical Layers

This paper is a theoretical study of nonlinear wave propagation in homogeneous and stratified shear flows. For a wave packet, it is known that levels where the flow velocity is equal to the phase or group velocity are regions where nonlinear effects are especially significant. In this study certain aspects of the flow configuration are examined in the neighborhood of each of these regions.     

The Nonlinear Instability Characteristics of Waves in Free Shear Layers

A more general mean flow first harmonic theory is derived and some consequences are discussed. The theory is applied to the Bickley jet and tanh mixing layer profiles.     

非线性球形薄膜的膨胀失稳

本文应用分支理论研究了非线性球形薄膜在轴对称大变形膨胀过程中的失稳问题.证明了所论非线性边值问题的奇点只能是单重极限点,并讨论了载荷和材料两个参数对球形薄膜平衡状态及其稳定性的影响.     

Properties of a Time-Dependent Nonlinear Viscous Critical Layer

The time-dependent, nonlinear, viscous critical-layer problem posed by Gajjar and Smith is studied analytically and numerically, for various values of the time-dependence parameter µ and the viscous parameter γ_c, to help to complete the understanding of the solution. The analysis concerns the nearly inviscid limit γ_c → 0 which corresponds to increasing disturbance amplitude, other limits for weaker disturbances having been studied previously. On the numerical side, computational results obtained for order-1 values of µ, γ_c are described and are compared with analytical predictions. Particular attention is given to the phase shift produced across the critical layer.     

Subcritical Rossby Waves in Zonal Shear Flows with Nonlinear Critical Layers

It was shown by Benney and Bergeron [ 1 ] that singular neutral modes with nonlinear critical layers are mathematically possible in a variety of shear flows. These are usually subcritical modes; i.e., they occur at values of the flow parameters where their linear, viscous counterparts would be damped. One question raised then is how such modes might be generated.
This article treats the problem of Rossby waves propagating in a mixing layer with velocity profile ū = tanh y . The beta parameter, which is a measure of the stabilizing Coriolis force, is taken to be large enough so that linear instability cannot occur. First, computed dispersion curves are presented for singular modes with nonlinear critical layers. Then, full numerical simulations are employed to illustrate how these modes can be generated by resonant interaction with conventional nonsingular Rossby waves, even when the singular mode is absent initially.     

Lagrangian Description of Three-Dimensional Viscous Flows at Large Reynolds Numbers

Computational Mathematics and Mathematical Physics - Boundary layer theory is used to show that, at large Reynolds numbers, the three-dimensional Navier–Stokes equations can be rewritten in a...     

重力场中Navier-Stokes方程的线性不稳定性

研究了三维不可压粘性Navier-Stokes方程的线性不稳定性.即当流体处在重力场时,若稳态密度有一定的连续性并随着高度的增加而增加时(即Rayleigh-Taylor密度),重力场中的Navier-Stokes流体是线性不稳定的.利用变分法解出线性方程的线性不稳定解.     

Instability in Porous Layers with Depth-Dependent Viscosity and Permeability

The paper is concerned with a multicomponent porous horizontal layer L with depth-dependent viscosity and permeability, heated from below and salted partly from below and partly from above. The instability of the thermal conduction solution, due to the growth of the gradient of temperature or of the gradient of chemical species salting L from above, is investigated.     

Coupled Amplitude-Streaming Flow Equations for Nearly Inviscid Faraday Waves in Small Aspect Ratio Containers

Summary. We derive a set of asymptotically exact coupled amplitude-streaming flow ({CASF}) equations governing the evolution of weakly nonlinear nearly inviscid multimode Faraday waves and the associated streaming flow in finite geometries. The streaming flow is found to play a particularly important role near mode interactions. Such interactions come about either through a suitable choice of parameters or through breaking of degeneracy among modes related by symmetry. An example of the first case is provided by the interaction of two nonaxisymmetric modes in a circular container with different azimuthal wavenumbers. The second case arises when the shape of the container is changed from square to slightly rectangular, or from circular to slightly noncircular but with a plane of symmetry. The generation of streaming flow in each of these cases is discussed in detail and the properties of the resulting CASF equations are described. A preliminary analysis suggests that these equations can resolve discrepancies between existing theory and experimental results in the first two of the above cases.     

The Nonlinear Critical Layer in a Slightly Stratified Shear Flow

An attempt is made in this paper to extend the nonlinear critical layer analysis, as developed for homogeneous shear flows by Benney and Bergeron [1] and Davis [2], to the case of a stratified shear flow. Although the analysis is restricted to small values of the Richardson number evaluated at the edge of the critical layer, it is definitely shown that buoyancy leads to the formation within the critical layer region of thin velocity and thermal boundary layers which tend to reduce the local Richardson number. We suggest that this result has considerable relevance to the phenomenon of clear air turbulence. As in the homogeneous case, no phase change of the disturbance takes place across the nonlinear critical layer.     

含周期脉动的大密度比气液同轴射流的Floquet稳定性分析

基于周期脉动速度激励下气液同轴射流的数学模型,运用线性稳定性理论,采用Chebyshev配点法和Floquet理论,将含周期脉动分层流的Floquet稳定性分析扩展到大密度比的情况.研究了液铝-氮气射流的参数共振特性,分析了不同的物理参数对系统稳定性的影响,计算了实验工况并和实验结果进行了比较.     

Displacement of Viscous Fluids in a Set of Parallel Pipes

Computational Mathematics and Mathematical Physics - The process of pumping water in a formation filled with a more viscous fluid is considered using the simplest model of the interwell space...     

平面Poiseuille流中弱非线性理论和二次失稳理论的关系*

文献[1]提出了平面Poiseuille流的二次失稳理论,本文则用弱非线性理论研究了同一问题.所得结果和二次失稳理论的结果是一致的,说明在平面Poiseuille流中弱非线性理论和二次失稳理论有内在联系.     

On the Nonlinear Development of Small Three-Dimensional Perturbations in Plane Poiseuille Flow: Single-Mode Approach

Nonlinear aspects of developing three-dimensional perturbations in plane Poiseuille flow have been elucidated at the primary, instead of the conventional secondary, level. Three-dimensional perturbation velocities generate normal vorticity by stretching and tilting the basic-flow vorticity. The amplitude of the induced normal vorticity, and hence that of the streamwise perturbation velocity, can grow temporally to significant peak values before the exponential decay predicted by the linear theory sets in. These growths, according to the linear theory, do not influence the amplitudes of the normal perturbation velocity that are monotonically decaying with time. It is shown in this study that the normal velocity continues to be oblivious to the development of induced normal vorticity, even in the nonlinear regime, if the perturbation velocities are described by waves traveling in a single oblique direction. Also, the Reynolds number dependence of the amplitude of the normal vorticity is discussed.     

环面薄膜的膨胀失稳

本文从有限弹性理论出发对超弹性薄膜轴对称大变形问题进行了一般的数学描述.基于本文所导出的基本方程,应用打靶法数值地分析了Mooney-Rivlin型类橡胶环面薄膜的大变形膨胀失稳问题.给出了上、下极限载荷和位移载荷曲线.     

Existence and Nonlinear Stability of Stationary Solutions to the Viscous Two-Phase Flow Model in a Half Line

The outflow problem for the viscous two-phase flow model in a half line is investigated in the present paper. The existence and uniqueness of the stationary solution is shown for both supersonic state and sonic state at spatial far field, and the nonlinear time stability of the stationary solution is also established in the weighted Sobolev space with either the exponential time decay rate for supersonic flow or the algebraic time decay rate for sonic flow.