Steady Plane Flow of Viscoelastic Fluid Past an Obstacle

We consider the steady plane flow of certain classes of viscoelastic fluids in exterior domains with a non-zero velocity prescribed at infinity. We study existence as well as asymptotic behaviour of solutions near infinity and show that for sufficiently small data the solution decays near infinity as fast as the fundamental solution to the Oseen problem.     

流体流过下凹地形的共振流动

本文讨论流体流过下凹地形时共振产生非线性毛细重力波.采用摄动方法,导出了一个具负强迫力的KdV方程.采用拟谱方法,对所得方程进行了数值分析,给出了在超临界,亚临界以及精确共振情形的数值结果.     

粘弹流体的绕流特性研究

本文建立了分析粘弹流体平面流的基本方程,并采用摄动法和加权余量法.在小Deborah数条件下,进行了粘弹流体流动的有限元分析,探讨了粘弹流体的绕流特性,分析了粘弹流体在绕流中所表现的分离点滞后及减阻现象的机理.结果表明,本文的方法.对于粘弹流体流动特性的分析工作,具有简便和准确的优点.     

A Variational Problem for Steady Vortices in a Shear Flow Past an Obstacle

We prove existence of maximizers for a variational problem for a steady vortex anomaly of bounded extent in a shear flow, past an obstacle, in a planar exterior domain. Kinetic energy is maximized subject to the vorticity being a rearrangement of a prescribed function.     

Resonant Long–Short Wave Interactions in an Unbounded Rotating Stratified Fluid

A theoretical study is made of finite-amplitude modulated internal wavetrains and the attendant nonlinear interaction with the mean flow induced by the modulations, in an unbounded uniformly stratified Boussinesq fluid rotating around the vertical axis. When the rotation is relatively weak, in particular, 'flat' wavetrains, that feature stronger vertical than horizontal modulations, are resonantly coupled with the mean flow in a manner analogous to the resonant long–short wave interaction between gravity and capillary waves on the surface of deep water. A coupled set of evolution equations for the vertical wavenumber, the wave amplitude, and the mean flow is derived under resonant conditions, and is used to examine the propagation of locally confined wavetrains with initially uniform wavenumber and no pre-existing mean flow. The resonant interaction causes radiation of energy away from a flat wavetrain by means of the induced mean flow which forms a trailing wake; this furnishes a possible mechanism for generating low-frequency inertial–gravity waves in the atmosphere, as suggested by field observations. Moreover, owing to refraction by the mean flow, a finite-amplitude wavetrain may experience rapid wavenumber variations in certain locations, consistent with prior numerical simulations. Eventually, in these regions, the wavenumber tends to become multi-valued, suggesting the formation of caustics.     

粘塑性流体在旋转圆盘上的流动

本文对两种情况导出了描述粘塑性流体在旋转圆盘上流动的基本方程.分别用摄动方法和数值方法得到了方程的解.这就有可能去计算薄膜的厚度分布.经计算发现有两种类型的厚度分布.对于粘度和屈服应力都与径向坐标r无关的粘塑性流体,厚度h随r的增加而减小.对于粘度和屈服应力都是时间和r的函数的Bingham流体,厚度h随r的增加而增加.     

作旋转流动时非线性流体的改进模型

在圆环结构中研究拟塑性流体作圆形的Couette流动.流体的粘度依赖于对守恒方程有直接影响的剪切率,守恒方程采用谱方法求解.可以证明所采用的拟塑性模型,可以被适当地表示为典型的非线性流动.在早期研究中,为了方便数值计算,粘度表达式中只考虑了剪切率的二次项,与此不同,这里考虑了二次幂项.圆形Couette流动中弯曲的流线,造成离心的不稳定性,引起环形的漩涡,称之为Taylor漩涡.进而发现,随着拟塑性影响的增加,临界Taylor数下降.与已有圆形Couette流动的实验相比较,两者有着良好的一致性.     

二阶流体在旋转坐标系中的三维管道流动

就两个水平板构成的旋转系统,在磁场作用下分析二阶磁流体在其间的流动.下表面是一块可伸展的平面,上面是一块多孔的固体平板.选用合适的变换,将质量和动量的守恒方程,简化为耦合的非线性常微分方程组.应用最强大的分析技术,即同伦分析法(HAM),得到该非线性耦合方程组的级数解.结果用图形给出,并详细地讨论了无量纲参数Re,λ,Ha2,α和K2对速度场的影响.     

Flow of a Newtonian Fluid between Eccentric Rotating Cylinders and Related Problems

An incompressible Newtonian fluid is contained in the annular region between two infinite cylinders, one or both of which rotate with constant angular velocities about their respective axes. The first-order inertial correction to the forces exerted by the fluid on the cylinders is obtained in explicit algebraic form. The results are applied to the related problem in which the inner cylinder executes a planetary motion about the axis of the outer cylinder. They are also applied to the problem of the transverse sedimentation of a long cylinder in a half space of fluid bounded by a rigid wall. Certain anomalies which arise in this case are noted.     

计及Hall和离子滑移电流的旋转流体在与时间相关初值条件下的MHDCouette流动

考虑Hall和离子滑移电流的影响,在旋转系统中研究导电流体非稳定的MHD Couette流动．在小数值磁场Reynolds数假定下,推导出基本的控制方程,使用著名的Laplace变换技术,数值地求解该基本方程．分两种情况:磁场相对于流体或者移动平板固定时,得到速度和表面摩擦力统一的闭式表达式．用图形讨论了问题的不同参数,对速度和表面摩擦力的影响．所得结果显示,主流速度u和次生速度v随着Hall电流而增大．离子滑移电流的增大,也会导致主流速度u的增大,但会使次生速度v减小．还给出了旋转、Hall和离子滑移参数的综合影响,确定了次生运动对流体流动的贡献．     

Mixed Convection Flow Past a Horizontal Plate: The Global Flow

The mixed convection flow past a horizontal plate which is aligned under a small angle of attack to a uniform free stream will be considered in the limit of large Reynolds number and small Richardson number. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Motion of a Viscous Fluid Past an Impulsively Started Semi-infinite Flat Plate

It is shown that by employing a suitable numerical method, theproblem of determining the motion of a viscous fluid past asemi-infinite flat plate which is started impulsively from restwith constant velocity parallel to itself can be solved in termsof similarity variables. The numerical solution is comparedwith previous numerical and theoretical work on the problem.The final decay to the steady-state solution described by theBlasius velocity profile is exponential in character and isfound to be substantially in agreement with theoretical predictions.     

Spin-Down in a Rotating Stratified Fluid: Part I

Stress driven flow of a stratified rotating fluid is studied in the context of a linearized Boussinesq cylindrical model, with particular interest in the long term quasi-steady state. The importance of the non-linear terms is estimated by considering a numerical model for the full non-linear equations.     

Resonant Generation of Finite-Amplitude Waves by Flow Past Topography on a β-Plane

The forced Korteweg-de Vries (fKdV) equation is the generic equation for resonant flow past an obstacle. However, for flow past topography on a β-plane, the case when the upstream flow is uniform is anomalous in that there is no quadratic nonlinear term in the fKdV equation. Here we show that in this important case an alternative theory is required and obtain a new evolution equation, which has some similarities to the fKdV equation with two significant differences. These are that a small-amplitude topography now produces finite-amplitude waves and the flow response is limited by a wave breakdown characterized by an incipient flow reversal. Various numerical solutions are described.     

Mathematical Justification of an Obstacle Problem in the Case of a Plate

In this paper the modeling of a thin plate in unilateral contact with a rigid plane is properly justified.Starting from the three-dimensional nonlinear Signorini problem,by an asymptotic approach the convergence of the displacement field as the thickness of the plate goes to zero is studied.It is shown that the transverse mechanical displacement field decouples from the in-plane components and solves an obstacle problem.     

在有一级化学反应时粘弹性流体流经无限竖直多孔平板时的边界层流动

在有一级化学反应时,研究不可压缩的粘弹性流体,在竖直多孔连续运动平板上的不稳定自然对流.控制方程用隐式有限差分法进行数值求解.与解析解的结果比较,证明所选用的数值方法有效.详细图示了速度分布的数值结果.研究了粘弹性参数、无量纲化学反应参数和平板运动速度,对稳定的速度分布、与时间相关的摩擦因数、Nusselt数和Sherwood数的影响.     

The Effect of Sidewalls on Overstable Convection in a Rotating Fluid

A simple two-dimensional model is used to demonstrate some interestingeffects which arise when Chandrasekhar's (1962) theory of overstableconvection in an infinite rotating fluid layer is modified totake account of lateral walls. The aim of the investigationis to determine how sidewalls aligned with the convective rollsaffect the critical Rayleigh number and frequency of oscillationand also how the overstable eigensolutions are related to thepreviously determined stationary solutions of the equations(Daniels, 1977). For containers of large aspect ratio, L, thecritical Rayleigh number for overstability is R_o+O(L^–1)(where R_o is the value for the infinite layer) and in the neighbourhoodof this single perturbed value it is found that there is aninfinite spectrum of overstable eigenvalues with frequencieswhich differ by O(L^–1). The O(L^–1) correction toR_o is determined analytically for the case of small Prandtlnumber and rapid rotation.     

Mixed Convection Flow Past a Horizontal Plate: The Trailing Edge

The mixed convection flow past a horizontal plate which is aligned under a small angle of attack to a uniform free stream will be considered in the limit of large Reynolds number and small Richardson number close to the trailing edge. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Scattering of Inertial Waves in a Rotating Fluid

The scattering of plane inertial waves by both a flat strip and a circular cylinder whose generators are perpendicular to the rotation vector is examined. The properties of the reflected and diffracted fields, viz. spatial decay, propagation, structure, etc....are contrasted with those of the classical scattering fields in the limit where the wave length is small compared to the size of the scatterer.