ON THE STABILITY OF DISTORTED LAMINAR FLOW(Ⅲ)—THE NONLINEAR STABILITY ANALYSIS OF DISTORTED PARALLEL SHEAR FLOW

Based on the hydrodynamic stability theory of distorted laminar flow and the kind ofdistortion profiles on the mean velocity in parallel shear flow given in paper[1].this paperinvestigates the nonlinear stability behaviour of parallel shear flow,carries on stabilitycalculation taking account of the perturbations of background turbulence noise undercertain assumption,and obtains some results in accordance qualitatively with those ofexperiment for plane Poiseuille flow and pipe Poiseuille flow.     

ON THE STABILITY OF DISTORTED LAMINAR FLOW(Ⅱ)——THE LINEAR STABILITY ANALYSIS OF DISTORTED PARALLEL SHEAR FLOW

Based on the hydrodynamic stability theory of distorted laminar flow and the kind ofdistortion profiles on the mean velocity in parallel shear flow given in paper[1],this paperinvestigates the linear stability behaviour of parallel shear flow.presents unstable results ofplane Couette flow and pipe Poiseuille flow to two-dimensional or axisymmetricdisturbances for the first time,and obtains neutral curves of these two motions under certaindefinition.     

ON THE STABILITY OF DISTORTED LAMINAR FLOW(Ⅰ)—BASIC IDEAS AND THEORY

This paper suggests a hydrodynamic stability theory of distorted laminar flow,andpresents a kind of distortion profile,of mean velocity in parallel shear flow.With suchdistortion profiles,the new theory can be used to investigate the stability behaviour ofparallel shear flow,and thus suggests a new possible approach to instability.     

ON THE STABILITY OF DISTORTED LAMINAR FLOW (I)—BASIC IDEAS AND THEORY

This paper suggests a hydrodynamic stability theory of distorted laminar flow, and presents a kind of distortion profile of mean velocity in parallel shear flow. With such distortion profiles, the new theory can be used to investigate the stability behaviour of parallel shear flow, and thus suggests a new possible approach to instability. The Project Supported by National Natural Science Foundation of China.     

THE APPLICATION OF MULTI－SCALE PERTURBATION METHOD TO THE STABILITY ANALYSIS OF PLANE COUETTE FLOW

ＴＨＥＡＰＰＬＩＣＡＴＩＯＮＯＦＭＵＬＴＩ－ＳＣＡＬＥＰＥＲＴＵＲＢＡＴＩＯＮＭＥＴＨＯＤＴＯＴＨＥＳＴＡＢＩＬＩＴＹＡＮＡＬＹＳＩＳＯＦＰＬＡＮＥＣＯＵＥＴＴＥＦＬＯＷＺｈｏｕＺｈｅ－ｗｅｉ（周哲玮）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｌｙ;Ｓｈａｇ...     

INVESTIGATION OF THE STABILITY FOR INVISCID COMPRESSIBLE SWIRLING FLOW BETWEEN CONCENTRIC CYLINDERS

The temporal stability on inviscid compressible swirling flow between two concntric cylinders is investigated. First. a linearized differential equation is derived. Two stbility criteria are derired for compressible swirling flow by an analytic method analogous to Ludwieg's method. A finite-difference numerical method is then used to solve the eigenvalue problem of this differential equation, to get temporal growth rate and to check these stability criteria derived. Finally, The effect of compressbility for stability is disscused.     

STABILITY STUDY OF AN UNSTEADY OSCILLATION FLOW

（王发民）（赵烈）（于欣）ＳＴＡＢＩＬＩＴＹＳＴＵＤＹＯＦＡＮＵＮＳＴＥＡＤＹＯＳＣＩＬＬＡＴＩＯＮＦＬＯＷ￥ＷａｎｇＦａｍｉｎ；ＺｈａｏＬｉｅ；ＹｕＸｉｎ（ＩｎｓｔｉｌｕｔｅｏｆＭｅｃｈａｎｉｃｓ．ＡｃａｄｅｍｉａＳｉｎｉｃａ．Ｂｅｉｊｉｎｇ１００...     

THE NONLINEAR STABILITY OF PLANE POISEUILLE FLOW FOR NON－NEWTONIAN POWER SERIES FLUID

ＴＨＥＮＯＮＬＩＮＥＡＲＳＴＡＢＩＬＩＴＹＯＦＰＬＡＮＥＰＯＩＳＥＵＩＬＬＥＦＬＯＷＦＯＲＮＯＮ－ＮＥＷＴＯＮＩＡＮＰＯＷＥＲＳＥＲＩＥＳＦＬＵＩＤＷａｎｇＺｈｅｎｄｏｎｇ（王振东）ＺｈｏｕＺｈｏｎｋｅ（周宗科）（Ｄｅｐｔ．ｏｆＭｅｃｈａｎｉｃｓ．Ｔ...     

THE SPECTRAL PROBLEM OF POISEUILLE FLOW

For Poiseuille flow the Orr-Sommerfeld equation is solved exactly. Regular solutionsare obtained, thereby eigenvalue equation can be analyzed analytically and explicitly. Thebifurcation solutions will be discussed subsequently.     

THE THEOREM OF THE STABILITY OF LINEAR NONAUTONOMOUS SYSTEMS UNDER THE FREQUENTLY-ACTING PERTURBATION

In the paper a theorem on the stability of linear nonautonomous system under thefrequently-acting perturbation has been given and proved on the basis of Malkin＇sTheorem.     

THE NEW GEOMETRIC CRITERION OF POLYNOMIAL STABILITY

In this paper, we apply the coniugacy and boundedness of the zeros for a polynomial f_n(z) with real coefficienta (i=0,1,2,...n). A new simple geometric criterion for stability off_n(z) is given which is very convenient for application.     

ON THE STABILITY BOUNDARY OF HAMILTONIAN SYSTEMS

ＩｎｔｒｏｄｕｃｔｉｏｎＭａｎｙｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｓｃａｎｂｅｖｉｅｗｅｄａｓｌｉｎｅａｒＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓ.Ｗｈｅｎｗｅｓｔｕｄｙｔｈｅｅｆｆｅｃｔｓｏｆｓｙｓｔｅｍｐａｒａｍｅｔｅｒｓｏｎｔｈｅｂｅｈａｖｉｏｒｏｆｔｈｅｓｙｓｔｅｍｓ,ｔｈｅｓｙｓｔｅｍｃａｎｂｅｒｅｇａｒｄｅｄａｓｔｈｅｓｙｓｔｅｍｄｅｐｅｎｄｉｎｇｏｎｐａｒａｍｅｔｅｒｓ.Ｖｅｒｙｉｍｐｏｒｔａｎｔｓｙｓｔｅｍｐａｒａｍｅｔｅｒｓ ,ｓｕｃｈａｓｃｒｉｔｉｃａｌｌｏａｄ ,ｃｒｉｔｉｃａｌａｎｇ…     

THE BLOOD FLOW AND THE MOTION OF VESSEL WALL

The correlation problem between the blood fiow and the motion of vessel wall in the mammalian circulatory system is discussed in this paper. Supposing the blood flow is under the stable oscillatory condition, a set of formulas for velocity distribution, pressure distribution, displacement of vessel wall and constraining stress are obtained. Kuchar's formulas are extended from steady flow to unsteady oscillatory flow by means of the formulas obtained in this paper. The problem of elasticity effect of vessel wall is also discussed.     

A THREE-FLUID MODEL OF THE SAND-DRIVEN FLOW

ＡＴＨＲＥＥ－ＦＬＵＩＤＭＯＤＥＬＯＦＴＨＥＳＡＮＤ－ＤＲＩＶＥＮＦＬＯＷ￥(刘大有，董飞)ＬｉｕＤａｙｏｕ；ＤｏｎｇＦｅｉ（ＩｎｓｔｉｔｕｔｅｏｆＭｅｃｈａｎｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｐ．Ｒ．Ｃｈｉｎａ）Ａｂｓ...     

ON THE CRITERION FOR THE ABSOLUTE STABILITY OF THE CONTROL SYSTEM

In this paper,firstly we give the criterion for the absolutestability of the second canonical form for the control system,in-cluding.the equation of the longitudinal motions of a plane as aparticular example.The corresponding result in[8],[9]is a par-ticular example given in this paper.Secondly,we give the criteriafor the absolute stability of the first canonical form in the usualcase and in the critical case.Finally,we give some criteria forthe absolute stability of the general form for the direct controlsystem.All the results in this paper merelg depend upon the relationsbetween the parameters of the system itself to give an explicit al-gebraic discriminant.     

THE MIXING OF GAS-LIQUID FLOW WITH VAPOR AND GAS-SOLID FLOW

In the industrial production,the mixing of gas-liquid flow with vapor and gas-solidflow is a very common problem.In the process of the mixing,solid particle-clusters willform,and will have steady radii when the effect of the gathering of particles is balanced withthat of the breaking of particle-clusters.Then,the population distribution functionn(a,(?)t)of size of particles per unit length per unit volume is introduced,and its governingequation is derived on the analogy of the molecular kinetic theory.Finally,when the gasflow is very slow,the expression of steady average radius of particle-clusters is obtained.     

EFFECTS OF TENSOR CLOSURE MODELS AND 3-D ORIENTATION ON THE STABILITY OF FIBER SUSPENSIONS IN A CHANNEL FLOW

IntroductionFlowoffibresuspensionshasbeenveryfamiliarinmanyindustrialfields.Fibreadditivesplayanimportantroleindragreductioninmanytypesofflow[1- 3].Inthesuspensions,somebehavioroftheflowmaybealteredbythefibres.Oneoftheimportantexamplesisthehydrodynamicsta…     

A CRITERION FOR THE STABILITY OF MOTION OF NONLINEAR SYSTEM

As to an autonomous nonlinear system, the stability of the equilibrium state in a sufficiently small neighborhood of the equilibrium state can be determined by eigenvalues of the linear part of the nonlinear system provided that the eigenvalues are not in a critical case. Many methods may be used to detect the stability for a linear system. A lot of researches for determining the stability of a nonlinear system are completed by mathematicians and mechanicians but most of them are methods for the special forms of nonlinear systems. Till now, none of these methods can be conveniently applied to all nonlinear systems. The method introduced by this paper gives the necessary and sufficient conditions of the stability of a nonlinear system. The familiar Krasovski's method is a special case of this method     

ON THE STABILITY OF FORCED DISSIPATIVE NONLINEAR SYSTE

ＯＮＴＨＥＳＴＡＢＩＬＩＴＹＯＦＦＯＲＣＥＤＤＩＳＳＩＰＡＴＩＶＥＮＯＮＬＩＮＥＡＲＳＹＳＴＥＭ￥ＣｈｅｎＤａｄｕａｎ（陈达段）ＬｉｕＸｉａｏｍｉｎｇ（刘晓明）ＳｈｉＷｅｉｈｕｉ（施惟慧）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙ．Ｓｈａｎｇｈａｉ２００...     

THE CALCULATION OF EIGENVALUES FOR THE STATIONARY PERTURBATION OF COUETTE－POISEUILLE FLOW

ＴＨＥＣＡＬＣＵＬＡＴＩＯＮＯＦＥＩＧＥＮＶＡＬＵＥＳＦＯＲＴＨＥＳＴＡＴＩＯＮＡＲＹＰＥＲＴＵＲＢＡＴＩＯＮＯＦＣＯＵＥＴＴＥ－ＰＯＩＳＥＵＩＬＬＥＦＬＯＷＳｏｎｇＪｉｎｂａｏ（宋金宝）ＣｈｅｎＪｉａｎｎｉｎｇ（陈建宁）（ＲｅｃｅｉｖｅｄＤｅｃ．３...