Zhou Zhe-wei. On the Stability of Distorted Laminar Flow(Ⅰ)——Basic Ideas and Theory[J]. Applied Mathematics and Mechanics, 1989, 10(2): 115-129.
Citation: Zhou Zhe-wei. On the Stability of Distorted Laminar Flow(Ⅰ)——Basic Ideas and Theory[J]. Applied Mathematics and Mechanics, 1989, 10(2): 115-129.

On the Stability of Distorted Laminar Flow(Ⅰ)——Basic Ideas and Theory

  • Received Date: 1987-12-04
  • Publish Date: 1989-02-15
  • 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.
  • loading
  • [1]
    Reynolds,O.,An experiment investigation of the circumstances which determine whether the motion of water shall be direct or sinuous,and of the law of resistance in parallel channels,Phil.Trans.R.Soc.,174(1883),935.
    [2]
    Reynolds,O.,Papers on Mechanical and Physical Subjects,Vol.II,Cambridge University.Press,Cambridge(1901).
    [3]
    Tollmien,W.,Ein allgemeines Kriterium der Instabilitat laminarer Geschwindigkeits verteilungen,Nachr.Akad.Wiss.Gottingen Math.Phys.Klasse,50(1935),79.
    [4]
    Drazin,P.G.and W.H.Reid,Hydrodynamic stability,Cambridge University Press(1981).
    [5]
    Leite,R.J.,An experimental investigation of the stability of Poiseuille flow,J.Fluid Mech.,5(1959),81.
    [6]
    Kuethe,A.M.,Some features of boundary layers and transition to turbulent flow,J.Aero.Sci,23(1956),446.
    [7]
    Fox,J.A.,M.lessen and W.V.Bhat,Experimental investigation of the stability of Hagen-Poiseuille flow,Phys.Fluids,11(1968),1.
    [8]
    Davis,S.J.and C.M.White,An experimental study of the flow of water in pipes of rectangular section,Proc.Roy.Soc.,A119(1928),92.
    [9]
    Kao,T.W.and C.Park,Experimental investigations of the stability of channel flow:Part 1,Flow of a single liquid in a rectangular channel,J.Fluid Mech.,43(1970),145.
    [10]
    Patel,V.C.and M.R.Head,Some observations on skin friction and velocity profiles in fully developed pipe and channel flows,J.Fluid Mech.,38(1969),181.
    [11]
    Nishoka,M.,S.lida and Y.Ichikawa,An experimental investigation of the stability of plane Poiseuille flow,J.Fluid Mech.,72(1975),244.
    [12]
    Robertson,J.M.,On turbulent plane-Couette flow,Proc.6th Midwestern Conference on Fluid Mechanics,University of Texas(1959),169.
    [13]
    Reichardt,H..Gesetzmassigkeiten der geradlinigen turbulenten Couettestromung,Mitteilungen aus dem Max-Planck Institute fur stromungsforschung und der Aerodynamischen Versuchsanstalt,22(1959).
    [14]
    Squire,H.B.,On the stability of three-dimensional distribution of viscous fluid between parallel walls,Proc.Roy,Soc.London,A142(1933),621.
    [15]
    Heisenberg,W.,Über Stabilitat und Turbulenz von Flussigkeitsstromen,Ann.Phys.Lpz.74. 4(1924).577.
    [16]
    Tollmien,W.,Über die Entstehung der Turbulenz,Nachr Ges.Wiss.Gottingen,Math.Phys.Klasse(1929).21.
    [17]
    Lin.C.C.On the stability of two-dimensional parallel flows,Quart.Appl.Math.3(1945),117-142;218-234;277-301.
    [18]
    Landau.L.D.,On the problem of turbulence C.R.Acad.Sci.U.R.S.S.44(1944).311.
    [19]
    Meksyn,D.,J.T.Stuart,Stability of viscous motion between parallel planes for finite disturbances.Proc.Roy Soc.,A208(1951),517.
    [20]
    Palm,E.,On the tendency towards hexagonal cells in steady convection.J.Fluid Mech.,8(1960),83.
    [21]
    Stuart,I.T.and J.Watson,On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows.Part 1. Part 2. J.Fluid Mech.,9(1960),353-370,371-389.
    [22]
    Orszag.S.A and A.T.Patera,Secondary instability of wall-bounded shear flows,J.Fluid Mech 128(1983).347.
    [23]
    Herbert.T.,Secondary instability of plane channel flow to subharmonic three-dimensional disturbances.Phys.Fluids,26(1983),871.
    [24]
    Davey.A.and H.P.F.Nguyen,Finite-amplitude stability of pipe flow,J.Fluid Mech.,45(1971),701.
    [25]
    Itoh.N..Nonlinear stability of parallel flows with subcritical Reynolds numbers,part 2,Stability of pipe Poiseuille flow to finite axisymmetric disturbances,J.Fluid Mech.,82(1977),469.
    [26]
    Rosenblat,S.and S.H.Davis,Bifurcation from infinity,SIAM J.Appl.Math.,37,1(1979),1.
    [27]
    Zhou,H.,On the nonlinear theory of plane Poiseuille flow in the subcritical range,Proc.R.Soc.London,A381(1982),407.
    [28]
    Gill,A.E.,A mechanism for instability of plane Couette flow and of Poiseuille flow in a pipe,J.Fluid Mech.,21(1962),503.
    [29]
    朱洪元,《量子场论》,科学出版社(1960).
    [30]
    周哲玮,圆管Poiseuille流动中平均速度的一种修正剖面及其稳定性研究,应用数学和力学,1 (1988).73-82.
    [31]
    Herbert,T.,On peturbation methods in nonlinear stability theory, J. Fluid Mech., 126(1983),167.
    [32]
    Taylor, G.L, Statistical theory of turbulence, Part V, Eftect of turbulence on boundary layer, Theoretical discussion of relationship between scale of turbulence and critical resistance of spheres, Proc. Roy. Soc. London, A166 (1936), 307.
    [33]
    Schubauer, G.B. and H.K. Skramstad, Laminar boundary layer oscillations and stability of laminar flow, National Bureau of Standards Research Paper(1772).
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2124) PDF downloads(590) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return