Stability of the flow around a cylinder: The spin-up problem

Abstract : Our concern is with the flow around an infinite cylinder, which at a certain instant is impulsively started to spin. The growth of vortices in the resulting boundary layer occurring outside the cylinder is investigated. This layer is essentially a Rayleigh layer which grows with time, so the mechanism involved is similar to that studied in Hall (1983). Vortices with wavenumber comparable to the layer thickness are shown to be described by partial differential equations that govern the system numerically. We assume that the Rayleigh layer is thin so particles are confined to move in a path with radius of curvature the same as the cylinder. The Goertler number is a function of time, so we consider the time scale which produces an order one Goertler number. We consider the right hand branch calculation by letting the time tend to infinity. Inviscid Goertler modes are also considered.

[1]  Philip Hall,et al.  On the receptivity problem for Görtler vortices: vortex motions induced by wall roughness , 1991, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[2]  Michael M Sprinkel,et al.  Performing Organization Name and Address , 1990 .

[3]  J. M. Floryan.  Görtler instability of boundary layers over concave and convex walls , 1986 .

[4]  Philip Hall,et al.  The linear development of Görtler vortices in growing boundary layers , 1983, Journal of Fluid Mechanics.

[5]  P. Hall.  Centrifugal instabilities of circumferential flows in finite cylinders: the wide gap problem , 1982, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[6]  P. Hall.  TAYLOR-GORTLER VORTICES IN FULLY DEVELOPED OR BOUNDARY LAYER FLOWS , 1982 .

[7]  C. V. Kerczek.  The instability of oscillatory plane Poiseuille flow , 1982, Journal of Fluid Mechanics.

[8]  Frank T. Smith,et al.  On the non-parallel flow stability of the Blasius boundary layer , 1979, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[9]  G. Seminara,et al.  Centrifugal instability of a Stokes layer: linear theory , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[10]  S. H. Davis,et al.  The instability of a stratified periodic boundary layer , 1976, Journal of Fluid Mechanics.

[11]  M. Gaster.  On the effects of boundary-layer growth on flow stability , 1974, Journal of Fluid Mechanics.

[12]  A. Smith,et al.  On the growth of Taylor-Görtler vortices along highly concave walls , 1955 .

[13]  H. Gortler.  On the three-dimensional instability of laminar boundary layers on concave walls , 1954 .

[14]  G. Taylor.  Stability of a Viscous Liquid Contained between Two Rotating Cylinders , 1923 .