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On the spin-up and spin-down of a rotating fluid. Part 2. Measurements and stability

Published online by Cambridge University Press:  11 April 2006

Patrick D. Weidman
Patrick D. Weidman
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles
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Abstract

Measurements of the azimuthal velocity inside a cylinder which spins up or spins down at constant acceleration were obtained with a laser-Doppler velocimeter and compared with the theoretical results presented in part 1. Velocity profiles near the wave front in spin-up indicate that the velocity discontinuity given by the inviscid Wedemeyer model is smoothed out in a shear layer whose thickness varies with radius and time but scales with hE1/4Ω. The spin-down profiles are always in excellent agreement with theory when the flow is stable. Visualization studies with aluminium tracers have made possible the determination of the stability boundary for Ekman spiral waves (principally type II waves) observed on the cylinder end walls during spin-up. For spin-down to rest the flow always experienced a centrifugal instability which ultimately disrupted the interior fluid motion.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 77 , Issue 4 , 22 October 1976 , pp. 709 - 735
Copyright
© 1976 Cambridge University Press

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References

Brayton, D. B. 1969 A simple laser, Doppler shift, velocimeter with self-aligning optics. Aedc.TR. 70–45.Google Scholar
Caldwell, D. R. & VAN Atta, C. W. 1970 Characteristics of Ekman boundary layer instabilities. J. Fluid Mech. 44, 79–95.Google Scholar
Cerasoli, C. P. 1975 Free shear layer instability due to probes in rotating source-sink flow. J. Fluid Mech. 72, 559–586.Google Scholar
Faller, A. J. 1963 An experimental study of the instability of the laminar Ekman boundary layer. J. Fluid Mech. 15, 560–576.Google Scholar
Faller, A. J. & Kaylor, R. E. 1965 Investigations of stability and transition in rotating boundary layers. Dynamics of Fluids and Plasmas (ed. S. I. Paid), pp. 309–329. Academic.Google Scholar
Faller, A. J. & Kaylor, R. E. 1966 A numerical study of the instability of the laminar Ekman boundary layer. J. Atmos. Sci. 23, 466–480.Google Scholar
Goldsmith, J. L. & Mason, S. O. 1962 Particle motions in sheared suspensions. Xiii. The spin and rotation of disks. J. Fluid Mech. 12, 88–96.Google Scholar
Goller, H. & Ranov, T. 1968 Unsteady rotating flow in a cylinder with a free surface. Trans. A.S.M.E., J. Basic Engng, 90, 445–454.Google Scholar
Görtler, H. 1940 Uber eine dreidimensionale Instabilitit laminarer Grenzschichten an konkaven Wiinden. Nachr. Ces. Wiss. 2, 1–26.Google Scholar
Greenspan, H. P. & Howard, L. N. 1963 On a time dependent motion of a rotating fluid. J. Fluid Mech. 17, 385–404.Google Scholar
Greqory, N., Stuart, J. T. & Walker, W. S. 1955 On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk. Phil. Trans. A 248, 155–199.Google Scholar
Hammerlin, G. 1955 Ifber das Eigenwertproblem der dreidimensionalen Instabilitat Laminarer Grenzschichten an konkaven Wanden. J. Rat. Mech. Anal. 4, 279–321.Google Scholar
Ingersoll, A. P. & Venezian, G. 1968 Non-linear spin-up of a contained fluid. Dept. Geolog. Sci., Calif. Inst. Tech., Pasadena, Contribution, no. 1612.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. Roy. Soc. A 102, 161–179.Google Scholar
Lrlly, D. K. 1966 On the instability of Ekman boundary flow. J. Atmos. Sci. 23, 481–494.Google Scholar
Ludwieq, H. 1964 Experimentelle Nachprüfung der Stabilitätstheorien für reibungsfreie Stromungen mit schraubenlinienformigen Stromlinien. Z. Plugwisa. 12, 304–309.Google Scholar
Mcleod, A. R. 1922 The unsteady motion produced in a uniformly rotating cylinder of water by a sudden change in the angular velocity of the boundary. Phil. Mug. 44, 1–14.Google Scholar
Maxwortry, T. 1971 A simple observational technique for the investigation of boundary-layer stability and turbulence. Turbulence Measurements in Liquids (ed. G. K. Paterson & J. L. Zakin), pp. 32–37. Dept. Chemical Engineering, Univ. Missouri-Rolla.Google Scholar
Pedlosey, J. & Greenspan, H. P. 1967 A simple laboratory model for the oceanic circulation. J. Fluid Mech. 27, 291–304.Google Scholar
Sxiith, A. M. O. 1965 On the growth of Taylor-Gortler vortices along highly concave walls. Quart. Appl. Math. 13, 233–262.Google Scholar
Smite, N. H. 1947 Exploratory investigations of laminar boundary layer oscillations on a rotating disk. N.A.C.A. Tech. Note, no. 1227.Google Scholar
Tatro, P.R. & Mollo-Christensen, E. L. 1967 Experiments on Ekman layer instability. J. Fluid Mech. 28, 531–543.Google Scholar
Tillmann, W. 1967 Development of turbulence during the build-up of a boundary layer at a concave wall. Phys. Fluids Suppl. 10, S108–111.Google Scholar
Venezian, G. 1970 Non-linear spin-up. Topics in Ocean Engineering, 2, 87–96. Gulf Publishing Co.Google Scholar
Wateins, W. B. & Hussey, R. G. 1976 Spin-up from rest in cylinder. Phys. Fluids (in press).CrossRefGoogle Scholar
Wedemeyer, E. H. 1964 The unsteady flow within a spinning cylinder. J. Fluid Mech. 20, 383–399.Google Scholar
Weidman, P. D. 1973 On the spin-up and spin-down of a contained fluid. Ph.D. thesis, Dept. Aerospace Engineering, University of Southern California, Los Angeles.Google Scholar