Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-18T18:45:55.557Z Has data issue: false hasContentIssue false
  • English
  • Français

Ekman pumping in compact astrophysical bodies

Published online by Cambridge University Press:  26 April 2006

Mark Abney  and
Richard I. Epstein
Mark Abney
Affiliation:
Department of Astronomy and Astrophysics, The Enrico Fermi Institute, The University of Chicago, Chicago, IL 60637, USA and NASA/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, Batavia, IL 60510, USA e-mail: abney@oddjob.uchicago.edu Los Alamos National Laboratory, MS D436, Los Alamos, NM 87545, USA e-mail: epstein@lanl.gov
Richard I. Epstein
Affiliation:
Los Alamos National Laboratory, MS D436, Los Alamos, NM 87545, USA e-mail: epstein@lanl.gov
Get access Rights & Permissions [Opens in a new window]

Abstract

We examine the dynamics of a rotating viscous fluid following an abrupt change in the angular velocity of the solid bounding surface. We include the effects of a density stratification and compressibility which are important in astrophysical objects such as neutron stars. We confirm and extend the conclusions of previous studies that stratification restricts the Ekman pumping process to a relatively thin layer near the boundary, leaving much of the interior fluid unaffected. We find that finite compressibility further inhibits Ekman pumping by decreasing the extent of the pumped layer and by increasing the time for spin-up. The results of this paper are important for interpreting the spin period discontinuities (‘glitches’) observed in rotating neutron stars.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 312 , 10 April 1996 , pp. 327 - 340
Copyright
© 1996 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barcilon, V. & Pedlosky, J. 1967 Linear theory of rotating stratified fluid motions. J. Fluid Mech. 29, 1.Google Scholar
Bark, F. H., Meijer, P. S. & Cohen, H. I. 1978 Spin up of a rapidly rotating gas. Phys Fluids 21, 531–539.Google Scholar
Benton, E. R. & Clark, A. 1974 Spin up. Ann. Rev. Fluid Mech. 6, 257–280.Google Scholar
Buzyna, G. & Veronis, G. 1971 Spin-up of a stratified fluid: theory and experiment. J. Fluid Mech. 50, 579–608.Google Scholar
Clark, A., Clark, P. A., Thomas, J. H. & Lee N. 1971 Spin-up of a strongly stratified fluid in a sphere. J. Fluid Mech. 45, 131–149.Google Scholar
Epstein, R. I. 1988 Acoustic properties of neutron stars. Astrophys. J. 333, 880–894.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
Howard, L. N., Moore, D. W. & Spiegel, E. A. 1967 Solar spin-down problem. Nature 214, 1297–1299.Google Scholar
Hyun, J. M. 1983 Axisymmetric flows in spin-up from rest of a stratified fluid in a cylinder. Geophys. Astrophys. Fluid Dyn. 23, 127–141.Google Scholar
Hyun, J. M. & Park, J. S. 1990 Early time behavior of the Ekman layers in spin-up of a rapidly rotating gas. J. Phys. Soc. Japan 59, 3584–3594.Google Scholar
Hyun, J. M. & Park, J. S. 1992 Spin-up from rest of a compressible fluid in a rapidly rotating cylinder. J. Fluid Mech. 237, 413–434.Google Scholar
Lindblad, I. A. A., Bark, F. H. & Zahrai, S. 1994 Spin-up of a rapidly rotating heavy gas in a thermally insulated annulus. J. Fluid Mech. 274, 383–404.Google Scholar
Linden, L. N. & Heijst, G. J. F.van 1984 Two-layer spin up and frontogenesis. J. Fluid Mech. 143, 69–94.Google Scholar
O'Donnell, J. & Linden, P. F. 1992 Spin-up of a two-layer fluid in a rotating cylinder. Geophys. Astrophys. Fluid Dyn. 66, 47–66.Google Scholar
Park, J. S. & Hyun, J. M. 1994 Dynamical structure of compressible fluid flows in an abruptly rotating cylinder. J. Phys. Soc. Japan 63, 528–535.Google Scholar
Pedlosky, J. 1967 The spin-up of a stratified fluid. J. Fluid Mech. 28, 463–479.Google Scholar
Pedlosky, J. 1979 Geophysical Fluid Dynamics. Springer.
Reisenegger, A. & Goldreich, P. 1992 A new class of g-modes in neutron stars. Astophys. J. 395, 240–249.Google Scholar
Rieutord, M. 1992 Ekman circulation and the synchronization of binary stars. Astron. Astrophys. 259, 581–584.Google Scholar
Sakurai, T. 1969 Spin down problem of a rotating stratified fluid in thermally insulated circular cylinders. J. Fluid Mech. 37, 689–699.Google Scholar
Sakurai, T., Clark, A. & Clark, P. A. 1971 Spin-down of a Boussinesq fluid of small Prandtl number in a circular cylinder. J. Fluid Mech. 49, 753–773.Google Scholar
Sakurai, T. & Matsuda, T. 1974 Gasdynamics of a centrifugal machine. J. Fluid Mech. 62, 727–736.Google Scholar
Spence, G. S. M., Foster, M. R. & Davies, P. A. 1992 The transient response of a contained rotating stratified fluid to impulsively started surface forcing. J. Fluid Mech. 243, 33–50.Google Scholar
Tassoul, J.-L. & Tassoul, M. 1990 A time dependent model for synchronization in close binaries. Astrophys. J. 359, 155–163.Google Scholar
Tassoul, M. & Tassoul, J.-L. 1992 On the efficiency of Ekman pumping for synchronization in close binaries. Astrophys. J. 395, 604–611.Google Scholar
Walin, G. 1969 Some aspects of a time-dependent motion of a stratified rotating fluid. J. Fluid Mech. 36, 289–307.Google Scholar