Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-05T10:32:09.272Z Has data issue: false hasContentIssue false
  • English
  • Français

Laminar boundary layer on an impulsively started rotating sphere

Published online by Cambridge University Press:  28 March 2006

Edward R. Benton
Edward R. Benton
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado
Get access Rights & Permissions [Opens in a new window]

Abstract

Viscous, incompressible, axially symmetric flow about an impulsively started rotating sphere is studied in terms of non-steady, partially linearized Navier-Stokes equations. The non-linear centripetal acceleration is included in full, but the other non-linear terms are neglected because of the restriction in interest to the case of large (but subcritical) Reynolds or Taylor numbers, a2Ω/v. Approximate closed-form solutions for u(r,θ,t), v(r,θ,t), w(r,θ,t) are found which satisfy all relevant boundary and initial conditions. The linearization approximation is checked for consistency and a restriction on Ωt is found. The velocity profiles, in the range of validity, are shown to be approximately similar in time, so their shapes may be qualitatively correct for larger values of Ωt. Some comparison with existing steady-state theories is given and the boundary-layer displacement thickness and viscous torque on the sphere are calculated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 23 , Issue 3 , November 1965 , pp. 611 - 623
Copyright
© 1965 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

Carrier, G. 1953 Boundary layer problems in applied mechanics. Advances in Applied Mechanics, 3, 1–19. New York: Academic Press.Google Scholar
Carrier, G. & DiPrima, R. C. 1956 On the torsional oscillations of a solid sphere in a viscous fluid. J. Appl. Mech. 23, 601–605.Google Scholar
Erdélyi, A. 1954 Tables of Integral Transforms, vol. I. New York: McGraw-Hill.
Howarth, L. 1951 Note on the boundary layer on a rotating sphere. Phil. Mag., 42, 1308–1315.Google Scholar
Kobashi, Y. 1957 Measurements of boundary layer of a rotating sphere. J. Sci. Hiroshima Univ. A, 29, 149–156.Google Scholar
Kreith, F., Roberts, L. G., Sullivan, J. A. & Sinha, S. N. 1963 Convection heat transfer and flow phenomena of rotating spheres. Int. J. Heat and Mass Transfer, 6, 881–895.Google Scholar
Nigam, S. D. 1951 Rotation of an infinite plane lamina: boundary layer growth: motion started impulsively from rest. Quart. Appl. Math., 9, 89–91.Google Scholar
Nigam, S. D. 1954 Note on the boundary layer on a rotating sphere. ZAMP, 5, 151–155.Google Scholar
Schlichting, H. 1960 Boundary Layer Theory, 4th ed. New York: McGraw-Hill.
Stewartson, K. 1958 On rotating laminar boundary layers. Boundary Layer Research, pp. 59–71. Symposium Freiburg/BR. Berlin: Springer-Verlag.
Stokes, G. G. 1845 On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids. Trans. Camb. Phil. Soc., 8, 287–319.Google Scholar