Skip to main content
SpringerLink
Log in

Stability of spherical Couette flow in thick layers when the inner sphere revolves

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

A natural generalization of cylindrical Couette flow is the flow of a viscous incompressible liquid between two concentric spheres rotating about the same axis with different angular velocities. As has often been noted, spherical Couette flow is, despite the apparent similarity, considerably more complex than cylindrical flow. It consists of differential rotation about the axis and one- or two-eddy circulation (depending on the ratio between the angular velocities of the two spheres ω = ω2/ω1) in the meridional plane and depends significantly on the Reynolds number Re = ω1r 21 and the relative thickness of the layer δ = (r2-r1)/r1 (ω1, ω2 and r1, r2 are the angular velocities and radii of the inner and outer spheres, respectively. The investigation of spherical Gouette flow and its stability has begun relatively recently (within the last 10 years) and has evidently been stimulated by applied problems associated with astro- and geophysics. Because of the great computational difficulties encountered in investigating such flow theoretically, experimental investigations have yielded more extensive and interesting results [1–8], although all the published results refer to the case of rotation of one inner sphere (ω = 0).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. G. N. Khlebutin, “Stability of liquid motion between rotating and fixed concentric spheres,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6 (1968),

  2. O. Sawatzky and J. Zierep, “Das Stromfeld in Spalt zwischen zwei konzentrischen Kugelflachen von denen die innere rotiert,” Acta Mech.,9, Nos. 1–2 (1970).

  3. I. M. Yavorskaya, Yu. N. Belyaev, and A. A. Monakhov, “Experimental investigation of spherical Couette flow,” Dokl. Akad. Nauk SSSR,221, No. 5 (1975).

  4. B. R. Munson and R. Menguturk, “Viscous incompressible flow between concentric rotating spheres,” J. Fluid Mech.,69, Part 4 (1975).

  5. G. I. Petrov, I. M. Yavorskaya, Yu. N. Belyaev, A. A. Monakhov, I. M. Slezinger, A. A. Goryainov, and V. I. Fuks, Modeling Dynamic Processes in Planetary Atmospheres. Part 1. Apparatus for Investigating the Stability of Shear Flow in Spherical Layers [in Russian], Preprint No. 225, Institute of Cosmic Research, Moscow (1975).

    Google Scholar 

  6. J.-P. Bonnet and A. Alziary de Roquefort, “Ecoulement entre deux spheres concentriques en rotation,” J. Mech.,15, No. 3 (1976).

  7. M. Wimmer, “Experiments on a viscous fluid flow between concentric rotating spheres,” J. Fluid Mech.,78, Part 2 (1976).

  8. Yu. N. Belyaev, I. M. Yavorskaya, and A. A. Monakhov, “Instability of spherical Couette flow (experiment and some theoretical problems),” in: Fourth All-Union Conference on Theoretical and Applied Mechanics (Summary of Papers) [in Russian], Naukova Dumka, Kiev (1976).

    Google Scholar 

  9. V. I. Yakushin, “Stability of liquid flow in a spherical layer,” Uch. Zap. Permsk. Gos. Univ., No. 248 (1971).

  10. C. A. Pearson, “A numerical study of the time-dependent viscous flow between two rotating spheres,” J. Fluid Mech.,28, Part 2 (1967).

  11. I. M. Yavorskaya, “Effect of latitudinal temperature gradient on spherical Couette flow,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2 (1975).

  12. V. S. Sorokin, “Nonlinear phenomena in closed flows close to critical Reynolds number,” Prikl. Mat. Mekh.,25, No. 2 (1961).

  13. N. M. Astaf'eva, I. Yu. Brailovskaya, and I. M. Yavorskaya, “Nonsteady motion of incompressible viscous liquid in a spherical layer,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3 (1972).

  14. N. Gregory, J. T. Stuart, and W. S. Walker, “On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk,” Phil. Trans. Roy. Soc. London,A248, No. 943 (1955).

  15. H. A. Snyder, “Stability of rotating Couette flow. I. Asymmetric waveforms,” Phys. Fluids,11, No. 4 (1968).

Download references

Author information

Authors and Affiliations

  1. Moscow

    Yu. N. Belyaev, A. A. Monakhov & I. M. Yavorskaya

Authors
  1. Yu. N. Belyaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Monakhov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. M. Yavorskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 9–15, March–April, 1978.

It remains to thank S. A. Shcherbakov for help in organizing automatic input of the signals to the BÉSM-6 computer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belyaev, Y.N., Monakhov, A.A. & Yavorskaya, I.M. Stability of spherical Couette flow in thick layers when the inner sphere revolves. Fluid Dyn 13, 162–168 (1978). https://doi.org/10.1007/BF01091664

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01091664

Keywords

Search

Navigation