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Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 329))

Abstract

Planets and stars are rotating objects and large scale fluid motions relative to the planets solid body rotation are constrained by rotation. Theoretical treatment of these fluid motions must, therefore, include rotation effects and it is for this reason that most of the advances in the understanding of rotating fluids have been made in the context of Geophysical Fluid Dynamics (GFD) and Astrophysical Fluid Dynamics (AFD). GFD can be considered a special case of AFD and many approximations made in GFD (see for instance Pedlosky [1]) are not valid in AFD [2]. For example, in GFD horizontal scales of motion L are much less than the radius of the planet, allowing the use of a constant or linearly varying Coriolis frequency f=2Q. The fluid layer depth H is much less than L so that only the component of Q perpendicular to the planets surface needs to be considered. The Boussinesq approximation has also only limited validity in AFD. All the lectures in this course use approximations current in GFD when problems of geophysical interest are considered.

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References

  1. Pedlosky, J.: Geophysical Fluid Dynamics, Springer Verlag, 1979.

    Book  MATH  Google Scholar 

  2. Spiegel, E.A.: Stellar fluid dynamics, in: WHOI Course Lecture Notes (Ed. B. E. DeRemer), WHOI report n° 91–03, 1990.

    Google Scholar 

  3. Greenspan, H.P.: The Theory of Rotaing Fluids, Cambridge Univ. Press, 1968.

    Google Scholar 

  4. Mory, M. Inertial waves, this volume

    Google Scholar 

  5. Read, P. L.: Ekman layers and Stewartson layers, this volume.

    Google Scholar 

  6. Maxworthy, T.: Wave motions in a rotating and/or stratified fluid, this volume.

    Google Scholar 

  7. Klein, P.: Transition to chaos in unstable baroclinic systems: a review, Fluid Dyn.Res.,5 (1990), 235.

    Article  ADS  Google Scholar 

  8. Zahn, J.-P.: Shear flow instability and the transition to turbulence, in: WHOI Course Lecture Notes (Ed. B. E. DeRemer), WHOI report n° 91–03, 1990.

    Google Scholar 

  9. Read, P.L.: Long-lived eddies in the atmosphere of major planets, this volume.

    Google Scholar 

  10. Maxworthy, T., Redekopp, L. G. and Weidman, P.: On the production and interaction of planetary solitary waves: application to the Jovian atmosphere, Icarus, 33 (1978), 388.

    Article  ADS  Google Scholar 

  11. Sommeria, J., Meyers, S.D. and Swinney, H.L.: Laboratory simulation of Jupiter’s great red spot, Nature, 331 (1988), 1.

    Article  Google Scholar 

  12. Dowling, T. E. and Ingersoll, A.P.: Potential vorticity and layer thickness variations in the flow around Jupiter’s Great Red Spot and White Oval BC, J. Atmos. Sci. 45 (1988), 1380.

    Article  ADS  Google Scholar 

  13. Griffiths, R.W. and Hopfinger, E.J.: Coalescing of geostrophic vortices. J. Fluid Mech. 178 (1987), 73.

    Article  ADS  Google Scholar 

  14. Verron, J., Hopfinger, E.J. and McWilliams, J. C: Sensitivity to initial conditions in the merging of two-layer baroclinic vortices. Phys Fluids A, 2 (6) (1990), 886.

    Article  ADS  Google Scholar 

  15. Kloosterziel, R.C. and van Heijst, G.J.F.: An experimental study of unstable barotropic vortices in a rotating fluid. J. Fluid Mech. 223 (1991), 1.

    Article  ADS  Google Scholar 

  16. Carton, X. J., Flierl, G.R. and Polvani, L.M.: The generation of tripoles from unstable axisymmetric solated vortex structures. Europhys. Lett. 9 (1989), 339.

    Article  ADS  Google Scholar 

  17. Nagib, H.M., Lavan, Z. and Fejer, A.A.: Stability of pipe flow with superposed solid body rotation, Phys Fluids, 14 (1971), 766.

    Article  ADS  Google Scholar 

  18. Maslowe, S.A.: Instability of rigid rotating flows to non-axisymmetric disturbances, J.Fluid Mech., 64 (1974), 307.

    Article  ADS  MATH  Google Scholar 

  19. Lessen, M., Singh,P.J. and Paillet, F.: The stability of a trailing line vortex, Part 1, inviscid theory, J.Fluid Mech., 63 (1974), 723.

    Article  ADS  Google Scholar 

  20. Johnston, J. P., Halleen, R.M. and Lezius, J.D.: Effect of span wise rotation on the structure of twodimensional fully developed turbulent channel

    Google Scholar 

  21. Maxworthy, T.: Convective and shear flow turbulence with rotation, this volume.

    Google Scholar 

  22. Bradshaw, P.: The analogy between streamline curvature and buoyancy in turbulent shear flow, J. Fluid Mech. 36 (1969), 177.

    Article  ADS  MATH  Google Scholar 

  23. Matsson, O. J. E. and Alfredsson, H.I.: Curvature and rotation induced instability in channel flow, J. Fluid Mech., 210 (1990), 537.

    Article  ADS  Google Scholar 

  24. Leibovich, S.: Vortex stability and breakdown: survey and extension, AIA A 22 (1984), 1192.

    ADS  Google Scholar 

  25. Moore, D. W.: Dynamics of vortex filaments, this volume.

    Google Scholar 

  26. Escudier, M.: Confined vortices in flow machinery. Ann. Rev. Fluid Mech., 19 (1987), 27.

    Article  ADS  Google Scholar 

  27. Brombach, H.: Vortex flow controllers in sanetary engineering, Trans. ASME J. Dyn. Sys. Meas. Control, 106 (1984), 129.

    Google Scholar 

  28. Greenspan G.H. and Ungarish, M.: On the enhancement of centrifugal separation, J. Fluid Mech. 178 (1985), 73.

    Google Scholar 

  29. Bergström, L.: Wakes behind the caulks in a disc stack centrifuge. Presented at Euromech 245, Cambridge (see report J.Fluid Mech. 211, p. 417), 1989.

    Google Scholar 

  30. Spall, R.E. Gatski, T.B. and Grosch, C.E.: A criterion for vortex breakdown, Phys. Fluids 30 (1987), 3434.

    Article  ADS  Google Scholar 

  31. Hopfinger, E.J., Browand, F.K. and Gagne, Y.: Turbulence and waves in a rotating tank. J. Fluid Mech 125 (1982), 505.

    Article  ADS  Google Scholar 

  32. Spiegel, E.A.: Lecture III. Photogasdynamics, in: WHOI Course Lecture Notes (Ed. B. E. DeRemer), WHOI report n° 91–03, 1990.

    Google Scholar 

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© 1992 Springer-Verlag Wien

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Hopfinger, E.J. (1992). Concepts and Examples of Rotating Fluids. In: Hopfinger, E.J. (eds) Rotating Fluids in Geophysical and Industrial Applications. International Centre for Mechanical Sciences, vol 329. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2602-8_1

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  • DOI: https://doi.org/10.1007/978-3-7091-2602-8_1

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82393-4

  • Online ISBN: 978-3-7091-2602-8

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