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Two-dimensionalization of the flow driven by a slowly rotating impeller in a rapidly rotating fluid

Nathanaël Machicoane, Frédéric Moisy, and Pierre-Philippe Cortet

  • Laboratoire FAST, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France

Phys. Rev. Fluids 1, 073701 – Published 29 November, 2016

DOI: https://doi.org/10.1103/PhysRevFluids.1.073701

Abstract

We characterize the two-dimensionalization process in the turbulent flow produced by an impeller rotating at a rate ω in a fluid rotating at a rate Ω around the same axis for Rossby number Ro=ω/Ω down to 102. The flow can be described as the superposition of a large-scale vertically invariant global rotation and small-scale shear layers detached from the impeller blades. As Ro decreases, the large-scale flow is subjected to azimuthal modulations. In this regime, the shear layers can be described in terms of wakes of inertial waves traveling with the blades, originating from the velocity difference between the nonaxisymmetric large-scale flow and the blade rotation. The wakes are well defined and stable at low Rossby number, but they become disordered at Ro of order of 1. This experiment provides insight into the route towards pure two-dimensionalization induced by a background rotation for flows driven by a nonaxisymmetric rotating forcing.

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References (35)

  1. H. Greenspan, The Theory of Rotating Fluids (Cambridge University Press, Cambridge, UK, 1968).
  2. P. A. Davidson, Turbulence in Rotating, Stratified, and Electrically Conducting Fluids (Cambridge University Press, Cambridge, UK, 2013).
  3. F. S. Godeferd and F. Moisy, Structure and dynamics of rotating turbulence: A review of recent experimental and numerical results, Appl. Mech. Rev. 67, 030802 (2015).
  4. P. Clark di Leoni, P. J. Cobelli, P. D. Mininni, P. Dmitruk, and W. H. Matthaeus, Quantification of the strength of inertial waves in a rotating turbulent flow, Phys. Fluids 26, 035106 (2014).
  5. E. Yarom and A. Sharon, Experimental observation of steady inertial wave turbulence in deep rotating flows, Nat. Phys. 10, 510 (2014).
  6. A. Campagne, B. Gallet, F. Moisy, and P.-P. Cortet, Disentangling inertial waves from eddy turbulence in a forced rotating-turbulence experiment, Phys. Rev. E 91, 043016 (2015).
  7. A. D. McEwan, Inertial oscillations in a rotating fluid cylinder, J. Fluid. Mech. 40, 603 (1970).
  8. N. Machicoane, P.-P. Cortet, B. Voisin, and F. Moisy, Influence of the multipole order of the source on the decay of an inertial wave beam in a rotating fluid, Phys. Fluids 27, 066602 (2015).
  9. B. Gallet, Exact two-dimensionalization of rapidly rotating large-Reynolds-number flows, J. Fluid Mech. 783, 412 (2015).
  10. J. Pedlosky, Geophysical Fluid Dynamics (Springer-Verlag, New York, 1987).
  11. G. K. Vallis, Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation (Cambridge University Press, Cambridge, UK, 2006).
  12. Yasir Bin Baqui and P. A. Davidson, A phenomenological theory of rotating turbulence, Phys. Fluids 27, 025107 (2015).
  13. A. Campagne, B. Gallet, F. Moisy, and P.-P. Cortet, Direct and inverse energy cascades in a forced rotating turbulence experiment, Phys. Fluids 26, 125112 (2014).
  14. E. Yarom, Y. Vardi, and A. Sharon, Experimental quantification of inverse energy cascade in deep rotating turbulence, Phys. Fluids 25, 085105 (2013).
  15. L. Bourouiba, D. N. Straub, and M. L. Waite, Non-local energy transfers in rotating turbulence at intermediate Rossby number, J. Fluid Mech. 690, 129 (2012).
  16. T. Teitelbaum and P. D. Mininni, Decay of Batchelor and Saffman rotating turbulence, Phys. Rev. E 86, 066320 (2012).
  17. E. Deusebio, G. Boffetta, E. Lindborg, and S. Musacchio, Dimensional transition in rotating turbulence, Phys. Rev. E 90, 023005 (2014).
  18. A. Delache, C. Cambon, and F. S. Godeferd, Scale by scale anisotropy in freely decaying rotating turbulence, Phys. Fluids 26, 025104 (2014).
  19. A. Alexakis, Rotating Taylor-Green flow, J. Fluid Mech. 769, 46 (2015).
  20. A. Campagne, N. Machicoane, B. Gallet, P.-P. Cortet, and F. Moisy, Turbulent drag in a rotating frame, J. Fluid Mech. 794, R5 (2016).
  21. R. Hide and C. W. Titman, Detached shear layers in a rotating fluid, J. Fluid Mech. 29, 39 (1967).
  22. K. Stewartson, On almost rigid rotations, J. Fluid Mech. 3, 17 (1957).
  23. F. H. Busse, Shear flow instabilities in rotating systems, J. Fluid Mech. 33, 577 (1968).
  24. H. Niino and N. Misawa, An experimental and theoretical study of barotropic instability, J. Atmos. Sc. 41, 1992 (1984).
  25. F. V. Dolzhanskii, V. A. Krymov, and D. Yu Manin, Stability and vortex structures of quasi-two-dimensional shear flows, Sov. Phys. Usp 33, 495 (1990).
  26. J. A. van de Konijnenberg, A. H. Nielsen, J. J. Rasmussen, and B. Stenum, Shear-flow instability in a rotating fluid, J. Fluid Mech. 387, 177 (1999).
  27. W. G. Früh and P. L. Read, Experiments on a barotropic rotating shear layer, part 1: Instability and steady vortices, J. Fluid Mech. 383, 143 (1999).
  28. R. Hollerbach, Instabilities of the Stewartson layer, part 1: The dependence on the sign of Ro, J. Fluid Mech. 492, 289 (2003).
  29. N. Schaeffer and P. Cardin, Quasigeostrophic Model of the instabilities of the Stewartson layer in flat and depth-varying containers, Phys. Fluids 17, 104111 (2005).
  30. M. J. Lighthill, On waves generated in dispersive systems to traveling forcing effects, with applications to the dynamics of rotating fluids, J. Fluid Mech. 27, 725 (1967).
  31. K. S. Peat and T. N. Stevenson, The phase configuration of waves around a body moving in a rotating stratified fluid, J. Fluid Mech. 75, 647 (1976).
  32. S. Galtier, Weak inertial-wave turbulence theory, Phys. Rev. E 68, 015301 (2003).
  33. C. Cambon, R. Rubinstein, and F. S. Godeferd, Advances in wave turbulence: Rapidly rotating flows, New J. Phys. 6, 73 (2004).
  34. S. Nazarenko, Wave Turbulence (Springer-Verlag, Berlin, 2011).
  35. A. Ranjan and P. A. Davidson, Evolution of a turbulent cloud under rotation, J. Fluid Mech. 756, 488 (2014).

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