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Structure formation in homogeneous freely decaying rotating turbulence

Published online by Cambridge University Press:  25 February 2008

P. J. STAPLEHURST ,
P. A. DAVIDSON  and
S. B. DALZIEL
P. J. STAPLEHURST
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
P. A. DAVIDSON
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
S. B. DALZIEL
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Rd, Cambridge CB3 0WA, UK
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Abstract

One of the most striking features of rotating turbulence is the inevitable appearance of large-scale columnar structures. Whilst these structures are frequently observed, the processes by which they are created are still poorly understood. In this paper we consider the emergence of these structures from freely decaying, rotating turbulence with Ro ∼ 1. Our study follows the conjecture by Davidson, Staplehurst & Dalziel (J. Fluid Mech., vol. 557, 2006, p. 135) that the structure formation may be due to linear inertial wave propagation, which was shown to be consistent with the growth of columnar eddies in inhomogeneous turbulence. Here we extend that work and consider the case of homogeneous turbulence.

We describe laboratory experiments where homogeneous turbulence is created in a rotating tank. The turbulence is generated with Ro ∼ 1, and as the energy decays, the formation of columnar vortices is observed. The axial growth of these columnar structures is then measured using two-point correlations and in all cases the results are consistent with structure formation via linear inertial wave propagation. In particular, we obtain a self-similar collapse of the two-point correlations when the axial coordinate is normalized by Ωtb, where b is a measure of the integral scale in the horizontal plane and Ω is the rotation rate. Although our results do not exclude the possibility of significant nonlinear dynamics, they are consistent with the conjecture of Davidson et al. (2006) that linear dynamics play a strong guiding hand in structure formation.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 598 , 10 March 2008 , pp. 81 - 105
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Bartello, P., Metais, O. & Lesieur, M. 1994 Coherent structures in rotating three-dimensional turbulence. J. Fluid Mech 273, 1–29.CrossRefGoogle Scholar
Bracewell, R.N. 1986 The Fourier Transform and its Applications, 2nd edn. McGraw-Hill.Google Scholar
Cambon, C., Mansour, N.N. & Godeferd, F. S. 1997 Energy transfer in rotating turbulence. J. Fluid Mech 337, 303–332.CrossRefGoogle Scholar
Cambon, C. & Scott, F. S. 1999 Linear and nonlinear models of anisotropic turbulence. Annu. Rev. Fluid Mech 31, 1–53.CrossRefGoogle Scholar
Dalziel, S.B., Carr, M., Sveen, J. K. & Davies, P. A. 2007 Simultaneous synthetic schlieren and PIV measurements for internal solitary waves. Meas. Sci. Tech 18, 533–547.Google Scholar
Davidson, P.A. 2007 On the large-scale structure of homogeneous two-dimensional turbulence. J. Fluid Mech 580, 431–450.CrossRefGoogle Scholar
Davidson, P. A., Staplehurst, P. J. & Dalziel, S. B. 2006 On the evolution of eddies in a rapidly rotating system. J. Fluid Mech 557, 135–144.CrossRefGoogle Scholar
Gence, J. N. & Frick, C 2001 Naissance des corrélations triples de vorticité dans une turbulence statistiquement homogène soumise à une rotation. CR Acad. Sci. Paris II 329, 351–356.Google Scholar
Greenspan, H. P. 1968 Theory of Rotating Fluids. Cambridge University Press.Google Scholar
Hopfinger, E. J., Browand, F. K. & Gagne, Y. 1982 Turbulence and waves in a rotating tank. J. Fluid Mech 125, 505–534.CrossRefGoogle Scholar
Hopfinger, E. J., Griffiths, R. W. & Mory, M. 1983 The structure of turbulence in homogeneous and stratified rotating fluids. J. Mech. Theoriq. Appl. (special issue) 44, 21–44.Google Scholar
Jacquin, L., Leuchter, O., Cambon, C. & Mathieu, J. 1990 Homogeneous turbulence in the presence of rotation. J. Fluid Mech 220, 1–52.CrossRefGoogle Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161–179.Google Scholar
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
McKenna, S. P. & McGillis, W. R. 2004 Observations of flow repeatability and secondary circulation in an oscillating grid-stirred tank. Phys. Fluids 16, 3499.CrossRefGoogle Scholar
Morize, C. & Moisy, F. 2006 Energy decay of rotating turbulence with confinement effects. Phys. Fluids 18, 065107.CrossRefGoogle Scholar
Morize, C., Moisy, F. & Rabaud, M. 2005 Decaying grid-generated turbulence in a rotating tank. Phys. Fluids 17, 095105.CrossRefGoogle Scholar
Morize, C., Moisy, F., Rabaud, M. & Sommeria, J. 2006 On the cyclone–anticyclone asymmetry in decaying rotating turbulence. In Conference on Turbulence and Interactions TI2006.Google Scholar
Ruppert-Felsot, J. E., Praud, O., Sharon, E. & Swinney, H. L. 2005 Extraction of coherent structures in a rotating turbulent flow experiment. Phys. Rev. E 72, 016311.Google Scholar
Savas, O. 1985 On flow visualization using reflective flakes. J. Fluid Mech 152, 235–248.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flows. Cambridge University Press.Google Scholar
Waleffe, F. 1993 Inertial transfers in the helical decomposition. Phys. Fluids A 5, 667–685.CrossRefGoogle Scholar