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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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