Conference on Turbulence and Interactions TI2006 May June Porquerolles France

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Conference on Turbulence and Interactions TI2006, May 29 - June 2, 2006, Porquerolles, France THE DECAY LAW OF GRID TURBULENCE IN A ROTATING TANK F. Moisy?, C. Morize, M. Rabaud Fluides, Automatique et Systemes thermiques (FAST), CNRS UMR 7608, Universities Pierre et Marie Curie - Paris 6 and Paris-Sud 11, Bat. 502, Campus Universitaire, 91405 Orsay Cedex, France. ?Email: ABSTRACT The energy decay of grid-generated turbulence in a rotating tank is experimentally investigated by means of particle image velocimetry. For times smaller than the Ekman timescale, a range of approximate self-similar decay is found, in the form u2(t) ? t?n, with the exponent n decreasing from 2 to values close to 1 as the rotation rate is increased. This observation is interpreted in the frame of a phenomenological model based on the exponent of the energy spectrum, in which both the effects of the rotation and the confinement are taken into account. INTRODUCTION Assuming self-similarity, the decay of high Reynolds number homogeneous and isotropic turbulence is usually described by a power law [1–4], u2 ? (t? t?)?n, (1) where u is the velocity variance, n is the decay exponent and t? is a virtual origin.

  • self-similar decay

  • ground rotation

  • rived assuming

  • rotation

  • caying rotating

  • rotating containers

  • energy decay

  • generated turbulence


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Conference on Turbulence and Interactions TI2006, May 29  June 2, 2006, Porquerolles, France
THE DECAY LAW OF GRID TURBULENCE IN A ROTATING TANK
F. Moisy, C. Morize, M. Rabaud
Fluides, Automatique et Syste`mes thermiques (FAST), CNRS UMR 7608, Universities Pierre et Marie Curie  Paris 6 and ParisSud 11, Baˆt. 502, Campus Universitaire, 91405 Orsay Cedex, France. Email: moisy@fast.upsud.fr
ABSTRACT The energy decay of gridgenerated turbulence in a rotating tank is experimentally investigated by means of particle image velocimetry. For times smaller than the Ekman timescale, a range of approximate selfsimilar 2n decay is found, in the formu(t)t, with the exponentndecreasing from 2 to values close to 1 as the rotation rate is increased. This observation is interpreted in the frame of a phenomenological model based on the exponent of the energy spectrum, in which both the effects of the rotation and the confinement are taken into account.
1/2 INTRODUCTIONEkman timescale,tE=h(νΩ)(wherehis the size of the experiment along the rotation axis). The ratio of the turbulent time scale and the ro Assuming selfsimilarity, the decay of high tation rate is the Rossby number,Ro=u/`. Reynolds number homogeneous and isotropic While the primary effect of the rotation is to re turbulence is usually described by a power duce the energy dissipation [5], the effect of the law [1–4], Ekman friction is to accelerate the decay at large times, shortening the temporal range for the tur 2∗ −n u(tt),(1) bulent decay even at large Reynolds numbers. Based on the assumption that the energy transfers 1 time scale is governed byΩ, Squires et al. [6] whereuis the velocity variance,nis the decay have proposed a selfsimilar decay with an expo exponent andtis a virtual origin. The value 23/5 nent half of that without rotation,ut, in of the exponentndepends on whether the size the limit of zero Rossby number. of the energycontaining eddies is free to grow (n= 6/5) or is is bounded by the experiment In experiments, where both confinement and fi size (n= 2), with a possible changeover between nite Rossby numbers are to be considered, the these two regimes [4]. situation is more complex. In small experiments 1/2 In the presence of rotation, in addition to thein whichh'O((ν/Ω) )(e.g. Ibbetson & Trit turnover time`/u(where`ton [7]), the inhibition of the energy decay is hidis the size of the energycontaining eddies), two other timescalesden by the extra dissipation in the Ekman lay are present in the problem, which have oppoers, and is not observed. Larger experiments (e.g. site effects on the turbulence decay: the rotationJacquin et al. [5]), in which a significant range 11 timescale,Ω, and, for bounded systems, theΩ¿t¿tEexists, have indeed confirmed