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.
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- self-similar decay
- ground rotation
- rived assuming
- rotation
- caying rotating
- rotating containers
- energy decay
- generated turbulence
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 ParisSud 11, Baˆt. 502, Campus Universitaire, 91405 Orsay Cedex, France. ∗ Email: moisy@fast.upsud.fr
ABSTRACT The energy decay of gridgenerated 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 selfsimilar 2−n 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 selfsimilarity, the decay of high tation rate is the Rossby number,Ro=u/2Ω`. 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∝(t−t),(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 selfsimilar decay with an expo exponent andtis a virtual origin. The value 2−3/5 nent half of that without rotation,u∝t, in of the exponentndepends on whether the size the limit of zero Rossby number. of the energycontaining 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 hidis the size of the energycontaining eddies), two other timescalesden by the extra dissipation in the Ekman lay are present in the problem, which have oppoers, and is not observed. Larger experiments (e.g. site effects on the turbulence decay: the rotationJacquin et al. [5]), in which a significant range −1−1 timescale,Ω, and, for bounded systems, theΩ¿t¿tEexists, have indeed confirmed
