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Meandering due to large eddies and the statistically self-similar dynamics of quasi-two-dimensional jets

Published online by Cambridge University Press:  06 January 2012

Julien R. Landel ,
C. P. Caulfield  and
Andrew W. Woods
Julien R. Landel*
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
C. P. Caulfield
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
Andrew W. Woods
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

We investigate experimentally the structure of quasi-two-dimensional plane turbulent jets discharged vertically from a slot of width into a fluid confined between two relatively close rigid boundaries with gap . At large vertical distances the jet structure consists of a meandering core with large counter-rotating eddies, which develop on alternate sides of the core. Using particle image velocimetry, we observe an inverse cascade typical of quasi-two-dimensional turbulence where both the core and the eddies grow linearly with and travel at an average speed proportional to . However, although the present study concerns quasi-two-dimensional confined jets, the jets are self-similar and the mean properties are consistent with both experimental results and theoretical models of the time-averaged properties of fully unconfined planar two-dimensional jets. We believe that the dynamics of the interacting core and large eddies accounts for the Gaussian profile of the mean vertical velocity as shown by the spatial statistical distribution of the core and eddy structure. The lateral excursions (caused by the propagating eddies) of this high-speed central core produce a Gaussian distribution for the time-averaged vertical velocity. In addition, we find that approximately 75 % of the total momentum flux of the jet is contained within the core. The eddies travel substantially slower (at approximately 25 % of the maximum speed of the core) at each height and their growth is primarily attributed to entrainment of ambient fluid. The frequency of occurrence of the eddies decreases in a stepwise manner due to merging, with a well-defined minimum value of the corresponding Strouhal number .

JFM classification

Wakes/Jets: Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 692 , 10 February 2012 , pp. 347 - 368
Copyright
Copyright © Cambridge University Press 2012

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