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The turbulence boundary of a temporal jet

Published online by Cambridge University Press:  18 December 2013

Maarten van Reeuwijk  and
Markus Holzner
Maarten van Reeuwijk*
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, SW7 2AZ London, UK
Markus Holzner
Affiliation:
Institute of Environmental Engineering, ETH Zürich, CH-8039 Zürich, Switzerland
*
†Email address for correspondence: m.vanreeuwijk@imperial.ac.uk
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Abstract

We examine the structure of the turbulence boundary of a temporal plane jet at $\mathit{Re}= 5000$ using statistics conditioned on the enstrophy. The data is obtained by direct numerical simulation and threshold values span 24 orders of magnitude, ranging from essentially irrotational fluid outside the jet to fully turbulent fluid in the jet core. We use two independent estimators for the local entrainment velocity ${v}_{n} $ based on the enstrophy budget. The data show clear evidence for the existence of a viscous superlayer (VSL) that envelopes the turbulence. The VSL is a nearly one-dimensional layer with low surface curvature. We find that both its area and viscous transport velocity adjust to the imposed rate of entrainment so that the integral entrainment flux is independent of threshold, although low-Reynolds-number effects play a role for the case under consideration. This threshold independence is consistent with the inviscid nature of the integral rate of entrainment. A theoretical model of the VSL is developed that is in reasonably good agreement with the data and predicts that the contribution of viscous transport and dissipation to interface propagation have magnitude $2{v}_{n} $ and $- {v}_{n} $, respectively. We further identify a turbulent core region (TC) and a buffer region (BR) connecting the VSL and the TC. The BR grows in time and inviscid enstrophy production is important in this region. The BR shows many similarities with the turbulent–non-turbulent interface (TNTI), although the TNTI seems to extend into the TC. The average distance between the TC and the VSL, i.e. the BR thickness is about 10 Kolmogorov length scales or half a Taylor length scale, indicating that intense turbulent flow regions and viscosity-dominated regions are in close proximity.

JFM classification

Wakes/Jets: Wakes/Jets Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 739 , 25 January 2014 , pp. 254 - 275
Copyright
©2013 Cambridge University Press 

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