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Unconfined turbulent entrainment across density interfaces

Shrinivas, AB and Hunt, GR (2014) Unconfined turbulent entrainment across density interfaces. Journal of Fluid Mechanics, 757. pp. 573-598. ISSN 0022-1120

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© 2014 Cambridge University Press. We present theoretical models describing the quasi-steady downward transport of buoyant fluid across a gravitationally stable density interface separating two unbounded quiescent fluid masses. The primary transport mechanism is turbulent entrainment resulting from the localised impingement of a vertically forced high-Reynolds-number axisymmetric jet with steady source conditions. The entrainment across the interface is examined in the large-time asymptotic state, wherein the interfacial gravity current, formed by the fluid entrained from the upper layer and the jet, becomes infinitesimally thin and a two-layer stratification persists. Characterising flows with small interfacial Froude numbers Fr<inf>i</inf>) as an axisymmetric semi-ellipsoidal impingement dome, we combine conservation equations with a mechanistic model of entrainment and reveal that, in this regime, the dimensionless entrainment flux E<inf>i</inf> across the interface follows the power law E<inf>i</inf> = 0.24Fr<inf>i</inf><sup>2</sup>. For large-Fr<inf>i</inf> impingements, modelled as a fully penetrating turbulent fountain, we show that E<inf>i</inf> no longer scales with Fr<inf>i</inf><sup>2</sup>, but linearly on Fr<inf>i</inf>, following E<inf>i</inf> = 0.42Fr<inf>i</inf>. We establish the intermediate range of Fr<inf>i</inf> over which there is a transition between these quadratic and linear power laws, thus enabling us to classify the dynamics of entrainment across the interface into three distinct regimes. Finally, the close agreement of our solutions with existing experimental results is illustrated.

Item Type: Article
Divisions: Div A > Fluid Mechanics
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 18:57
Last Modified: 19 Jul 2018 07:03