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Inertial gravity current produced by the drainage of a cylindrical reservoir from an outer or inner edge
Technion Israel Inst Technol, Dept Comp Sci, IL-32000 Haifa, Israel..
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0002-3443-0709
Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA..
2019 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 874, p. 185-209Article in journal (Refereed) Published
Abstract [en]

We consider the time-dependent flow of a fluid of density rho(1) in a vertical cylindrical container embedded in a fluid of density rho(2) (<rho(1)) whose side boundary is suddenly removed and the fluid drains freely from the edge. We show that in the inertial-buoyancy regime (large initial Reynolds number) the flow is modelled by the shallow-water equations and bears similarities to a gravity current released from a lock (the dam-break problem) driven by the reduced gravity g' = (1 - rho(2)/rho(1))g. This formulation is amenable to an efficient finite-difference solution. Moreover, we demonstrate that similarity solutions exist, and show that the flow created by the dam break approaches the predicted self-similar behaviour when the volume ratio nu(t)/nu(0) approximate to 1/2 where t is time elapsed from the dam break. We considered two cases of drainage: (i) outward from the outer boundary in a full-radius reservoir; and (ii) inward from the inner radius in an annular-shaped reservoir. For the first case the similarity solution is expressed analytically, while the second case is more complicated and requires a numerical solution. In both cases nu(t)/nu(0) decays like t(-2), but the details are different. The similarity solutions admit an adjustable virtual-origin constant, which we determine by matching with the finite-difference solution. The analysis is valid for both Boussinesq and non-Boussinesq systems, and a wide range of geometric parameters (inner and outer radii, and height). The importance of the neglected viscous terms increases with time, and eventually the inertial-buoyancy model becomes invalid. An estimate for this occurrence is also provided. The predictions of the model are compared to results of direct numerical simulations; there is good agreement for the position of the interface and for the averaged radial velocity, and excellent agreement for nu(t)/nu(0). A box model is used for estimating the effect of a partial (over a sector) dam break. This study is an extension of the work for a rectangular reservoir of Momen et al. (J. Fluid Mech., vol. 827, 2017, pp. 640-663). We demonstrate that there are some similarities, but also significant differences, between the rectangular and the cylindrical reservoirs concerning the velocity, shape of the interface and rate of drainage, which are of interest in applications. The overall conclusion is that this simple model captures very well the flow field under consideration.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS , 2019. Vol. 874, p. 185-209
Keywords [en]
geophysical and geological flows, gravity currents, shallow water flows
National Category
Geophysical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-255396DOI: 10.1017/jfm.2019.452ISI: 000473909800001Scopus ID: 2-s2.0-85068527773OAI: oai:DiVA.org:kth-255396DiVA, id: diva2:1342821
Note

QC 20190814

Available from: 2019-08-14 Created: 2019-08-14 Last updated: 2019-08-14Bibliographically approved

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Zhu, Lailai

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