Initial stages of gravity-driven flow of two fluids of equal depth

Korobkin, Alexander ORCID: and Yilmaz, Oguz (2023) Initial stages of gravity-driven flow of two fluids of equal depth. Physics of Fluids, 35 (2). ISSN 1070-6631

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Short-time behavior of gravity-driven free surface flow of two fluids of equal depth and different densities is studied. Initially, the fluids are at rest and separated with a vertical rigid plate of negligible thickness. Then, the plate disappears suddenly and a gravity-driven flow of the fluids starts. The flow in an early stage is described by the potential theory. The initial flow in the leading order is described by a linear problem, which is solved by the Fourier series method. The motions of the interface between the fluids and their free surfaces are investigated. The singular behaviors of the velocity field at the bottom point, where the interface meets the rigid bottom, and the top point, where the interface meets both free surfaces, are analyzed in detail. The flow velocity is shown to be log-singular at the bottom point. The leading-order inner asymptotic solution is constructed in a small vicinity of this point. It is shown that the flow close to the bottom point is self-similar. The motion of the interface is independent of any parameters, including the density ratio, of the problem in specially stretched variables. In the limiting case of negligible density of one of the fluids, the results of the classical dam break problem are recovered. The Lagrangian representation is employed to capture the behavior of the interface and the free surfaces at the top, where the fluid interface meets the free surfaces. The shapes of the free surfaces and the interface in the leading order computed by using the Lagrangian variables show a jump discontinuity of the free surface near the top point where the free surfaces and the interface meet. Inner region formulation is derived near the top point.

Item Type: Article
Additional Information: Funding Information: This work was partly supported by TUBITAK (Scientific and Technological Research Council of Turkey, Grant No. 111M209), and this support is greatly acknowledged. The authors are also grateful to the referees, who suggested several important improvements to the presentation of the results. Publisher Copyright: © 2023 Author(s).
Uncontrolled Keywords: computational mechanics,condensed matter physics,mechanics of materials,mechanical engineering,fluid flow and transfer processes ,/dk/atira/pure/subjectarea/asjc/2200/2206
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Fluid and Solid Mechanics
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Depositing User: LivePure Connector
Date Deposited: 04 Mar 2024 18:35
Last Modified: 04 Mar 2024 18:35
DOI: 10.1063/5.0138868


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