Gravity current escape from a topographic depression

Edward Skevington, Andrew J Hogg*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review


An inertial gravity current released within a topographic depression may climb up the incline from a lower to an upper plateau if it is sufficiently energetic, and then continue to flow unsteadily away from the step while simultaneously draining back into the depression. This density-driven motion is investigated theoretically using the shallow-water equations to simulate the flow up a smooth step from a lower to an upper horizontal plane and to compute the volume of fluid that escapes from the depression. It is shown that it is possible for all of the fluid to drain back down the step, and that the volume of the escaped fluid diminishes with a power-law dependence upon time. This phenomenon is explained by analysing the unsteady flow of a gravity current along a semi-infinite horizontal plane along which the front advances, but simultaneously fluid drains from the rear edge of the plane. The dynamics of this motion at early times is calculated both numerically and analytically. The latter exploits the hodograph transformation of the shallow water equation, a technique which allows rapid and precise evaluation of flow features such as reflections and the onset of bores. The flow at later times becomes self-similar, and the self-similarity is of the second kind. It features an anomalous exponent that provides the power-law dependence of the volume of fluid upon time, and this exponent is a function of the imposed Froude number at the front of the current. In this way the diminishing volume of fluid that escapes from a topographic depression is explained quantitatively. Eventually the flow may transition to a regime in which drag becomes non-negligible; the model of simultaneous propagation and draining is extended to this regime to show that the escaped volume of fluid also decays temporally and ultimately vanishes.
Original languageEnglish
Article number014802
JournalPhysical Review Fluids
Publication statusPublished - 9 Jan 2024

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© 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the ""Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.


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