Development of supercritical motion and internal jumps within lock-release radial currents and draining flows

We present an experimental study of inertial gravity currents (GCs) propagating in a cylindrical wedge under different drainage directions (inward/outward), lock-release (full/partial gate width) and geometry (annulus/full cylinder). We investigate the following combinations representative of operational conditions for dam-break flows: (i) inward drainage, annular reservoir, full gate; (ii) outward drainage, full reservoir, full gate; and (iii) outward drainage, full reservoir, partial gate. A single-layer shallow-water (SW) model is used for modelling the first two cases, while a box model interprets the third case; the results of these approximations are referred to as “theoretical”. We performed a first series of experiments with water as ambient fluid and brine as intruding fluid, measuring the time evolution of the volume in the reservoir and the velocity profiles in several sections; in a second series, air was the ambient and water was the intruding fluid. Careful measurements, accompanied by comparisons with the theoretical predictions, were performed for the behaviour of the interface, radial velocity and, most important, the volume decay $${\mathcal {V}}(t)/{\mathcal {V}}(0)$$ V ( t ) / V ( 0 ) . In general, there is good agreement: the theoretical volume decay is more rapid than the measured one, but the discrepancies are a few percent and the agreement improves as the Reynolds number increases. Velocity measurements show a trend correctly reproduced by the SW model, although often a delay is observed and an over- or under-estimation of the peak values. Some experiments were conducted to verify the role of inconsistencies between experimental set-up and model assumptions, considering, for example, the presence or absence of a top lid, wedge angle much less than $$2\pi $$ 2 π , suppression of the viscous corner at the centre, reduction of disturbances in the dynamics of the ambient fluid: all these effects resulted in negligible impacts on the overall error. These experiments provide corroboration to the simple models used for capturing radial drainage flows, and also elucidate some effects (like oscillations of the radial flux) that are beyond the resolution of the models. This holds also for partial width lock-release, where axial symmetry is lost.

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Experimental verification of theoretical approaches for radial gravity currents draining from an edge

Petrolo

Ungarish

Chiapponi

et al. 2021

Acta Mech

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Gravity current escape from a topographic depression

Skevington,

Hogg

2024

Phys. Rev. Fluids

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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 on time. This phenomenon is explained by analyzing 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 on 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. Published by the American Physical Society 2024

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Development of supercritical motion and internal jumps within lock-release radial currents and draining flows

Cited by 2 publications

References 27 publications

Experimental verification of theoretical approaches for radial gravity currents draining from an edge

Experimental verification of theoretical approaches for radial gravity currents draining from an edge

Gravity current escape from a topographic depression

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