Unsteady draining of reservoirs over weirs and through constrictions

Skevington, Edward W. G.; Hogg, Andrew J.

doi:10.1017/jfm.2019.808

Cited by 4 publications

(11 citation statements)

References 35 publications

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“…The shock is then reflected from the origin and propagates forwards, moving faster than the local fluid velocity and reaches the front, before again being reflected towards the origin. This pattern of shock reflections superimposed upon a bulk flow is similar to the reflections of continuous waves in two-dimensional gravity currents [14] and draining flows from partially-breached reservoirs [28].…”

Section: Lock-release Gravity Currentssupporting

confidence: 52%

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

2021

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The unsteady radial flow of relatively dense fluid released from an axisymmetric lock is analysed when it freely drains over an edge and when it generates a gravity current propagating over a horizontal surface. In both situations when modelled using the shallow water equations, despite initiation from rest within a lock, the flow thins, accelerates and becomes supercritical in a region close to the symmetry axis. For free-drainage, this alters the outflow, while for radial gravity currents, it leads to the formation of an internal jump connecting rapidly moving fluid to more tranquil flow at the front. Both scenarios share the same supercritical flow structure, which is related to their initiation from lock-release conditions and is a function of axisymmetry; the phenomena is not found in analogous two-dimensional flows. Through analysis and numerical integration of the governing equations, the common onset and consequences of supercriticality are revealed in both flows, and in particular, the progression of the fluid motions to self-similar states that develop at late times.

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Section: Lock-release Gravity Currentssupporting

confidence: 52%

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

2021

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“…Hodograph techniques yield precise quasianalytical results for unsteady hydraulic flows and provide significant insight into the ensuing fluid motions. Flows analysed using these methods have included unsteady collapses of finite length reservoirs into 2D channels (24); the run-up of swash on an inclined planar beach and the formation of the backwash bore (25); and the collapse of a fluid reservoir over a weir and through a constriction (26). Although the hodograph techniques appear cumbersome at first sight, the approach permits the quasi-analytical solution of complicated flows and the precise identification of the onset and evolution of shocks and locations at which the gradients of the dependent variables are discontinuous.…”

Section: Introductionmentioning

confidence: 99%

Dam-break reflection

Hogg

Skevington

2021

The Quarterly Journal of Mechanics and Applied Mathematics

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Summary The unsteady reflection of dam-break flow along a horizontal channel by a remote barrier is modelled using the nonlinear shallow water equations. The interaction generates an upstream moving bore that connects the collapsing reservoir of fluid to a rapidly deepening fluid layer adjacent to the barrier. These motions are modified when the fluid is released into a channel containing a pre-wetted layer, because the oncoming flow is itself headed by a bore that alters the initial reflection. Solutions for these flows are calculated using quasi-analytical techniques that utilise the method of characteristics and the hodograph transformation of the governing equations, and the results are validated by comparison with direct numerical integration of the shallow water equations. The analytical solutions enable the precise identification of dynamical features in the flow, including the onset and development of discontinuous solutions that are manifest as bores, as well as their long term behaviour, the rate at which energy is dissipated, and for flows generated from the release of a finite reservoir, the maximum depth of the fluid layer at the barrier.

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“…We suppose that, at the instant the current reaches the barrier, which determines , thus We then compare the total inertia of the flow at the instant of collision (from the simulation of a lock-release current) with that of the asymptotic , producing the ratio where thus Our simulations suggest that, so long as then , see figure 12( b ). We see then that the requirement for limiting to the draining discussed in Skevington & Hogg (2020) is that the inertia is not too much greater than that of the asymptotic solution, . This bound is surprisingly weak, a priori it may be anticipated that is required; it seems the asymptotic solution is unusually robust.…”

Section: Numerical Evaluation Of Fluid Outflow Over a Critical Barriermentioning

confidence: 77%

“…These calculations have utilised a sophisticated boundary condition to model the effects of a barrier, modifying that of Cozzolino et al. (2014) and generalising that of Skevington & Hogg (2020). The resulting model has been explored in the case of a collision with a spatially and temporally uniform current, § 3, which is a similar flow scenario to the studies of Long (1954, 1970) and Baines (1995), except that we require that the flow beyond the barrier is supercritical which yields a unique solution.…”

Section: Discussionmentioning

confidence: 99%

“…If, after is calculated, we have , then we cease performing further computations, and approximate . We simulate for , with a resolution of 1000 cells, and include in our plots that all the fluid escapes for , and that the fluid drains to a height for as discussed in Skevington & Hogg (2020). We now explore the overtopping that occurs for , for which the escaped volume is shown in figure 12( a ).…”

Section: Numerical Evaluation Of Fluid Outflow Over a Critical Barriermentioning

confidence: 99%

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The unsteady overtopping of barriers by gravity currents and dam-break flows

Skevington

Hogg²

2023

J. Fluid Mech.

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The collision of a gravitationally driven horizontal current with a barrier following release from a confining lock is investigated using a shallow water model of the motion, together with a sophisticated boundary condition capturing the local interaction. The boundary condition permits several overtopping modes: supercritical, subcritical and blocked flow. The model is analysed both mathematically and numerically to reveal aspects of the unsteady motion and to compute the proportion of the fluid trapped upstream of the barrier. Several problems are treated. Firstly, the idealised problem of a uniform incident current is analysed to classify the unsteady dynamical regimes. Then, the extreme regimes of a very close or distant barrier are tackled, showing the progression of the interaction through the overtopping modes. Next, the trapped volume of fluid at late times is investigated numerically, demonstrating regimes in which the volume is determined purely by volumetric considerations, and others where transient inertial effects are significant. For a Boussinesq gravity current, even when the volume of the confined region behind the barrier is equal to the fluid volume, $30\,\%$ of the fluid escapes the domain, and a confined volume three times larger is required for the overtopped volume to be negligible. For a subaerial dam-break flow, the proportion that escapes is in excess of $60\,\%$ when the confined volume equals the fluid volume, and a barrier as tall as the initial release is required for negligible overtopping. Finally, we compare our predictions with experiments, showing a good agreement across a range of parameters.

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Unsteady draining of reservoirs over weirs and through constrictions

Cited by 4 publications

References 35 publications

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

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

Dam-break reflection

The unsteady overtopping of barriers by gravity currents and dam-break flows

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