Unsteady draining of reservoirs over weirs and through constrictions
| Autor: | Andrew J. Hogg, Edward W. G. Skevington |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Asymptotic analysis
Hydraulics Mechanical Engineering hydraulic control hydraulics 0208 environmental biotechnology Flow (psychology) 02 engineering and technology Mechanics Condensed Matter Physics gravity currents 01 natural sciences 010305 fluids & plasmas 020801 environmental engineering law.invention Numerical integration Hodograph Mechanics of Materials law 0103 physical sciences Weir Outflow Boundary value problem Geology |
| Zdroj: | Skevington, E & Hogg, A J 2019, ' Unsteady draining of reservoirs over weirs and through constrictions ', Journal of Fluid Mechanics, vol. 882, A9 . https://doi.org/10.1017/jfm.2019.808 |
| ISSN: | 1469-7645 0022-1120 |
| DOI: | 10.1017/jfm.2019.808 |
| Popis: | The gravitationally-driven flow of fluid from a reservoir following the partial collapse of its confining dam, or the partial opening of its confining lock, is modelled using the nonlinear shallow water equations, coupled to outflow conditions, in which the drainage is modelled as flow over a constricted, broad-crested weir. The resulting unsteady motion reveals systematic draining, on which strong and relatively rapid oscillations are imposed. The oscillations propagate between the outflow and the impermeable back wall of the reservoir. These dynamics are investigated utilising three methods: hodograph techniques to yield quasi-analytical solutions, asymptotic analysis at relatively late times after initiation, and numerical integration of the governing equations. The hodograph transformation is used to find exact solutions at early times, revealing that from initially quiescent conditions the fluid drains and yet repeatedly generates intervals during which there are regions of constant depth and velocity adjacent to the boundaries. A novel modified multiscale asymptotic analysis designed for late times is employed to determine the limiting rate of draining and wave structure. It is shown that the excess height drains as $t^{-2}$ and, when the obstacle has finite height, the velocity field decays as $t^{-3}$, and exhibits a wave structure that tends towards a constant and relatively rapid phase speed. In the case of a pure constriction, for which all the fluid ultimately drains out of the reservoir, the motion adjusts to a self-similar state in which the velocity field decays as $t^{-1}$. Oscillations around this state have an exponentially increasing period. Numerical simulations with a novel implementation of boundary conditions are performed; they confirm the hodograph solution and provide data for the asymptotic results. |
| Databáze: | OpenAIRE |
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