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Fluids 2017, 2(4), 49; doi:10.3390/fluids2040049

A Non-Hydrostatic Depth-Averaged Model for Hydraulically Steep Free-Surface Flows

David & James–Engineering and Environmental Consultancy, 204 Albion Road, Victoria 3350, Australia
Received: 5 August 2017 / Revised: 16 September 2017 / Accepted: 18 September 2017 / Published: 23 September 2017
(This article belongs to the Special Issue Advances in Hydrodynamics)
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Abstract

This study describes the results of a numerical investigation aimed at developing and validating a non-hydrostatic depth-averaged model for flow problems where the horizontal length scales close to flow depth. For such types of problems, the steep-slope shallow-water equations are inadequate to describe the two-dimensional structure of the curvilinear flow field. In the derivation of these equations, the restrictive assumptions of negligible bed-normal acceleration and bed curvature were employed, thus limiting their applicability to shallow flow situations. Herein, a Boussinesq-type model is deduced from the depth-averaged energy equation by relaxing the weakly-curved flow approximation to deal with the non-hydrostatic steep flow problems. The proposed model is solved with an implicit finite difference scheme and then applied to simulate steady free-surface flow problems with strong curvilinear effects. The numerical results are compared to experimental data, resulting in a reasonable overall agreement. Further, it is shown that the discharge characteristics of free flow over a round-crested weir are accurately described by using a Boussinesq-type approximation, and the drawbacks arising from a standard hydrostatic approach are overcome. The suggested numerical method to determine the discharge coefficient can be extended and adopted for other types of short-crested weirs. View Full-Text
Keywords: open channel hydrodynamics; curvilinear transcritical flow; flow-structure interactions; non-hydrostatic flow; critical flow conditions; numerical models open channel hydrodynamics; curvilinear transcritical flow; flow-structure interactions; non-hydrostatic flow; critical flow conditions; numerical models
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Zerihun, Y.T. A Non-Hydrostatic Depth-Averaged Model for Hydraulically Steep Free-Surface Flows. Fluids 2017, 2, 49.

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