Nonhydrostatic Formulation of Unsteady Single and Two-Layer Flow over Topography
Publication: Journal of Hydraulic Engineering
Volume 147, Issue 2
Abstract
A new, concise theoretical model for simulation of unsteady, nonhydrostatic two-layer flow is presented. The formulation is systematically developed from the equations of motion of an ideal fluid using a perturbation technique with shallowness as the small parameter. The advantage of this model over many models in the field is that the shape of streamlines, or velocity and pressure distributions, are dictated by the model rather than being predetermined. This model also relaxes further assumptions involved in the previous formulations and can be used to simulate different two-layer flow cases. In some situations, simulation is impossible without considering the nonhydrostatic pressure, one of which is a two-layer approach-controlled flow. A laboratory transient two-layer flow experiment is conducted to examine transition to the approach-controlled flow, and the new equations are successfully applied to model this transient flow using a total variation diminishing (TVD) MacCormack scheme. Furthermore, new equations for single layer unsteady nonhydrostatic flow are presented and two-steady flow cases of flow over an obstacle and an undular hydraulic jump are excellently simulated.
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Data Availability Statement
Some data and the generated code in the study are available in an online repository. The Fortran code for simulation of single layer flows and the two-layer flow experiment along with the measured data and the Matlab code for displaying the graphs are available at GitHub (Homayoon 2020).
Acknowledgments
The authors are grateful to Prof. Mohammad Javad Abedini for his helpful comments, and also thankful to the support received from Sharif University of Technology.
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Published In
Journal of Hydraulic Engineering
Volume 147 • Issue 2 • February 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Mar 14, 2019
Accepted: Jul 14, 2020
Published online: Nov 22, 2020
Published in print: Feb 1, 2021
Discussion open until: Apr 22, 2021
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