Space and Time Fractional Governing Equations of Unsteady Overland Flow
Publication: Journal of Hydrologic Engineering
Volume 26, Issue 7
Abstract
Combining fractional continuity and motion equations, the space and time fractional governing equations of unsteady overland flow were derived. The kinematic and diffusion wave approximations were obtained from the space and time fractional continuity and motion equations of the overland flow process. When the fractional powers of space and time derivatives go to 1, the fractional governing equations become the conventional governing equations of unsteady overland flow, and the conventional equations can be obtained as the special cases of the proposed fractional governing equations. Similar to findings of the fractional open channel flow process reported previously, the numerical example herein demonstrated that as the fractional powers of the space and time derivatives decrease from 1, overland flows have longer durations, and both the occurrence time and magnitude of the peak flows decrease. The proposed space and time fractional unsteady overland flow equations may allow modeling anomalous hydrographs by taking into account nonlocality in time and space, and may provide further insights into nonlocal transport in hillslopes reported in the literature.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
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Published In
Journal of Hydrologic Engineering
Volume 26 • Issue 7 • July 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Dec 22, 2020
Accepted: Mar 12, 2021
Published online: May 6, 2021
Published in print: Jul 1, 2021
Discussion open until: Oct 6, 2021
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Cited by
- Ninghu Su, Fengbao Zhang, Anomalous overland flow on hillslopes: A fractional kinematic wave model, its solutions and verification with data from laboratory observations, Journal of Hydrology, 10.1016/j.jhydrol.2021.127202, 604, (127202), (2022).