Journal cover Journal topic
Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
doi:10.5194/hess-2016-364
© Author(s) 2016. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
28 Jul 2016
Review status
This discussion paper has been under review for the journal Hydrology and Earth System Sciences (HESS). The manuscript was not accepted for further review after discussion.
Numerical Solution and Application of Time-Space Fractional Governing Equations of One-Dimensional Unsteady Open Channel Flow Process
Ali Ercan1 and M. Levent Kavvas2 1Research Fellow, J. Amorocho Hydraulics Laboratory, Dept. of Civil and Environmental Engineering, University of California, Davis, CA, 95616, USA
2Professor, J. Amorocho Hydraulics Laboratory, Dept. of Civil and Environmental Engineering, University of California, Davis, CA, 95616, USA
Abstract. Although fractional integration and differentiation have found many applications in various fields of science, such as physics, finance, bioengineering, continuum mechanics and hydrology, their engineering applications, especially in the field of fluid flow processes, are rather limited. In this study, a finite difference numerical approach is proposed to solve the time-space fractional governing equations of one-dimensional unsteady/non-uniform open channel flow process. By numerical simulations, results of the proposed fractional governing equations of the open channel flow process were compared with those of the standard Saint Venant equations. Numerical simulations showed that flow discharge and water depth can exhibit heavier tails in downstream locations as space and time fractional derivative powers decrease from 1. The fractional governing equations under consideration are generalizations of the well-known Saint Venant equations, which are written in the integer differentiation framework. The new governing equations in the fractional order differentiation framework have the capability of modeling nonlocal flow processes both in time and in space by taking the global correlations into consideration. Furthermore, the generalized flow process may shed light into understanding the theory of the anomalous transport processes and observed heavy tailed distributions of particle displacements in transport processes.

Citation: Ercan, A. and Kavvas, M. L.: Numerical Solution and Application of Time-Space Fractional Governing Equations of One-Dimensional Unsteady Open Channel Flow Process, Hydrol. Earth Syst. Sci. Discuss., doi:10.5194/hess-2016-364, 2016.
Ali Ercan and M. Levent Kavvas
Ali Ercan and M. Levent Kavvas

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A finite difference numerical approach is proposed to solve the time-space fractional governing equations of one-dimensional unsteady/non-uniform open channel flow process. Numerical simulations showed that flow discharge and water depth can exhibit heavier tails in downstream locations as space and time fractional derivative powers decrease from 1. The fractional governing equations under consideration are generalizations of the well-known Saint Venant equations.
A finite difference numerical approach is proposed to solve the time-space fractional governing...
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