Fractional Governing Equations of Diffusion Wave and Kinematic Wave Open-Channel Flow in Fractional Time-Space. I. Development of the Equations

Date

2015-09-01

Author

Kavvas, M. L.
Ercan, Ali

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In this study the fractional governing equations for diffusion wave and kinematic wave approximations to unsteady open-channel flow in prismatic channels in fractional time-space were developed. The governing fractional equations were developed from the mass and motion conservation equations in order to provide a physical basis to these equations. A fractional form of the resistance formula for open-channel flow was also developed. Detailed dimensional analyses of the derived equations were then performed in order to ensure dimensional consistency of the derivations. It is shown that these fractional equations of unsteady open-channel flow are fundamentally nonlocal in terms of nonlocal fluxes. The derived fractional governing equations of diffusion wave and kinematic wave open-channel flow can accommodate both the long-memory nonlocal behavior of open-channel flow as well as its local, finite memory behavior, as is numerically demonstrated in the accompanying paper by the authors. (C) 2014 American Society of Civil Engineers.

Subject Keywords

Unsteady open channel flow, Fractional diffusion wave, Fractional kinematic wave, DISPERSION MODEL, HURST PHENOMENON, ADVECTION

URI

https://hdl.handle.net/11511/100102

Journal

JOURNAL OF HYDROLOGIC ENGINEERING

DOI

https://doi.org/10.1061/(asce)he.1943-5584.0001136

Collections

Department of Civil Engineering, Article

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Citation Formats

M. L. Kavvas and A. Ercan, “Fractional Governing Equations of Diffusion Wave and Kinematic Wave Open-Channel Flow in Fractional Time-Space. I. Development of the Equations,” JOURNAL OF HYDROLOGIC ENGINEERING, vol. 20, no. 9, pp. 0–0, 2015, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/100102.