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Analytical Solution for Linearized Saint-Venant Equations with a Uniformly Distributed Lateral Inflow in a Finite Rectangular Channel

Author

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  • Shiva Kandpal

    (Indian Institute of Technology Guwahati)

  • Swaroop Nandan Bora

    (Indian Institute of Technology Guwahati)

Abstract

In this work, we find the discharge corresponding to linearized full Saint-Venant equations by considering a uniformly distributed lateral inflow along the channel length for a finite-length rectangular channel. The discharge due to the lateral inflow is presented as the convolution of two functions: the lateral inflow distributed along the channel length and the lateral channel response function. We study the behaviour of the lateral channel response function for different cases of the reference discharge, channel width, Manning roughness coefficient, and bottom slope. This response function gets affected by the presence of the upstream and downstream boundary conditions. We observe the maximum peak of the response function near the midpoint location of the channel. For a given channel width, the choice of reference discharge, Manning roughness and slope of the channel plays a crucial role in the accuracy of the hydrographs. The meaning of semi-infinite channels also seems to vary with the slope of the channel. One of the key observations of this study is that the downstream boundary cannot always be ignored and, for those cases, its influence is clearly observed on the hydrographs plotted upstream.

Suggested Citation

  • Shiva Kandpal & Swaroop Nandan Bora, 2023. "Analytical Solution for Linearized Saint-Venant Equations with a Uniformly Distributed Lateral Inflow in a Finite Rectangular Channel," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(14), pages 5655-5676, November.
    • Handle: RePEc:spr:waterr:v:37:y:2023:i:14:d:10.1007_s11269-023-03623-9
    DOI: 10.1007/s11269-023-03623-9
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    References listed on IDEAS

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    1. Dariusz Gąsiorowski & Romuald Szymkiewicz, 2022. "Inverse Flood Routing Using Simplified Flow Equations," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(11), pages 4115-4135, September.
    2. Payam Sarkhosh & Amgad Salama & Yee-Chung Jin, 2021. "Implicit Finite-Volume Scheme to Solve Coupled Saint-Venant and Darcy–Forchheimer Equations for Modeling Flow Through Porous Structures," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(13), pages 4495-4517, October.
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