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

Shiva Kandpal () and Swaroop Nandan Bora ()
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Shiva Kandpal: Indian Institute of Technology Guwahati
Swaroop Nandan Bora: Indian Institute of Technology Guwahati

Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), 2023, vol. 37, issue 14, No 13, 5655-5676

Abstract: 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.

Keywords: Linearized Saint-Venant equations; Lateral inflow; Response function; Convolution; Hydrograph; Laplace transform (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11269-023-03623-9

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