Applicability of Kinematic Wave Model for Flood Routing under Unsteady Inflow: Fid-Bau Portal

Applicability of Kinematic Wave Model for Flood Routing under Unsteady Inflow

Hanwu Zheng / Er Huang / Ming Luo

This study implemented kinematic wave and dynamic wave approximation of flood routing for a prismatic rectangular channel. The results of the two methods were compared by differences in maximum flow depth, and the applicability of kinematic wave equation was discussed. The influences of hydraulic and geometrical factors on the applicability of kinematic wave equation were considered. It was found that a portion of the numerical results violated existing criteria used to indicate the applicability of kinematic wave equation, particularly when geometrical and hydraulic factors were considered together. This is because the characteristics of upstream inflow were rarely or incompletely considered in these criteria. Therefore, the present study proposed a new criterion. The theoretical influence of all factors was considered using three parameters, namely, ${K F}_{0}^{2}$ , $η_{t s} / T_{0}^{'}$ and $Q_{b o t t o m} / Q_{p e a k}$ ( $K, F_{0}, η_{t s}, T_{0}^{'}, Q_{b o t t o m}$ , and $Q_{p e a k}$ represent the kinematic wave number, Froude number, the time span of discharge exceeding 90% of maximum discharge in hydrograph, wave travel time in the channel, base flow discharge, and peak discharge, respectively, while the subscript 0 represent the value of reference discharge). The influences of these three parameters were illustrated by the momentum equation of one-dimensional Saint-Venant equation. The numerical results showed that the value of $η_{t s} / T_{0}^{'} {(K F_{0}^{2})}^{D}$ could be used to determine the relative error $ξ_{h}$ of kinematic wave equation. In addition, for each $Q_{b o t t o m} / Q_{p e a k}$ the value of $η_{t s} / T_{0}^{'} {({K F}_{0}^{2})}^{D}$ used to depict the same relative error $ξ_{h}$ was different. This new criterion was validated using two real case studies, and it showed a good performance.