Variable density bore interaction with block obstacles

Abstract

A horizontally variable density flow model is used to simulate hydraulic bore interactions with idealised urban obstacles. The 2D non-linear shallow water equations are solved using a second-order Monotonic Upstream-centered Schemes for Conservation Laws-Hancock Godunov-type HLLC approximate Riemann scheme. Validation test results are reported for wave propagation over a hump, a constant-density circular dam break and two 1D dam breaks involving different spatial distributions of solute concentration. Detailed parameter studies are then considered for hydraulic bore interactions with single and multiple-square obstacles under subcritical, critical and supercritical flow conditions. In all cases, reflected and diffracted wave patterns are generated immediately after the bore impacts the obstacle(s). Later, the incident bore reconstitutes itself downstream of the obstacle(s). Variable density flows are also considered, with the upstream volumetric concentrations set to values corresponding to water–sediment mixture densities of 1165 and 1495 kg/m³. It is found that the upstream Froude number, gap spacing between obstacles and upstream to downstream density difference influence the strength of the bore–structure interaction, run-up at the front face of the obstacle(s), and subsequent wave–wave interactions.

Keywords:

• urban flooding
• shallow water equations
• Godunov scheme
• Riemann solver
• bores

Acknowledgements

The first named author was supported by an Overseas Research Student (ORS) Award and Clarendon Fund Award. The Scatcherd European Scholarship and Charterhouse European Bursary from the University of Oxford are also appreciated. The second named author would like to acknowledge support from EPSRC Grant No. EP/F020511 as part of the UK Flood Risk Management Research Consortium (FRMRC-II). The authors would also like to thank Professor Paul Taylor of the University of Oxford, Dr Feifei Leighton of Halcrow Group plc and Dr Qiuhua Liang of Newcastle University. The authors are grateful to the anonymous reviewers on whose advice the paper was greatly improved, in particular the description of the hydraulic behaviour of the early stages of a density dam break.