Open channel flow through a linear contraction

In this work we study the open channel flow through a linear contraction. We focus on the flow configuration with a two-dimensional jump in the contraction discussed by Akers and Bokhove [Phys. Fluids 20, 056601 (2008)] and propose a simple quasi-two-dimensional model to assess equilibrium conditions and explore their stability. We show that both bed friction and bed slope contribute to the stability of this flow configuration, which otherwise would be unstable. Results of the theoretical model are compared to both experimental data and the results of numerical simulations, and the comparison confirms the reliability of the proposed model. We also show that channel flow through a linear contraction can experience two different nested hysteretic loops.