Viscous Undular Hydraulic Jumps of Moderate Reynolds Number Flows

We report simulations of undular hydraulic jumps occuring in a two-phase flow. Unlike undular bores (in rivers), where the inter- face remains horizontal the low Reynolds hydraulic jumps show linear increase in height of the incoming flow due to viscosity. Consequently, the presence or absence of the undulations depends both on the inlet Froude and Reynolds number unlike bores where a Froude number criterion is traditionally considered sufficient. In our simulations, these undulations display a separated vortex underneath every crest. Despite the strong influence of viscosity, we show that the theory of Benjamin & Lighthill, Proc. Roy. Soc. Ser. A, 19546 remains relevant in understanding the occurrence of these undulations.