The Authors thank the Discussers for their interest in the abrupt drop hydraulic jump study. The Discussers provided constructive comments on two aspects of this study, namely, the characterization of the bottom roller dynamics, and a design modification for the bottom-drop or negative-stepped stilling basin to improve bottom velocity reduction and hydraulic jump stabilization. [...]@en

In high dam construction projects in China, stilling basin design with an abrupt bottom drop is sometimes introduced to reduce the bottom velocity and pressure loads by generating A-type hydraulic jumps. Although the stilling basin design is not new, A-type hydraulic jumps have not been studied taking into account the air entrainment and evolution of internal air–water flow structures. This paper presents an experimental study of self-aerated A-type jumps in terms of bubble transport and free-surface fluctuations over the bottom drop. Four Froude numbers from 4.1 to 10.3 are tested for three drop heights, in addition to the flat-bottom case. Compared to the classic hydraulic jumps, A-jumps are observed with longer jump lengths and weaker free-surface fluctuations. The downward deflection of the jet-shear flow and formation of a bottom roller in the step cavity require a modification to the analytical expression of velocity and void fraction distributions. The relationship between the bubble diffusivity and jump spreading rate differs from that in classic hydraulic jumps, suggesting a faster expansion of the bubble diffusion layer than the turbulent shear flow downstream of the drop, especially for large drop heights. At large approach velocities, the reattachment of the deflected jet-shear flow to the lowered bed may cause a local rise in bubble counts downstream the bottom roller. Further increase in drop height results in a W-jump with overwhelming bottom roller over the surface roller and an arced surface jet, which is beyond the scope of this study.

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