Time-periodic generalised solitary waves with a hydraulic fall

In an open channel flow, deviations to the lower topography can induce abrupt changes in the wave height, known as hydraulic jumps. This phenomenon occurs when the flow switches from subcritical to supercritical (or vice versa ), and is commonly observed in rivers, flumes and weirs. Theoretical insight is typically sought through the study of reduced models such as the forced Korteweg–de Vries equation, in which previous work has predominantly focused on either stationary formulations or the initial transient behaviour caused by perturbations. In a joint theoretical and numerical study of the free-surface Euler equations, Keeler & Blyth ( J. Fluid Mech. , vol. 993, 2024, A9) have detected a new class of unsteady solutions to this problem. These emerge from an unstable steady solution, and feature large-amplitude time-periodic ripples emitted from a sudden decrease in the water depth forced by topography, known as a hydraulic fall.