Hydraulic jumps: flow patterns, control mechanisms, and theoretical insights

ABSTRACT Schematic graphical abstract summarizing classical and forced hydraulic jumps downstream of hydraulic structures. The figure illustrates the effects of appurtenances, rough beds, negative steps, and channel expansions on hydraulic jump behavior, including transitions between repelled, spatial, and transitional jump types. Key hydraulic characteristics such as energy dissipation, jump stability, sequent depth reduction, and cavitation risk are qualitatively compared under different flow and channel modification conditions. Hydraulic jumps are key mechanisms for energy dissipation downstream of hydraulic structures; however, a coherent review that integrates geometric controls, operational trade-offs, and design implications is still lacking. This paper presents a comprehensive synthesis of hydraulic jump behavior, covering classical jumps as well as complex forced jumps generated by appurtenances such as sills and weirs, bed modifications including drops, channel expansions, and roughness, and combinations of these measures. Particular emphasis is placed on hydraulic jumps in expanding channels, where repelled, spatial, and transitional jump types develop and evolve in relation to the sequent depth ratio and flow stability. The main contribution of this review lies in a critical synthesis of both foundational and recent studies, culminating in a qualitative comparison table that clarifies the trade-offs among key design objectives, including reduction of jump length, control of sequent depth, jump stability, energy dissipation efficiency, and cavitation risk. Fundamental theoretical concepts, such as Bélanger's sequent depth relationship, pressure distributions on step faces, and empirical expressions for jump length and energy loss, are discussed to connect theory with engineering practice. By integrating flow patterns, control strategies, and theoretical insights, this study provides practical guidance for the design of efficient and stable stilling basins, with the aim of enhancing energy dissipation while limiting scour and structural risks under variable flow conditions.