Oblique Hydraulic Jumps in Power-Law Fluids: Combined Analytical, Experimental and Numerical Investigation

Hydraulic jumps generated by abrupt channel deviations are well known phenomena in open-channel hydraulics and granular flows, but their behaviour is less understood for non-Newtonian fluids. Many environmental and industrial flows involve fluids with shear-dependent viscosity, such as clay suspensions, drilling muds, mine tailings and food pastes. Here, we examine oblique shocks and hydraulic jumps in shallow, free-surface laminar flows of power-law fluids through a combined analytical, experimental and numerical approach. Building on classical oblique-jump theory, we developed two 1-D analytical formulations, either neglecting the effects of bed slope and wall friction (source terms) or considering them. The predictions are compared with laboratory experiments using Newtonian, shear-thinning and shear-thickening fluids, as well as with 2-D shallow-water simulations and fully three-dimensional CFD computations. For Newtonian and shear-thinning fluids on mild slopes, the analytical 1-D formulation including the source terms accurately reproduces the observed shock front geometry and closely matches the 2D results. For shear thickening fluids on steep slopes, the agreement deteriorates slightly. Moreover, 3D approaches are required to capture curvature and complex wall-bounded velocity structures. These results highlight the influence of fluid rheology, channel geometry and flow conditions in affecting hydraulic shock structures and clarify the limits of simplified depth-averaged models.