Oblique shocks in shallow flows of power-law fluids past abrupt channel deviations

Building on classical oblique jump theory, we develop a one-dimensional (1-D) analytical framework that incorporates non-Newtonian rheology to predict the onset of hydraulic jumps, their internal structure and the associated Mach-front geometry. Source terms representing bed slope and wall friction are included, and the resulting formulation is systematically assessed against laboratory experiments, two-dimensional (2-D) shallow water simulations and fully three-dimensional (3-D) computational fluid dynamics. Experiments with Newtonian, shear-thinning and shear-thickening fluids on converging sidewalls demonstrate a good match with the 1-D formulation. For Newtonian and shear-thinning fluids on mild slopes, the 1-D formulation with source terms closely reproduces the measured shock-front geometry and the 2-D simulation results. The analysis shows that upstream flow deceleration governs the reduction of the Mach angle and the resulting curvature. By contrast, in tests with shear-thickening fluids and steeper slopes, gravitational contributions produce detachment and strong front curvature that are not captured by the 1-D model. Comparisons of the transverse front position confirm that 1-D models lose validity when the upstream Froude number decreases sharply along the front. Fully 3-D simulations reveal concave front deformation driven by shear, strong dominance of tangential over normal velocities and flow features absent in depth-averaged models. The results demonstrate that 2-D shallow-water models capture the key dynamics for mild slopes and shear-thinning conditions, while accurate prediction for shear-thickening fluids requires 3-D approaches, motivating future hybrid strategies.