Impact of bed slope on a supercritical flow overpassing a forward-facing step non-orthogonal to the flow direction

This study investigates the behavior of a supercritical flow passing over a forward-facing step that is non-orthogonal to the flow direction. We first identify specific flow configurations that may develop across the step. Then, we explore the effects of bed slope, which is neglected in the theoretical analyses, through numerical simulations performed for varying values of step height, a, channel width, B, and bed slope, s. These parameters are demonstrated to critically influence the flow regimes in sloping channels. Specifically, simulations performed at constant sB/a exhibit the same nonlinear effects on flow acceleration, shock wave behavior, and flow field stability. The parameter sB/a emerges as a fundamental dimensionless parameter governing the interplay between vertical and horizontal length scales, the flow configurations, and the transition thresholds. In particular, it strongly influences the transition to choked flow, whose mechanisms are systematically analyzed, while the possible scenarios are identified and their governing conditions discussed.