Weakly undular hydraulic jump: effects of friction

Abstract

The undular hydraulic jump is a transitional flow phenomenon where both streamline curvature and frictional effects are important. In the past, streamline curvature effects were treated with the Boussinesq equations for the potential flow approach, thereby overlooking the real flow features. If friction is included, additional terms appear, because the specific energy variation along the undular jump is related to the boundary shear stress. However, these effects are neither addressed in the literature, nor compared with the classical Boussinesq-type solutions. Also, neither information on how boundary layer methods for adverse pressure gradients behave in undular flows is available, nor experimental data. Herein the frictional effects on the Boussinesq equations are systematically analysed using boundary layer methods for adverse pressure gradients. Based on these results, a new simplified approach is proposed to reasonably reproduce the oscillatory boundary layer characteristics in weakly undular hydraulic jumps under a steadily changing pressure gradient from adverse to favourable, and vice versa.