Basic two-layer shock-joining theories for internal hydraulic jumps in flows with upstream shear do not have solutions when the shear becomes large. These theories conserve momentum flux and layer volume flow rate across the jump, and conserve energy in either of the two layers to close the set of equations. Alternatively, a closed set of equations conserving vorticity and layer volume flow rate can be used to predict jumps. As shear increases, the physics of the jumps changes, and entrainment becomes important. The theories can be modified to allow entrainment and to indirectly account for continuous velocity profiles, producing solutions where the basic theories failed. These jumps are investigated to illuminate the changing physics as shear increases. Simulations show that the amount of entrainment is related to the square of the upstream shear in both two-dimensional (2D) and three-dimensional (3D) simulations. However, they also show that the two-layer approximation becomes increasingly inaccurate, and 2D and 3D simulations disagree, at very high shear values. Furthermore, super- to super-critical transitions are also possible at higher shear, and while they exhibit a more gradual transition than a hydraulic jump, they can be analyzed using the same framework. The simulation results also illustrate the changing structure, vorticity balance, mixing, and energetic properties of the jumps as the upstream shear increases.

• Received 16 October 2018
• Accepted 22 June 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.074803