Sack Lunch Seminar (SLS)

Internal hydraulic jumps in flows with upstream shear are investigated, motivated by applications such as the flow over sills in Knight Inlet and Hood Canal. The role of upstream shear has not previously been thoroughly investigated, although it is important in many natural flows, including exchange flows and flows over topography. Several two-layer theories are extended to include upstream shear, showing that solutions only exist for a limited range of upstream shear values. More realistic two-dimensional numerical simulations are guided by the two-layer theory predictions, and the results are used to evaluate the theories. The simulations also show the qualitative types of hydraulic transitions that occur, including undular bores, fully turbulent jumps, and conjugate state-like solutions. Numerical simulations are also used to investigate the mixing, and a few 3D numerical simulations are found to be consistent with the 2D results.

When the upstream shear is increased and the basic two-layer theories no longer exhibit solutions, entrainment is required. Furthermore, the downstream structure of the flow has an important effect on the jump properties. These factors are investigated by modifying a two-layer theory to allow entrainment and account for the downstream vertical velocity structure. The resulting theory indicates that entrainment and jump structure become important factors that influence the jump height. However, the results are very sensitive to how the downstream vertical profiles of velocity and density are incorporated into the layered model, highlighting the limitations of the two-layer approximation when the shear is large.

While these two layer theories provide insight into the types of jumps that can occur and the mixing that they cause, jumps such as those that occur in Knight Inlet are significantly influenced by factors such as topography, tidal forcing, and three-dimensional effects.