Abstracts Category : Other

Internal hydraulic jumps with upstream shear

by Kelly A Ogden

Internal hydraulic jumps in flows with upstream shear are investigated numerically andtheoretically. The role of upstream shear has not previously been thoroughly investigated,although it is important in many oceanographic flows such as exchange flows and stratifiedflow over topography. Several two-layer shock joining theories, characterized by their distributionof dissipation in the jump, are considered and extended to include upstream shear,entrainment, and topography. Theoretical results are also compared to 2D and some 3Dnumerical simulations of the full Navier-Stokes equations, which allow continuous velocityand density distributions.The solution space of idealized jumps with small upstream shear is identified using twolayertheories, which shows that upstream shear allows larger jumps to form and allows jumpsfor a larger range of parameters. Numerical simulations reveal several jump structures thatcan occur in these flows, including an undular bore, a fully turbulent jump, and a smoothfront turbulent jump. At low shear, the 2D mixing efficiency is constant across simulations.As shear increases, the basic two-layer theories no longer provide solutions. Numericalsimulations show that entrainment becomes significant as the shear increases, and addingentrainment and shape parameters to describe the continuous velocity profiles is requiredto accurately describe the simulations using two-layered theory. The entrainment dependson the upstream shear and can be predicted with a modified theory. However, use of thetheory is limited due to its sensitivity to the value of the shape parameters. The 2D mixingefficiency also decreases significantly as shear increases. Finally, more realistic 2D and some3D simulations including topography bridge the gap between the highly idealized simulationsand the very realistic work of others. Simulations with topography show additional jumptypes, including a higher mode jump with a wedge of homogeneous, stagnant fluid similarto a structure seen in Knight Inlet. In all cases, numerical simulations are used to identifytrends in the mixing and jumps structures that can occur in internal hydraulic jumps.