The breaking and mixing of interfacial waves at a bathymetric ridge [electronic resource]

The interactions between periodic, progressive, two-layer interfacial waves and a Gaussian ridge are investigated through laboratory experiments. In mild wave-ridge interactions, higher harmonic waves can be excited whereas more intense interactions can result in wave breaking and mixing. Higher harmonic waves excited in mild wave-ridge interactions then propagate downstream independently of the primary wave. The amount of energy transferred to higher harmonic frequencies increases with the non-linearity of the main wave over the ridge crest. When the wave non-linearity is increased to the point where breaking occurs over the ridge, harmonic generation can still occur. The length scale of the obstacle relative to the wavelength can also influence the energy transfer, which is consistent with analogous surface wave studies. The upper limit for which harmonic frequencies can be excited is set by the stratification. This wave-topography interaction provides a possible mechanism for transferring energy in the internal wave field to smaller scales. For wave-ridge interactions resulting in wave breaking, length scales of the incident wave and topography are used to parameterize when and how breaking occurs. Qualitative observations suggest both shear and convection play a role in the instability of waves breaking at the ridge. Simultaneous particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) measurements are used to calculate high resolution, 2D velocity and density fields from which the local gradient Richardson number is calculated and the transition to breaking occurred when the minimum Richardson number was between 0.2 and 0.4. In these wave-ridge breaking events, the destabilizing effects of waves steepening in shallow layers may be responsible for breaking at higher gradient Richardson number than for similar waves breaking through shear instability in deep water. Due to the effects of unsteadiness, non-linear shoaling, and flow separation, the canonical limit of stability when the gradient Richardson number is greater than 0.25 is not sufficient to predict the stability of interfacial waves. For wave amplitudes above the initial breaking transition, convective breaking events are also observed. An understanding of the efficiency with which internal waves mix the ocean is of critical importance to modeling ocean dynamics. The overall event efficiency is defined here as the energy converted irreversibly to potential energy as a fraction of the total energy lost in the wave breaking event. Using the tank as a control volume, the distribution of energy into reflected waves, transmitted waves as well as dissipation and irreversible mixing from the breaking event can be determined. Reflection from the ridge varies with the length scale of the wave, but is not impacted by whether or not the waves are breaking. The overall event efficiency is found to be 3-8% , increasing slightly with the incident wave amplitude. Spatial variation in the mixing processes may explain why the overall event efficiency is lower than typical values of around 20% for stratified shear instabilities. Local measurements of velocity and density gradients indicate that the local mixing efficiency may vary significantly for different regions in the flow. While there is significant wave energy dissipated within the lower layer over the ridge, there are essentially no density gradients to mix leading to a very low local mixing efficiency. On the other hand, parameterizations based on the turbulent Reynolds number and Froude number suggest that the local mixing efficiency is 10-17% within the overturning patch at the interface. This variation within mixing processes reinforces the importance of dynamic mixing efficiency parameterizations based local stratified turbulence parameters.

Advisor: Koseff Jeffrey Russell primary advisor. Thesis advisor
Fringer Oliver B. (Oliver Bartlett) advisor. Thesis advisor
Monismith Stephen Gene advisor. Thesis advisor
Troy Cary David advisor. Thesis advisor