The Energetics and Vortex Structure of Seamounts in Stratified, Rotating Flow
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This dissertation is an analytical and numerical investigation into the longstanding hypothesis that seamounts are the ``stirring rods'' of the ocean. Specifically, it has been proposed that the eddy motions generated by the interaction of underwater mountains with ocean currents might play a significant role in the broader field of ocean mixing. The energy associated with vertical mixing in the ocean is of critical importance for climate models. The effect of seamounts, however, must be parameterized in climate models due to finite computational resources. There remain open questions about the magnitude and mechanisms of seamount-induced mixing, which are not currently accounted for in climate models. To address this, as well as other questions, a series of numerical simulations of an idealized seamount interacting with a uniform flow are carried out. The effects of density stratification and the Coriolis force are included in the simulations, and a range of values are considered. This set of simulations spans a broad range of Froude and Rossby numbers that might be encountered in the ocean, and forms the basis for the analysis conducted in this dissertation. The first component to this thesis is tied to the fluid mechanical aspects of the simulations. The problem of rotating, stratified flow past a 3D obstacle is of fundamental interest; the wake structure had never previously been rigorously investigated for this type of flow. A Von K\'arm\'an vortex street is known to be produced, but the 3D structure of the vortices, as well as vertical variations in the Strouhal number, the nondimensional eddy shedding frequency, were unknown. The simulations show that the 3D structure of the vortices is controlled by the Burger number. For a small Burger number, eddies are shed as a vertically-uniform column, with a width defined by the baroclinic deformation radius. The shedding frequency is also vertically-uniform, which results in vortices that appear to locally violate the 2D prediction for the Strouhal number. At large Burger number, the eddies are vertically decoupled. Eddies are shed in accordance with 2D theory based on the local diameter of the mountain. The eddy size is approximately equal to the local seamount diameter, and the shedding frequency is such that the Strouhal number is vertically uniform. The energetic aspects the simulations are then addressed in two parts. In the first part, the rates at which energy was converted between various forms are calculated for each simulation. The energy components of interest were the mean flow kinetic energy, the eddy kinetic energy, the turbulent kinetic energy, the potential energy, and the dissipated energy. Terms to represent each conversion process between these components are derived and computed for each simulation. It is found that the conversion of mean energy to eddy kinetic energy is a dominant term, which can be parameterized using the Burger number. In the second part, the internal waves generated by the seamount are considered. It is shown that the lee waves are much less energetically significant than the unsteady wake for the simulations that are considered. It is shown that pre-existing topographic wave theory is inadequate to model the internal wave energy flux calculated from the simulations. Therefore, existing theories are extended into the strongly-stratified, strongly-rotating, 3D flow regime. The revised internal wave flux model is able to reproduce the structure and energy flux of the internal waves produced in the simulations.
- Mechanical engineering