Research
Gap Leaping Western Boundary Currents: (Advisor Dr. Vitalii Sheremet) Investigation is preformed on a one meter rotating table, imaged with a particle image velocimetry system (PIV). The system exhibits two main states, one in which the current leaps the gap and one in which the boundary current penetrates into the gap forming a loop current. Hysteresis and multiple steady states have been identified in the system. When a two-parameter space of table rotation rate and strength of the current is considered a cusp catastrophe is identified which explains the above phenomena. These results are for the single layer case. The two layer case is currently being investigated, with preliminary results indicating the continued presence of a cusp catastrophe. Along with this project, I intend to identify invariant manifold in the flow when the system is in the leaping state. This will allow calculation of chaotic mixing through the gap, even though time averaged stream line show a closed basin (Note time averages stream lines are not a barrier to transport!!!). This project is most applicable to the Luzon Strait between Luzon and Taiwan, and my also be applicable to the Gulf of Mexico.
Invariant Manifold Detection: (Advisor Dr. David Chelidze) A new method for the detection of invariant manifolds is explored using the concept of phase space warping. This work also considers methods of invariant manifold detection when only trajectory data is available. Several existing methods are modified for use on trajectory only data. This project is primarily concerned with vibration data, thus numerical investigation of the damped driven Duffing's Equation is considered.
