Department of Mathematics
University of California, Davis
The flow contained in a rotating circular split-cylinder with different associated boundary conditions leads to a variety of instabilities and complex dynamics. The study of a wide range of Direct Numerical Simulations of the three-dimensional Navier–Stokes equations elucidated the flow behavior. In the first configuration presented in detail, there exists a strong background rotation with oscillatory boundary conditions. By imposing a desired range of frequencies, inertial wave beams emanate from the corner and the split of the cylinder, leading to destructive/constructive interactions. The resulting flow produces peaks in vorticity for some specific frequencies which are related to the resonant Kelvin modes. The critical role of the symmetries of the boundary conditions with the different Kelvin modes excited was studied using the phase difference parameter, which easily allows imposing different symmetries. In the second configuration, both cylinder halves are in exact counter-rotation, producing an O(2) symmetry in the system. In the Basic State, the dynamic of the flow is dominated by the shear layer created in the midplane. By changing the speed rotation and the aspect ratio of the cylinder, the flow loses symmetries in a variety of ways creating static waves, rotating waves, direction reversing waves and slow-fast pulsing waves. The bifurcations were characterized and the flow dynamics were clarified. Additionally, preliminary experimental results for this case were performed.