Identifying Inertial Modes in a Hide-Titman Flow

Inertial modes are internal wave patterns present within a bounded, rotating fluid being restored by the Coriolis force. Hide and Titman\footnote{``Detached Shear Layers in a Rotating Fluid.'' Journal of Fluid Mechanics 29, pp39-60 (1967).} found that a cylindrical container filled with homogeneous liquid and having a thin disk mounted coaxially inside of it will display non-axisymmetric fluid flow when the differential rotation between the cylinder and the disk exceeds a critical threshold. Their essential geometry and setup were replicated and the fluid flow produced was analyzed to ascertain its relationship, if any, to the inertial modes of a cylinder annulus expressed in analytical form by Zhang, et al.\footnote{``On Inertial Waves in a Rotating Fluid Sphere.'' Journal of Fluid Mechanics 437, pp103-119 (2000).} Experimental data and analyses to correlate observed fluid flows with theoretical inertial modes will be presented.