First, a study is made of time-dependent flow of a viscous fluid driven by an oscillating shrouded disk in finite geometry. Numerical solutions to the Navier-Stokes equations are obtained for the flow in a cylindrical cavity with its upper endwall disk executing torsional oscillation at a velocity Ωcosλt. Details of the three-component velocity field are examined at high Reynolds number. The value of the nondimensional amplitude of disk oscillation, ε=Ω/λ, encompasses a range up to ε≥O(1). The numerical results for the azimuthal flow for ε≪1 are consistent with the predictions of the earlier analytical model. The azimuthal flow is largely confined to the Stokes layer thickness. The analytical predictions of the meridional flow, based on a straightforward expansion technique, display discrepancies from the numerical results. The steady meridional streaming at finite values of ε is exhibited. The qualitative patterns of meridional steady streaming are verified by laboratory flow visualizations. The explicit effect of Re on the overall flow character is scrutinized. The numerical data are processed to describe the behavior of the torque coefficient at the oscillating disk.
Second, an investigation is made of fluid flow and heat transfer characteristics in a vertically-mounted circular cylinder. Motions are generated by the top endwall disk, which oscillates about the central axis with rotation rate Ω=ελcos(λt). The temperature of the top disk is higher than that of the bottom disk, producing a stable stratification of Brunt-Vaisala frequency N. Numerical solutions are acquired to the time-dependent Navier-Stokes equations. Comprehensive velocity and temperature data are obtained, which illustrate salient features of quasi-steady periodic flows. As the stratification increases, the steady meridional streaming is confined to a narrow region close to the top disk. Resonance is identified at particular values of (N/λ), when the system is excited at correct natural frequencies. An elementary inviscid analysis indicates the modes of inertial-gravity oscillations, and the present numerical data are in close agreement with the inviscid results. The amplitudes of fluctuating parts of meridional flow and of Nusselt number display distinctive peaks under resonance conditions. Details of evolutions of fluctuating velocities and temperatures are scrutinized to offer physical explanations for resonance.
Finally, inertial waves in a fluid-filled rotating cylinder, which oscillates about the central axis with rotation rate $ \Omega_c = \Omega + lepsilon \lambda Cos (\lambda t)$, are studied using a numerical method. A time-marching finite volume method of the axisymmetric governing equations is used to obtain the flows and pressure fields. The object of this numerical simulation is to excite axisymmetric inertial oscillations through the pumping action of the oscillatory Ekman boundary layer near the top and bottom disk. Resonances are detected via the amplitude of non-dimensional pressure difference (Cp) and of non-dimensional kinetic energy (Cke) for various ratios of the excitation to the mean rotation frequency (Ω/λ) and are visualized.
