Turbulent Shear Flow in a Rapidly Rotating Spherical Annulus
Turbulent Shear Flow in a Rapidly Rotating Spherical Annulus
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Date
2010
Authors
Zimmerman, Daniel
Advisor
Lathrop, Daniel P
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Abstract
This dissertation presents experimental measurements of torque, wall shear stress, pressure, and velocity in the
boundary-driven turbulent flow of water between concentric, independently rotating spheres, commonly known as spherical Couette flow. The spheres' radius ratio is 0.35, geometrically similar to that of Earth's core. The measurements are performed at unprecedented Reynolds number for this geometry, as high as fifty-six million. The role of rapid overall rotation on the turbulence is investigated. A number of different turbulent flow states are possible, selected by the Rossby number, a dimensionless measure of the differential rotation. In certain ranges of the Rossby number near state borders, bistable co-existence of states is possible. In these ranges the flow undergoes intermittent transitions between neighboring states. At fixed Rossby number, the flow properties vary with Reynolds number in a way similar to that of other turbulent flows. At most parameters investigated, the large scales of the turbulent flow are characterized by system-wide spatial and temporal correlations that co-exist with intense broadband velocity fluctuations. Some of these wave-like motions are identifiable as inertial modes. All waves are consistent with slowly drifting large scale patterns of vorticity, which include Rossby waves and inertial modes as a subset. The observed waves are generally very energetic, and imply significant inhomogeneity in the turbulent flow.
Increasing rapidity of rotation as the Ekman number is lowered intensifies those waves identified as inertial modes with respect to other velocity fluctuations. The turbulent scaling of the torque on inner sphere is a focus of this dissertation. The Rossby-number dependence of the torque is complicated. We normalize the torque at a given Reynolds number in the rotating states by that when the outer sphere is stationary. We find that this normalized quantity can be considered a Rossby-dependent friction factor that expresses the effect of the self-organized flow geometry on the turbulent drag. We predict that this Rossby-dependence will change considerably in different physical geometries, but should be an important quantity in expressing the parameter dependence of other rapidly rotating shear flows.