An Experimental Study of the Interactions between Ekman Layers and an Annular Vortex

1.0 Introduction 2.0 The 2.1 2.2 2.3 2.4 2.4 Experiment Position Control Velocity Sensors Recording and Analysis Flux Control Rotation Control 3.0 Vibrations of An Annular~Vortex 3.1 An Old Problem 3.2 An Axisymmetric Annular Vortex 3.3 Equations of Motion 3.3.1 Perturbations and Scaling 3.3.2 Complete Equation for the Perturbation Pressure 3.3.3 The Rayliezh Discriminant -3.3.4 Boundary Conditions 3.4 The Normal Inertial Modes of an Annular Column of Fluid 3.4.1 An Approximation of Eigenvalues 3.5 Commentary on Future Work 4.0 Results 4.1 Correspondence of Boundary layer and Core Motion 4.2 Characteristics of the Zonal Waves 4.2.1 Amplitude Spectra 4.2.2 Relation of Rotation Rate and Flux to Observed Frequencies 4.2.3 Correlations of the Fluctuations 4.3 The Mean Motion 4.3.1 The Mean Zonal Profiles 4.3.2 Comparisons with other Experiments 4.3.3 Measurements of Mean Ekman Thickness 4.4 Ekman Layer Transition 5.0 Discussion 5.1 Resume'of Important Results 5.2 Ekman Layer Transition and Positive Vorticity States 5.3 Dissipation of Inertial Waves by Stable Ekman Layers 5.4 The Coupling Mechanisms 5.4.1 Incipient Ekman Instabilities in a Non-Steady Circular Flow 46 5.4.2 The "Vorticity Jump" 50 5.4.3 Inertial Modes and the Observed Frequencies 52 5.5 A Brief Summary 52 6.0 Possible Geophysical Implications 55