Robin Kung

Time-Dependent Modes of Behavior of Thermally Driven Rotating Fluids

Abstract The characteristics of amplitude vacillation, structural vacillation and geostrophic turbulence in two thermally driven rotating fluids with different viscosities are investigated. The data presented correspond to experiments performed at four points in dimensioniess-parameter space selected to illustrate the nature of these phenomena. They include synoptic temperature distributions, radial cross sections, time- averaged temperature variance spectra, and time and space variations of the eddy temperature variance as a function of wavenumber. Amplitude vacillation is characterized by periodic growth and decay of the temperature variance associated with a single azimuthal wavenumber and its immediate sidebands. Structural vacillation is characterized by almost periodic, modulated, radial redistributions of eddy temperature variance associated with a single azimuthal wavenumber and its higher harmonics, with little variation in the volume integrated eddy temperature variance. Geostrophic turbulence i...

Relationships Among Eddy Fluxes of Heat, Eddy Temperature Variances and Basic-State Temperature Parameters in Thermally Driven Rotating Fluids

Abstract Relationships are examined among radial eddy fluxes of heat, eddy temperature variances and basic-state temperature parameters (e.g., radial gradients and variances of the azimuthally averaged temperature) over a broad range of dimensionless parameters in thermally driven rotating annuli of fluid. We consider, first, changes of the time-averaged eddy heat flux and of the time and azimuthally averaged radial temperature gradient which take place when we conduct experiments at different imposed temperature differences With the rotation rate held fixed, or at different rotation rates with the imposed temperature difference held fixed. It is found that the observed changes of these variables cannot be described by a positive proportionality between the eddy heat flux and some positive power of the radial temperature gradient, except perhaps over limited ranges of dimensionless-parameter space. Within the regular wave regime, not too far from marginal stability, the eddy heat flux increases and the az...

A Study of Baroclinic Wave Behavior over Bottom Topography Using Complex Principal Component Analysis of Experimental Data

Abstract Complex principal component analysis is applied to data from three laboratory experiments of flow over two-wave sinusoidal bottom topography in a thermally driven, rotating annulus of fluid. The experiments are conducted at the same imposed temperature contrast (ΔT) and at three different rotation rates (Ω). In each case, the intensity of the wave activity is maximum downstream of the two topographic ridges. The analysis, however, reveals a fundamental difference in the behavior of the waves at lower rotation rates than at the highest rotation rate. At the lower Ωs, the baroclinic waves travel over the topographic ridges with diminished intensity and amplify on the other side of each ridge, with the result that the flows downstream of the two ridges are coherent. At the largest Ω, at which the Rossby number, Ro, is very small and the friction parameter, r = E½/Ro (where E is proportional to the Ekman number), is rather large, the waves downstream of each ridge are decoupled from those downstream...

Topographically Forced Waves in a Thermally Driven Rotating Annulus of Fluid—Experiment and Linear Theory

Abstract The amplitude and phase of a topographically forced wave in a baroclinic flow are studied both experimentally and theoretically. The experiments were conducted in a thermally driven fluid in a rotating annulus with two-wave bottom topography. Analysis of velocity data at a single level in seven different experiments at the same imposed temperature contrast and successively larger rotation rates (Ω) reveals that the forced wave is displaced upstream from the topography by an amount which increases with increasing Ω. The wave amplitude increases as we progress from low to moderate Ω, beyond Which it becomes smaller. Linear equivalent barotropic and baroclinic theory (the latter incorporating vertical density stratification) give an upstream phase displacement which increases with increasing Ω, in qualitative agreement with the experimental data. The phase lag in the theory is controlled by the “β-effect” (produced by the slope of the free surface) and by Ekman layer dissipation (measured by the rat...

Cyclic Variations of the Imposed Temperature Contrast in a Thermally Driven Rotating Annulus of Fluid

Abstract Rotating annulus experiments are described in which the imposed thermal forcing is varied periodically by means of cyclic variations of the cold inner-bath temperature. In the way of background the results of conventional annulus experiments, in which the imposed temperature contrast is not varied, and of hysteresis experiments, in which the imposed temperature contrast is varied slowly enough to be considered quasi-static, are reviewed. It is found that, in the region of dimensionless-parameter space in which our experiments were conducted, the flow configuration in conventional and hysteresis experiments is determinate in the following sense: once a flow is established at a given point in this region of dimensionless-parameter space, this flow will remain unless a critical value of the imposed parameters is reached for the onset of another state. The flow configuration in experiments in which the imposed temperature contrast is varied in a cyclic fashion is found to be indeterminate in the sens...

Kinematic Properties of Wave Amplitude Vacillation in a Thermally Driven Rotating Fluid

Abstract Empirical evidence is presented to the effect that amplitude vacillation in a thermally driven rotating annulus of fluid is due primarily to the interference of two modes with the same azimuthal wavenumber and different vertical structures and phase speeds. Higher order details of the amplitude vacillation cycle are attributable to one or two additional modes that are generated by the interaction of the primary pair with the mean zonal flow (i.e., wave-mean flow interactions). Wave-wave interactions appear to play a negligible role in accounting for amplitude vacillations observed in laboratory experiments. Sufficient theoretical evidence is available in the published literature to suggest that the two fundamental modes responsible for amplitude vacillation arise through the destabilization of neutral Eady modes by one or more critical layers in the fluid.

Barotropic flow over bottom topography— experiments and nonlinear theory

Abstract Barotropic flow over finite amplitude two-wave bottom topography is investigated both experimentally and theoretically over a broad parameter range. In the experiments, the fluid is contained in a vertically oriented, rotating circular cylindrical annulus. It is forced into motion relative to the annulus by a differentially rotating, rigid, radially sloping lid in contact with the top surface of the fluid. The radial depth variation associated with the slope of the lid, and an equal and opposite slope of the bottom boundary, simulates the effect of the variation of the Coriolis parameter with latitude (β) in planetary atmospheres and in the ocean. The dimensionless parameters which control the fluid behavior are the Rossby number (ϵ), the Ekman number (E), the β parameter, the aspect ratio (δ), the ratio of the mean radius to the gap width (α) and the ratio of the topographic height to the mean fluid depth (η). The Rossby and Ekman numbers are varied over an order of magnitude by conducting experiments at different rotation rates of the annulus. Velocity measurements using photographs of tracer particles suspended in the fluid reveal the existence of a stationary, topographically forced wave superimposed on an azimuthal mean current. With successively larger rotation rates (i.e. lower ϵ and E) the wave amplitude increases and then levels off, the phase displacement of the wave upstream of the topography increases and the azimuthal mean velocity decreases and then levels off. Linear quasigeostophic theory accounts qualitatively, but not quantitatively, for the phase displacement, predicts the wave amplitude poorly and provides no basis for predicting the zonal mean velocity. Accordingly, we have solved the nonlinear, steady-state, quasigeostrophic barotrophic vorticity equation with both Ekman layer and internal dissipation using a spectral colocation method with Fourier representation in the azimuthal direction and Chebyshev polynomial representation in the radial direction. For boundary conditions at the side walls, we specified zero velocity. Side wall boundary layers then appear explicitly in the numerical solution. At the bottom and top of the fluid, we specified that the vertical velocity at the mean height of each boundary is the sum of two components—one forced by Ekman suction in the absence of topography and the other by the condition that there can be no flow normal to the rigid boundary. We justify this choice by the smallness of the Ekman number and of the radial and azimuthal slopes of the topography. We have found that the use of three Fourier components and seven Chebyshev polynomials is sufficient to account qualitatively for the experimental results, although small quantitative discrepancies suggest that further investigation of the neglect of effects originally considered to be small is needed.

A Fluid Experiment of Large-Scale Topography Effect on Baroclinic Wave Flows

The effects of topography on baroclinic wave flows are studied experimentally in a thermally driven rotating annulus of fluid.Fourier analysis and complex principal component (CPC) analysis of the experimental data show that, due to topographic forcing, the flow is bimodal rather than a single mode. Under suitable imposed experimental parameters, near thermal Rossby numberROT =0.1 and Taylor numberTa = 2.2 × 107, the large-scale topography produces low-frequency oscillation in the flow and rather long-lived flow pattern resembling blocking in the atmospheric cir-culation. The ‘blocking’ phenomenon is caused by the resonance of travelling waves and the quasi-stationary waves forced by topography.The large-scale topography transforms wavenumber-homogeneous flows into wavenumber-dispersed flows, and the dispersed flows possess lower wavenumbers.

Velocity and temperature measurement with thermistor anemometers in a thermally stratified rotating fluid

The implementation of a new scheme for a thermistor anemometer for the measurement of both velocity and temperature in a two-dimensional horizontal flow is described. The anemometer is composed of a cluster of four bead thermistors, consisting of a central heater bead and three surrounding sensor beads. Empirical relationships for the dependence of flow direction on sensor/heater spacing, fluid flow speed, and fluid, heater and sensor temperatures are presented which permit in situ calibration of large numbers of thermistor anemometers. Fabrication details, calibration procedures and results of measurements from a large number of anemometers under actual experimental conditions in a thermally stratified, rotating fluid flow are included.

Some Effects of Rotation Rate on Planetary-Scale Wave Flows

A series of experiments were performed in a rotating annulus of fluid to study effects of rotation rate on planetary-scale baroclinic wave flows. The experiments reveal that change in rotation rate of fluid container causes variation in Rossby number and Taylor number in flows and leads to change in flow patterns and in phase and amplitude of quasi-stationary waves. For instance, with increasing rotation rate, amplitude of quasi-stationary waves increases and phase shifts upstream. On the contrary, with decreasing rotation rate, amplitude of quasi-stationary waves decreases and phase shifts downstream. In the case of the earth’s atmosphere, although magnitude of variation in earth’s rotation rate is very small, yet it causes a very big change in zonal velocity component of wind in the atmosphere and of currents in the ocean, and therefore causes a remarkable change in Rossby number and Taylor number determining regimes in planetary-scale geophysical flows. The observation reveals that intensity and geographic location of subtropic anticyclones in both of the Northern and Southern Hemispheres change consistently with the variation in earth’s rotation rate. The results of fluid experiments are consistent, qualitatively, with observed phenomena in the atmospheric circulation.