Rotating Annulus Experiments Research Articles

The atmosphere, the annulus and quasi-geostrophic theory

Andy White examines the contribution of Raymond Hide's rotating annulus experiments to meteorological modelling and theory.

Phase space structure and anomalous diffusion in a rotational fluid experiment

The transport of passive scalars is considered in a model of rotating annulus experiments. The system has a chain of vortices and a jet, separated by a stochastic layer. For special values of the control parameters, the boundary of the stochastic layer can contain self-similar structures of islands with regular trajectories. Two such values are identified, with the structure being on the jet boundary and on the vortex boundary, respectively. The transport properties for both cases were studied by high-precision direct numerical integration of the equations of motion. The presence of such structures is found to significantly affect the statistical properties of the trajectories and the transport exponent. The results of the computations are compared with various theoretical models of anomalous diffusion. The particle behavior was found to depend significantly on the time scale, with different theories being applicable on different time intervals. Some regimes do not match any of the existing theories. (c) 2000 American Institute of Physics.

Thermal waves of a nonaxisymmetric flow in a Czochralski-type silicon melt

Thermal waves due to a nonaxisymmetric flow were observed at a Czochralski-type silicon-melt surface with a carbon-dummy crystal. The wave number and pattern transition of the thermal waves were investigated at various crucible rotation rates. The thermal wave number increased as the crucible rotation rate increased and the rotation rate of the thermal wave was lower than the crucible rotation rate. The nonaxisymmetric flow region for the 5″ CZ silicon melt was located at the thermal Rossby numbers of 1–10 2 and was higher than the region obtained for rotating annulus experiments.

Progress in Characterizing the Route to Geostrophic Turbulence and Redesigning Thermally Driven Rotating Annulus Experiments

In this paper we calculate Lyapunov exponents and adapt a diagnostic tool, originally used for another purpose by Lorenz (1969), to characterize the degree and nature of the chaotic behavior observed in a thermally driven rotating fluid annulus at different points in parameter space as a control parameter (the rotation rate) is varied over a significantly wide range. We also report on our initial progress toward making the annulus experiments more relevant to the behavior of baroclinic waves in Earth's atmosphere. Owing to the existence of a background potential vorticity gradient, baroclinic waves in the atmosphere propagate both meridionally and vertically and are not trapped as they are in conventional annulus experiments. Our approach involves the redesign of such experiments through the application of radiational heating from above to provide a background potential vorticity gradient on which baroclinic waves can travel. These experiments are in their earliest stage of design and implementation. If successful, they promise to provide a new paradigm for future experiments with thermally driven rotating fluids.

Methods of Visualization for Observing Directly an Internal Structure of Steady Baroclinic Waves in Rotating Annulus Experiments

Methods of Visualization for Observing Directly an Internal Structure of Steady Baroclinic Waves in Rotating Annulus Experiments

Liquid crystal techniques of visualization in rotating annulus experiments

To the well-known rotating annulus experiments we applied liquid crystal techniques of visualization in order to obtain clear video-pictures of internal flow and temperature in the fluid. Then we developed the idea of simultaneously injecting several types of liquid crystals of different temperature ranges to observe the fluid with a wide temperature range. It was shown that with this idea it was possible to take clear video-pictures throughout the whole interior of the fluid. This revealed that the pattern of the bottom flow does not have the characteristics of the Eady type baroclinic waves. Furthermore, the typcial meridional gradient of temperature of the baroclinic wave was directly observed from isothermal lines appearing in the fluid as colour band lines.

41 回転円筒水槽実験における多液晶可視化法

In the well-known rotating annulus experiments we applied liquid crystal techniques of visualization in order to study the three-dimensional structure of differentially heated rotating fluid. Then we developed an idea of injecting several types of liquid crystal with different temperature ranges simultaneously for observing the fluid having a wide temperature. We call it multiple liquid crystal techniques (MLCT). Furthermore we use an apparatus having double rotating disks, on the small one of which an annular tank is put and on the large one a video-camera is set. In this talk we show, (1) simultaneous observations of surface flow and vertical one in a meridional sheet, (2)simultaneous observations of upper and lower flows in baroclinic wave, and (3) to what extent MLCT is useful for the quantative measurement of temperature in the analysis of zonal velocities of the axially symmetric flow by the wind thermal equation.

セミスペクトルモデルを用いた回転水槽中の流れパターンの遷移に関する数値的研究

Some of the rotating annulus experiments with radial differential heating show stepwise transitions of flow regimes from steady axi-symmetric flow to vacillation via a steady wave regime as the rotation rate increases. The stepwise regime transitions are investigated numerically with a semi-spectral model of a three-dimensional Boussinesq fluid, and the results are interpreted with bifurcation theories. The transition between axi-symmetric flow and a steady wave regime is characterized by hysteresis ; the criterion for the disappearance of an established steady wave differs from the criterion for the onset of the steady wave. The branch of the steady wave solution does not bifurcate from that of the axi-symmetric flow at the point where the axi-symmetric flow becomes unstable. Instead, the steady wave branch has another type of critical point (interpreted as a "limit point" ) at which it disappears. The transition from steady wave to tilted-trough vacillation is interpreted as a Hopf bifurcation ; a periodically fluctuating solution bifurcates from the steady wave branch when the steady wave solution loses its stability.

回転円筒水槽実験における多液晶可視化法

回転円筒水槽実験における多液晶可視化法

4 回転円筒水槽流体の流れと温度分布の液晶による立体的観測

4 回転円筒水槽流体の流れと温度分布の液晶による立体的観測

Finite amplitude, steady Rossby waves and mean flows: Analytical illustrations of the Charney‐Drazin non‐acceleration theorem

AbstractExact steady‐state solutions of the nonlinear quasi‐geostrophic equations are used to illustrate some important repercussions of the Charney—Drazin theorem on the non‐acceleration of zonal mean flows by steady conservative waves. The solutions, which are similar to those discussed by Kuo in 1959, consist of spatially non‐uniform zonal flows and barotropic and baroclinic Rossby waves each having the same three‐dimensional wavenumber; a uniform zonal flow is also allowed. Two examples, both consisting of an internal jet zonal flow, a barotropic Rossby wave and a baroclinic Rossby wave, are considered. The absence of wave/mean interaction in these steady‐state solutions is clearly reflected in the absence of poleward eddy potential vorticity fluxes, but is disguised by the existence of non‐zero poleward eddy heat and zonal momentum fluxes and active Lorenz energy cycles. The solutions thus exhibit the same behaviour as the linearized examples discussed previously by various workers, and emphasize the danger of inferring from incomplete vorticity, energy or heat budget analyses that wave forcing (or maintenance) of Eulerian mean flows by eddy motion is taking place.One of the solutions (which is valid in a laterally open domain) is examined as a possible theoretical model of the steady waves seen in rotating annulus experiments. The spatial variations of the zonal mean flow and the eddy heat and momentum fluxes are in reasonable agreement with the results of a numerical simulation of a steady annulus wave, but the analytical solution is unsatisfactory in some other respects. It is clear that dissipative effects must be represented in any complete theoretical model of these steady waves.

Thermally Driven Flow in a Rotating Spherical Shell: Axisymmetric States

A spherical analogue of the rotating annulus experiments modeling atmospheric motion, in which a liquid is contained between two rigid, corotating and concentric hemispheres upon both of which thermal gradients are imposed, is presently studied by means of numerical models. Temperatures are lower on the inner than on the outer sphere, and decrease towards the pole. Using Navier-Stokes equations which assume symmetry about the polar axis, finite difference numerical models yield steady-state solutions to the equations. Hydrostatic and nonhydrostatic solutions are compared for cylindrical and spherical cases, and it is found in the case of the spherical shell that the differences between hydrostatic and nonhydrostatic solutions are small and largely confined to the regions near the pole and equator. It is suggested that nonhydrostatic effects on the axisymmetric state will not affect the flow's baroclinic stability.

Some Characteristics of the Summer Circulation Over the Qinghai-Xizang (Tibet) Plateau and Its Neighborhood

Horizontal and vertical circulation patterns over the Qinghai-Xizang (Tibet) plateau during summer, derived from meteorological observations, are compared with results from rotating annulus experiments. There are several striking features during the season when the plateau acts as a huge elevated heat source: 1) a heat low dominates the planetary boundary layer over the plateau; 2) this heat low is broken up into several cells, giving rise to shear-line development; 3) surrounding the heat low is an anticyclonic belt; 4) the northern and southern portions of this belt approach each other as one proceeds into the upper troposphere and finally merge into a large anticyclone over the plateau; and 5) significant circulation cells appear in meridional and zonal cross sections, attesting to the strong influence of the plateau on the general circulation of the atmosphere.

The theory ot the index cycle in the general circulation of the atmosphere

Abstract The theory of the index cycle presented here is based on the action of the turbulent Coriolis force. Unlike the ordinary Coriolis force this force does work at a rate equal to the energy exchange between the kinetic energy of the regular motions and that of the turbulent motions. It is shown that in a rotating, differentially-heated fluid the turbulent Coriolis force generates a particular type of instability which we call “gyroturbulent instability”. Gyroturbulent instability is associated with barotropic transfer within the kinetic energy spectrum of a rotating turbulent fluid, and is connected with the conversion of kinetic energy between eddy energy and energy of mean flow as a result of the action of the turbulent Coriolis force. Gyroturbulent instability generates specific oscillations in the general circulation of the atmosphere between the state of high index with weak turbulence and that of low index with strong turbulence (the index cycle). In laboratory rotating annulus experiments, th...

Mars meteorology: Three seasons at the surface

We summarize some meteorological results from Viking for northern summer, autumn and winter. Little Sol‐to‐Sol meteorological change was observed during summer, except for secular pressure change. However, a regular sequence of weather disturbances, interpreted as baroclinic waves, appeared primarily at VL‐2 during autumn and winter. The number of Rossby waves present at a given instant is calculated to be 4 and 6 for these seasons. The extreme regularity and low wave number make these systems closely resemble the baroclinic waves of rotating annulus experiments.

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...

Direct Thermal Verification of Symmetric Baroclinic Instability

Direct temperature measurements are reported for two rotating annulus experiments. One shows the flow pattern interpreted by Stone et al. as a manifestation of symmetric baroclinic (inertial) instability, and the other shows the flow pattern typical of baroclinic waves. The mean value of the Richardson number in the former experiment is found to he 0.62. This value agrees with theoretical expectations for a symmetric haroclinic instability regime and thus verifies the original interpretation of the flow pattern. The mean value of the Richardson number in the baroclinic wave experiment is 83. In the symmetric instability experiment the thermal fields and Richardson number are not steady, but show a cyclic variation.

Thermal instabilities in rapidly rotating systems

Thermal instabilities of a contained fluid are investigated for a fairly general class of problems in which the dynamics are dominated by the effects of rotation. In systems of constant depth in the direction of the axis of rotation the instability develops when the buoyancy forces suffice to overcome the stabilizing effects of thermal conduction and of viscous dissipation in the Ekman boundary layers. Owing to the Taylor–Proudman theorem, a slight gradient in depth exerts a strongly stabilizing influence. The theory is applied to describe the instability of the ‘lower symmetric régime’ in the rotating annulus experiments at high rotation rates. An example of geophysical relevance is the instability of a self-gravitating, internally heated, rotating fluid sphere. The results of the perturbation theory for this problem agree reasonably well with the results of an extension of the analysis by Roberts (1968).

Preliminary Results of Experiments with Symmetric Baroclinic Instabilities

An experiment has been designed to test the predictions of nongeostrophic baroclinic stability theory. The apparatus is similar to the conventional rotating annulus experiments, except that the vertical temperature difference can be controlled as well as the horizontal temperature difference. Therefore, the Richardson number can be decreased by heating the bottom of the annulus relative to the top. The first qualitative observations derived from the experiment are described and are found to agree well with the theory. With no vertical temperature difference applied, the motion consists of a conventional baroclinic instability superimposed on the basic thermal wind. As the fluid is destabilized symmetric instabilities first appear superimposed on the baroclinic instability. As further destabilization occurs the symmetric instabilities completely replace the baroclinic instability, and are themselves subsequently replaced by small-scale, nonsymmetric instabilities.