Rotating Fluid Annulus Research Articles

On the structure and stability of the hurricane eyewall

This study examines the structure and related stability of the hurricane eyewall at the mature stage. By treating the hurricane eyewall as a rotating fluid annulus, it is shown that axisymmetric steady-state solutions for the hurricane wind field can be explicitly obtained in the eyewall region. Using the energy method, we show that this class of the steady-state solutions is nonlinearly stable, thus explaining the resilience of the hurricane eyewall structure and intensity at the mature stage as established from previous observational and modelling studies.

Phase synchronization of baroclinic waves in a differentially heated rotating annulus experiment subject to periodic forcing with a variable duty cycle.

A series of laboratory experiments in a thermally driven, rotating fluid annulus are presented that investigate the onset and characteristics of phase synchronization and frequency entrainment between the intrinsic, chaotic, oscillatory amplitude modulation of travelling baroclinic waves and a periodic modulation of the (axisymmetric) thermal boundary conditions, subject to time-dependent coupling. The time-dependence is in the form of a prescribed duty cycle in which the periodic forcing of the boundary conditions is applied for only a fraction δ of each oscillation. For the rest of the oscillation, the boundary conditions are held fixed. Two profiles of forcing were investigated that capture different parts of the sinusoidal variation and δ was varied over the range 0.1≤δ≤1. Reducing δ was found to act in a similar way to a reduction in a constant coupling coefficient in reducing the width of the interval in forcing frequency or period over which complete synchronization was observed (the "Arnol'd tongue") with respect to the detuning, although for the strongest pulse-like forcing profile some degree of synchronization was discernible even at δ=0.1. Complete phase synchronization was obtained within the Arnol'd tongue itself, although the strength of the amplitude modulation of the baroclinic wave was not significantly affected. These experiments demonstrate a possible mechanism for intraseasonal and/or interannual "teleconnections" within the climate system of the Earth and other planets that does not rely on Rossby wave propagation across the planet along great circles.

On the Hydromagnetic Stability of a Rotating Fluid Annulus

The linear stability of a rotating fluid in the annulus between two concentric cylinders is investigated in the presence of a magnetic field which is azimuthal as well as in axial direction. Several results of MHD stability have been derived by using the inner product method. It is shown that when the swirl velocity component is large, the hydromagnetic effects become small compared with those due to swirl. The presence of a velocity field and imposed magnetic field will lead to the basic state to more stability. Keywords: Hydromagnetic Stability; Rotating Fluid. © 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v2i2.3945 J. Sci. Res. 2 (2), 250-256 (2010)

Synchronization of modulated traveling baroclinic waves in a periodically forced, rotating fluid annulus

Frequency entrainment and nonlinear synchronization are commonly observed between simple oscillatory systems, but their occurrence and behavior in continuum fluid systems are much less well understood. Motivated by possible applications to geophysical fluid systems, such as in atmospheric circulation and climate dynamics, we have carried out an experimental study of the interaction of fully developed baroclinic instability in a differentially heated, rotating fluid annulus with an externally imposed periodic modulation of the thermal boundary conditions. In quasiperiodic and chaotic amplitude-modulated traveling wave regimes, the results demonstrate a strong interaction between the natural periodic modulation of the wave amplitude and the externally imposed forcing. This leads to partial or complete phase synchronization. Synchronization effects were observed even with very weak amplitudes of forcing, and were found with both 1:1 and 1:2 frequency ratios between forcing and natural oscillations.

Experiments to study the beta-effect in atmospheric dynamics

In atmospheric dynamics, it is well known that the beta-effect, namely, the variation of Coriolis force with latitude causes the mid-latitude large-scale tropospheric waves such as the westerlies to propagate vertically into the stratosphere. Although this has been well proved in the theoretical works and atmospheric observations, to test this also in a laboratory we demonstrate here rotating fluid annulus experiments setting a conical bottom in a tank to create an equivalent beta-effect. Three clear evidences of the beta-effect were observed in the wavenumber-2 flow: the wave flow propagated vertically, its critical level rose, and its drift velocity reduced. Then the quasi-geostrophic potential vorticity equation succeeded in describing this phenomenon below a height slightly lower than the critical level, but failed near that level.

Experiments to study interactions between baroclinic lower flows and a stably stratified upper layer

Experiments were conducted on a rotating fluid annulus to study the basic interactions between baroclinic lower flows and a stably stratified upper layer. Sufficiently stable stratification is necessary for steady flows to emerge in the lower layer. Upward fluid motions make the baroclinic flows permeate into the upper layer. The stable stratification, however, suppresses upward motions so that zonal fluid velocities decrease with height. In fact, their maximum appears at the top level of the baroclinic lower layer and the sign of the radial temperature gradient changes there; namely, it is warmer on the inner side of the annulus in the upper layer. This temperature profile is reflected in a meridional fluid circulation mixing both layers. In the upper layer of the wave flow, there exists a critical level below and above which the zonal fluid velocities have opposite directions for the wave to have a phase shift of half a wavelength in appearance. The experimental results correspond to real atmospheric phenomena.

An Experimental Study of Wave Dispersion in a Differentially Heated Rotating Fluid Annulus with a Radially Sloping Bottom

Baroclinic waves in a rotating fluid annulus with a downward sloping bottom in the radial direction and with a free upper surface have been studied experimentally. Dispersive wave flows due to the effect of the depth variation (the topographic β-effect) have been observed and analyzed with special attention to the interactions among the wave components. The internal structure, the upper transition, the drift angular speed and the radial heat transport, are compared with those in our previous experiments with a horizontal bottom. The similarity between the wave packet formed in the dispersive wave flow, and the wave packets in the mid- and upper troposphere, is also mentioned.

Meridional Flow Field of Axisymmetric Flows in a Rotating Annulus

Abstract Measurements of the flow field were made of the axisymmetric flow in a differentially heated rotating fluid annulus by using a long-term tracking of a tracer particle. Its meridional flow profile is composed of a flow circulating in a large direct (Hadley) cell, which consists of thin boundary and top horizontal layers, and another one in the interior of that cell. Our measurements show that little mixing of the flow between the Hadley cell and the interior occurs and two secondary cells exist in the interior. These cells cause a trajectory of the tracer particle to be chaotic, where the particle follows the main cyclic route but is occasionally trapped in the secondary cells for indefinite times. Very close to the transition to the wave regime, a mixed structure appears consisting of both the axisymmetric and the wave flows in the meridional flow field: an unsteady wave flow occurs in the interior of the Hadley cell.

Thermal convection in a rotating fluid annulus blocked by a radial barrier

There have been extensive previous laboratory studies of thermal convection in a vertical cylindrical annulus of fluid that rotates about its axis with angular velocity Ω (say) with respect to an inertial frame and is subject to an axisymmetric horizontal temperature gradient, as well as associated theoretical and numerical work. The relative flow produced by concomitant buoyancy forces is strongly influenced by Coriolis forces, which give rise to azimuthal circulations and promote, through the process of “baroclinic instàbility”, regimes of non-axisymmetric sloping convection which can be spatially and temporally regular or irregular (“chaotic geostrophic turbulence”). It is also known from previous work that such flows are changed dramatically by the presence of a thin rigid impermeable radial barrier blocking the cross-section of the annulus, and capable of supporting a net azimuthal pressure gradient and associated net azimuthal temperature gradient within the fluid. The presence of the barrier can thus render convective heat transport across the fluid annulus (as measured by the Nusselt number, Nu) virtually independent of Ω (as measured by the so-called Ekman or Taylor number) and dependent only on the Grashof number, G. The present study reports further systematic determinations of heat transport and of velocity and temperature fields in the presence of a radial barrier, with emphasis on the Ω-dependence of the crucially-important net azimuthal temperature gradient supported by the barrier and the physical interpretation of that dependence.

On the effects of rotation on fluid motions in cylindrical containers of various shapes and topological characteristics

Abstract Previous theoretical and laboratory studies of mechanically driven fluids in general rotation relative to an inertial frame have shown that there is a special class of flows for which the (Eulerian) flow field u ( r , t ) relative to the rotating frame of reference is unaffected by gyroscopic (Coriolis) forces, and therefore remains the same for all values of the rotation vector Ω . (Here t denotes time and r the position of a general point R in a reference frame attached to the rotating apparatus.) Such flows occur when (a) Ω is independent of time t ; (b) u ( r , t ) is independent of the coordinate z (say) parallel to Ω , (c) the fluid has constant density and is therefore ‘barotropic’ (i.e. no density variations on horizontal surfaces) and (d) the topology of the cross-section of the (cylindrical) container, in planes z = constant, is such that the bounding surfaces can support the concomitant field of (kinematic) pressure P 1 satisfying ▿ P 1 + 2 Ω × u = 0 Condition (d) is equivalent to the requirement that any fluid sources or siks within the system be multipole in character, but not monopole. In the present study the ‘baroclinic’ case is treated, where buoyancy forces due to the action of gravity (and centripetal forces) on horizontal density variations have to be taken into account. These include investigations of flows due entirely to buoyancy forces, such as thermal convection in fluids in rotating cylindrical containers of various shapes and topological characteristics subject to horizontal temperature gradients. The implications for the impressed temperature field of the mathematical requirements that the fields of kinematic pressure P 1 and density ϱ ϑ (where ϱ denotes the mean density) be everywhere single-valued are guiding such investigations and facilitating the interpretation of their findings. The investigations include laboratory studies, reported elsewhere, of convection in a rotating fluid annulus with a circular cross-section blocked by a radial barrier, where it is found inter alia that advective heat transfer is virtually independent of | Ω | over a wide range of conditions. They also include (as yet unpublished) studies of thermal convection in rotating systems with topologically triply connected cross-sections which can be rendered doubly or simply connected by the insertation of suitable barriers.

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.

Experimental Observations of Internal Vortex Structures in Steady Baroclinic Waves

Abstract The basic structures of steady baroclinic waves observed in a differentially heated rotating-fluid annulus are well known to be composed of high and low pressure vortices, upper (eastward) and lower (westward) jet streams meandering through the vortices, and boundary layers. In order to find the structure of the vortices, the authors have conducted a series of experiments on a rotating-fluid annulus by injecting a few drops of red ink (and/or uranine solution) into a vortex or a jet and observing the results in the corotating reference frame of the wave that drifted eastward (counterclockwise) relative to the rotating annulus. The observed 3D ink patterns appearing in the fluid revealed the inner regions of the vortices. Their structures are composed of a core and a transition zone (separatrix layer). The core is a rather well-isolated region around the axis of the vortex and is split into separate upper and lower layers. The transition zone is a thin layer next to the core and the fluid is frequ...

A laboratory study of baroclinic waves and turbulence in an internally heated rotating fluid annulus with sloping endwalls

New laboratory experiments have been performed in a rotating fluid annulus, subject to internal heating and sidewall cooling, in which a radial depth gradient has been created by the inclusion of oppositely sloping boundaries. Endwall configurations that cause the fluid depth (D) to increase with radius (∂D/∂r>0) and to decrease with radius (∂D/∂r<0) have been studied, as the former is applicable to the terrestrial atmosphere and oceans, while the latter may be relevant to deep atmospheres such as those of the giant planets.Even with the steepest boundary slopes, isolated or periodic chains of stable coherent eddies are observed with both endwall configurations, and these regular eddy modes are seen to drift relative to the walls of the convection chamber concordant with simple Rossby wave ideas. When the boundary slope (δ) is small, no difference is observed in the range of azimuthal wavenumbers seen in the regular wave regimes of the two endwall configurations. At larger values of δ, however, this symmetry is lost, since regular modes m=2 to 8 are observed with ∂D/∂r>0 endwalls, while only a large vertically trapped anticyclonic gyre is seen with ∂D/∂r<0 endwalls. The other effects of the radial depth gradient are the observed reduction in both the lateral and vertical scale of the eddy features, and the formation of two independent trains of eddies within the gap width at sufficiently high rotation rates in the ∂D/∂r>0 endwall experiments. The zonal mean flow is also found to develop a significant barotropic component, superimposed on the vertically and horizontally sheared zonal jets generated by the non-monotonic thermal gradient of the experiment. This barotropic component is predominantly prograde (retrograde) in the ∂D/∂r>0 (∂D/∂r<0) endwall experiments, and confined close to the outer (inner) wall where the fluid depth is greatest.There is evidence of the formation of increased numbers of zonal jets in the ∂D/∂r>0 endwall experiments above that expected from the form of the thermal forcing. These multiple zonal jets are highly localized in the vertical, and are trapped close to the top boundary. Their radial scale is, nevertheless, close to that given by the Rhines argument. No comparable increase in the radial wavenumber of the mean flow is observed in the ∂D/∂r<0 endwall experiments in the present system.

定常傾圧波動における3次元ラグランジュ運動の実験的観測

Chaotic Lagrangian motion in a steady baroclinic wave, which is highly relevant to meteorological and oceanographical problems, was investigated by Sugata and Yoden (1994) by tracing a marked fluid particle for a long time in a numerical solution of their model. To test their result, we have conducted experiments on steady baroclinic waves in a differentially-heated rotating fluid annulus by tracking a 3-D trajectory of one neutrally buoyant tracer particle suspended in the fluid for a long time. We show here four trajectories that have been analyzed up to now. In the wavenumber-5 wave, the observed trajectories include the preferred routes of region transitions expected from the numerical investigation. This supports the Lagrangian view of the heat transport presented by Sugata and Yoden: The jet absorbs a large number of hot fluid particles from the outer boundary layer and releases them in the inner boundary layer, while the fluid particles nearly conserve their temperature in the meandering jet. Furthermore, it is of great interest that there was found one event of region transtion which does not take place in the numerical simulation. In the wavenumber-4 wave, however, the tracer particle was observed to remain trapped within the jet for a long time. This leads to the orthodox view of the heat transport: The jet absorbs a large amount of heat from the outer boundary and releases it into the inner boundary so that heating and cooling of the fluid particles take place during every cycle of the meander of the jet.

B208 回転円筒水槽実験における定常傾圧波の渦の構造の観測

The basic structure of steady baroclinic waves observed in a differentially-heated rotating-fluid annulus is well known to be composed of high- and low-pressure vortices, upper (eastward) and lower (westward) jet-streams meandering through the vortices, and boundary layers. In order to find the structure of the vortices, we have conducted a series of experiments on a rotating-fluid annulus by injecting a few drops of red ink (and/or uranine solution) into a vortex or a jet and observing the results in the co-rotating reference frame of the wave which drifted eastward (counter-clockwise) relative to the rotating annulus. The observed 3-D ink patterns appearing in the fluid revealed the inner region of the vortices. Their structures are composed of a core and a transition zone (separatrix layer). The core is a rather well isolated region around the axis of a vortex and is split into separate upper and lower layers. The transition zone is a thin layer next to the core and the fluid. is frequently transported to and from its outside, but rarely to the core. Then a weak downwelling caused by the Ekman pumping was observed in the upper layer of the core in the high-pressure vortex and similarly a weak upwelling in the lower layer of the core in the low-pressure vortex. In addition, the present experiments were found to yield some results which are similar to those determined in the numerical simulations of Sugata and Yoden (1994) which followed the Lagrangian motion of a fluid particle in the annulus.

定常傾圧波動のラグランジュ運動を調べる実験

The basic structure of steady baroclinic waves observed in a differentially-heated rotating-fluid annulus is found to be composed of high- and low-pressure vortices, upper-level (eastward) and lower-level (westward) jet-streams meandering through the vortices, and boundary layers. On the basis of this structure, recently, Sugata and Yoden (1994) numerically studied the Lagrangian motion of a fluid particle in the annulus. Stimulated by their results, we conducted experiments on a rotating-fluid annulus by injecting drops of red ink into a jet or a vortex and observing the results in the co-rotating frame of the drifting wave. The observed 3-D ink patterns appearing in the fluid revealed the inner region of the vortices. That is, their structures are composed of a core region, which is rather well isolated and split into separate upper and lower layers, and next to the core a transition zone where fluid particles are frequently transported to and from its outside, but rarely to the core region. Several interesting phenomena observed in the annulus are also presented, such as one suggestive of the Ekman pumping found in the low-pressure vortex

A Multiple Liquid Crystal Technique of Visualization for Quantitative Measurements of a Temperature Field in Fluid.

A liquid crystal technique of visualization has been known to be suitable for qualitative, simultaneous observations of temperature and velocity fields in fluid. Here we tried to make it useful also for quantitative measurements of the temperature field by the use of a multiple liquid crystal technique (MLCT) in which we mix the test water with several types of liquid crystals with different narrow thermally active ranges. In order to see how useful MLCT is, we applied it to the rotating fluid annulus experiments and found that MLCT could afford enough number of isothermal lines in the fluid for proving experimentally the well-known thermal wind equation.

A NUMERICAL INVESTIGATION OF THE FLOW IN A FULLY BLOCKED DIFFERENTIALLY HEATED ROTATING FLUID ANNULUS

A computational model has been used to determine the terms in the dynamical equations which are responsible for the formation of a certain horizontal circulation seen in a simply connected, differentially heated rotating fluid annulus. Experiments with a differentially heated rotating fluid annulus that is fully blocked by a thin, rigid, vertical radial barrier at rotation rates of up to 5 rad.sec−1 and with an externally applied radial temperature difference of 4 or 10 °C show two principal circulations. This paper is concerned with the mechanism for one of those circulations, which occurs in a horizontal plane. Computer modelling shows that this circulation is caused by small radial temperature gradients in the fluid, rather than centrifugal effects.

回転水槽実験で観測されるアンプリチュード・バシレーションの数値シミュレーション

回転水槽実験で観測されるアンプリチュード・バシレーションの数値シミュレーション

回転水槽中に生じるティルティッド・トラフ・バシレーションの特性

回転水槽中に生じるティルティッド・トラフ・バシレーションの特性