Taylor Column Research Articles

On the structure of a Taylor column driven by a buoyant parcel in an unbounded rotating fluid

The velocity and pressure fields produced in a homogeneous rapidly rotating fluid driven by an isolated buoyant parcel are investigated. Gravity and rotation are allowed to have arbitrary orientations and the parcel shape is assumed Gaussian. Inertial forces and time-dependent effects are ignored. The linear problem is easily solved by three-dimensional Fourier transform, and the inversion is facilitated by assuming the Ekman number, E, to be very small. In this limit the fields form a Taylor column extended in the direction of the rotation axis. In the absence of rigid boundaries no boundary layers occur. The velocity and pressure in the vicinity of the parcel are found in closed form while elsewhere (within the Taylor column) they are expressed in terms of relatively simple scalar integrals which are easily evaluated.Within the buoyant parcel, the momentum balance is baroclinic, involving Coriolis, pressure and buoyancy forces. Outside the parcel, the balance is geostrophic at unit order. The viscous force is important at order E and determines the axial structure of the Taylor column. In contrast to the case of flow driven by a rigid body, no ‘Taylor slug’ of recirculating flow occurs. The velocity and pressure decay algebraically with distance from the parcel, with the scale of variation being a/E in the axial direction and a in the radial direction, where a is the parcel radius. In the vicinity of the parcel, the return flow occurs in a broad region surrounding the parcel. The structure of flow in the vicinity of the parcel is independent of the Ekman number. This return flow sweeps the fringes of the parcel backward, making the net rise speed significantly slower than that of a rigid sphere of identical buoyancy. The return flow also acts to deform the parcel; this deformation is quantified.

Generation of the Solar Subsurface Shear

It is well known that a thin layer of angular velocity shear exists just below the solar surface. We propose that this layer is primarily generated by the radial-meridional component of the Reynolds stress. This Reynolds stress component is created by a characteristic upward-equatorward (or equivalently, downward-poleward) correlation of the turbulence velocity over a region in which the shear layer is embedded. Using 2D and 3D numerical experiments, we illustrate that this correlation is caused by vortices that get sucked down from the surface and turn aligned with the rotation vector (a la Taylor columns).

Small-scale helicity and α -effect in the Earth's core

It is a commonly held belief that the combination of rotation and buoyancy creates a net helicity and electromotive force (EMF), known as an α -effect, and hence, dynamo action. We investigate this possibility for a simple, but dynamically complete, model, consisting of a small, isolated buoyant parcel rising in an infinite extent of rotating electrically conducting Boussinesq fluid in the presence of a large-scale magnetic field. We show that the leading order in the local magnetic Reynolds number, assumed small, is that the total helicity and EMF are identically zero, due to symmetry. This is in effect an anti-dynamo theorem, to be overcome if dynamo action is to occur. The helicity and EMF densities are found to be concentrated in wakes having spatial extent much larger than the scale of the buoyant parcel. The wakes are aligned with rotation if Coriolis force dominates Lorentz (forming a foreshortened Taylor column) and with the magnetic field if Lorentz dominates Coriolis. Consequently, the integrals of helicity and EMF over a half-space on either side of the parcel are non-zero. These distributions have the potential of creating wavelike dynamo action as the buoyant parcel rises through the outer core. In the case that the Coriolis force is dominant and the viscous force is very weak, it is found that the half-space integral of helicity is inversely proportional to the square root of the Ekman number. This is a counterintuitive result, depending on the action of a very weak viscous force at very large distance from the buoyant parcel.

Nonlinear Effects and Vortical Structures in Homogeneous Rotating Turbulence under Stable Density Stratification.

The generation mechanism of the vertical vortices associated with the baroclinic instability and the effects of nonlinear term the vortices are investigated by using both direct numerical simulation(DNS)and rapid distortion theory(RDT). Two kinds of the anisotropic flow fields are used as initial conditions. As a result, the initial anisotropy of Reynolds stresses is found to affect asymmetry of the vertical vortices. In the cases where the initial vertical velocity is set to be zero, the p.d.f.of the vertical vorticity tends to incline toward the anticyclonic side. When the vertical component of initial velocity is larger than the horizontal one, the cyclonic vortices are more enhanced. By comparing DNS and RDT, it is found that in both cases of the intial conditions the enhanced vortices of DNS are stretched in the vertical direction, which is not observed in the RDT results. This should be because the nonlinear vortex-stretching term intensifies and elongates vertical vortices in the vertical direction. The anticyclones are markedly augmented in low Prandtl number fluids, while the cyclones become dominant in the high Prandtl number case. In particular, the flow field becomes almost two-dimensionalized and Taylor columns are formed in the vertical direction in the low Prandtl number case. However, neither two-dimensionalization nor Taylor column is observed in the RDT analysis which neglects the nonlinear terms.

Comments on “On the Utility and Disutility of JEBAR”

where J is the Jacobian operator, c is the transport streamfunction, f and H are the Coriolis parameter and bottom topography, b [ ] f /]y, t is the kinematic surface wind stress vector, and pb is the bottom kinematic pressure. Equation (2) is the more physically appealing form containing the intuitive bottom torque term BT, which, however, renders it unsuitable for direct solution since pb contains the unknown surface elevation. Equations (1a) and (2a) reduce to the Sverdrup balance equation for a flat bottom, whence JEBAR 5 BT 5 0. Cane et al. state: ‘‘As a rule, we expect the flow to try to behave like Taylor columns, arranging itself to go around hills and valleys, avoiding vortex tube shrinking or stretching. Thus, we expect isolines of pb and H to be nearly parallel. If so, we expect the Sverdrup relation [Eq. (2) with BT 5 0] holds.’’ Cane et al. cite the solution to Eq. (1) by Mellor et al. (1982) and Greatbatch et al. (1991) and the implication is that their solutions may be greatly in error since they differ so much from the solution of the Sverdrup relation; therefore, I am moved to disagree. To illustrate and evaluate the possibility of error due to density and topographical measurement errors in solving Eq. (1), Cane et al. invoked a reduced-gravity

Nutrient distributions across the Porcupine Bank

Spring–summer hydrographic transects across the Porcupine Bank, west of Ireland, were made to characterize the nutrient distributions across this shelf edge region. An April transect indicated some surface depletion of nutrients in the region over the Porcupine Bank and across the Irish Shelf front with slightly increased surface values over deeper waters. Above the Porcupine Bank, within a dense dome of cold, relatively less-saline water, higher nutrient values relative to water at the same depth on either side were measured. By May, surface nitrogen was exhausted whilst a small [O(0.1 μM)] amount of phosphate remained indicating a nitrogen-limiting nutrient supply for phytoplankton production. The nitrogen to phosphate ratio was 15. The dome structure over the Porcupine Bank persisted until at least July when the last transect was made and retained relatively high nutrient values. The dome may be a result of a Taylor Column formation with an associated partly-closed circulation pattern around the bank. This suggests a region where reduced shelf–ocean exchange is occurring.

Eddy formation by dense flows on slopes in a rotating fluid

Properties of the flow generated by a continuous source of dense fluid on a slope in a rotating system are investigated with a variety of laboratory experiments. The dense fluid may initially flow down the slope but it turns (under the influence of rotation) to flow along the slope, and initial geostrophic adjustment gives it an anticyclonic velocity profile. Some of the dense fluid drains downslope in a viscous Ekman layer, which may become unstable to growing waves. Provided that the viscous draining is not too strong, cyclonic vortices form periodically in the upper layer and the dense flow breaks up into a series of domes. Three processes may contribute to the formation of these eddies. First, initial downslope flow of the dense current may stretch columns of ambient fluid by the ‘Taylor column’ process (which we term ‘capture’). Secondly, the initial geostrophic adjustment implies lower-layer collapse which may stretch the fluid column, and thirdly, viscous drainage will progressively stretch and spin up a captured water column. Overall this last process may be the most significant, but viscous drainage has contradictory effects, in that it progressively removes dense lower-layer fluid which terminates the process when the layer thickness approaches that of the Ekman layer. The eddies produced propagate along the slope owing to the combined effects of buoyancy–Coriolis balance and ‘beta-gyres’. This removes fluid from the vicinity of the source and causes the cycle to repeat. The vorticity of the upper-layer cyclones increases linearly with Γ=Lα/D (where L is the Rossby deformation radius, α the bottom slope and D the total depth), reaching approximately 2f in the experiments presented here. The frequency at which the eddy/dome structures are produced also increases with Γ, while the speed at which the structures propagate along the slope is reduced by viscous effects. The flow of dense fluid on slopes is a very important part of the global ocean circulation system and the implications of the laboratory experiments for oceanographic flows are discussed.

Taylor columns between concentric spheres

The motion of fluid contained between two concentric spherical surfaces is analysed in the limit of strong rotation appropriate to large scale flows and arbitrary gap width. To do so, the dynamical equations are written in the natural cylindrical co-ordinate system that gives a central role to the axis of rotation. The case of a homogeneous fluid allows us to give a general solution of the inviscid, steady flow when sources and sinks have prescribed boundary distributions. Fluid can cross the equatorial plane without breaking rotational constraints provided the source-sink forcing is antisymmetric. However the cylindrical surface tangent to the inner sphere at the equator is singular and calls for higher order inertial and/or viscous effects. No specific solution is obtained in the stratified case, instead a number of integral constraints along the axis of rotation are derived allowing us to relate the interior motion to the surface forcing distributions. The unsteady low frequency waves with Taylor column-like motions are obtained exactly and we extend the non dispersive limit of classical Rossby wave theory in concentric spheres of arbitrary gap width. In the stratified case, a new mode that has no counterpart in the classical, shallow fluid theory is found at the equator.

The effect of possible Taylor columns on the summer ice retreat in the Chukchi Sea

The Chukchi Sea topography consists of a broad, flat, 50‐m‐deep plain, with two prominent shoals, Herald and Hanna, which have horizontal dimensions of about 100 km and rise to depths of about 30 m. Herald Shoal in particular is a prominent, isolated seamount which, because of the warm water flux in summer through Bering Strait, has a warm 0.1 m s−1 flow incident upon it. Examination of active and passive microwave imagery of the region for 1992–1994 shows that as the general ice cover recedes, the ice remains preferentially over Herald Shoal for 3–4 weeks after the surrounding ice has melted. A scale analysis suggests that the cause of the ice persistence is the formation of a Taylor column over the shoal, which traps cold water and ice above it. A similar trapping of ice occurs over Hanna Shoal and on its eastern slope, but the response is complicated by a very different topography and the northward flow down Barrow Canyon.

Growth model of the inner core coupled with the outer core dynamics and the resulting elastic anisotropy

We present a growth tectonic model of Earth's inner core and the resulting model of the seismic anisotropy. The inner core grows anisotropically if the convection in the outer core is of Taylor column type. The anisotropic growth produces a flow field of the poloidal zonal order 2 type as a result of the isostatic adjustment of the viscous inner core. Crystals in the inner core align themselves under the stress field produced by the flow. We model the anisotropic structure of the inner core, using the theory of Kamb [1959] and elastic constants of Stixrude and Cohen [1995b]. We consider models for both hcp iron and fcc iron, which are the probable crystal structures for the inner core iron according to Stixrude and Cohen [1995a]. We have found that the c axis for hcp iron and [111] direction for fcc iron align in the polar direction. The alignment is consistent with seismic observations, which have revealed that the P wave velocity is faster in the polar direction. Our model predicts that the degree of the alignment decreases near the inner core boundary in accord with recent body wave observations. The radial dependence of the alignment would result from the following three effects: (1) crystals near the surface have not undergone stressed state long enough to acquire anisotropy after precipitation, (2) stress near the surface is different from that in the interior of the inner core due to shear stress free boundary condition, and (3) partially molten structure results in transversely isotropic stress condition near the inner core surface due to compaction. Thus the application of Kamb's theory successfully explains the seismic anisotropy in the inner core provided that the crystals have been subjected under the same stress condition for the timescale of the order of 109 years.

Atmospheric sampling of Supertyphoon Mireille with NASA DC‐8 aircraft on September 27,1991, during PEM‐West A

The DC‐8 mission of September 27, 1991, was designed to sample air flowing into Typhoon Mireille in the boundary layer, air in the upper tropospheric eye region, and air emerging from the typhoon and ahead of the system, also in the upper troposphere. The objective was to find how a typhoon redistributes trace constituents in the West Pacific region and whether any such redistribution is important on the global scale. The boundary layer air (300 m), in a region to the SE of the eye, contained low mixing ratios of the tracer species O3, CO, C2H6, C2H2, C3H8, C6H6 and CS2 but high values of dimethylsulfide (DMS). The eye region relative to the boundary layer, showed somewhat elevated levels of CO, substantially increased levels of O3, CS2 and all nonmethane hydrocarbons (NMHCs), and somewhat reduced levels of DMS. Ahead of the eye, CO and the NMHCs remained unchanged, O3 and CS2 showed a modest decrease, and DMS showed a substantial decrease. There was no evidence from lidar cross sections of ozone for the downward entrainment of stratospheric air into the eye region; these sections show that low ozone values were measured in the troposphere. The DMS data suggest substantial entrainment of boundary layer air into the system, particularly into the eye wall region. Estimates of the DMS sulphur flux between the boundary layer and the free troposphere, based on computations of velocity potential and divergent winds, gave values of about 69 μg S m−2 d−1 averaged over a 17.5° grid square encompassing the typhoon. A few hours after sampling with the DC‐8, Mireille passed over Oki Island, just to the north of Japan, producing surface values of ozone of 5.5 ppbv. These O3 levels are consistent with the low tropospheric values found by lidar and are more typical of equatorial regions. We suggest that the central eye region may act like a Taylor column which has moved poleward from low latitudes. The high‐altitude photochemical environment within Typhoon Mireille was found to be quite active as evidenced by significant levels of measured gas phase H2O2 and CH3OOH and model‐computed levels of OH.

Rotating flow past a sliced cylinder

Depending upon the relative sizes of the parameters of the problem, rotating flow of a vertically confined fluid past an asymmetric object—in this case a circular cylinder with top sliced at an angle—may induce flow inside the Taylor column, driven by the viscous stresses in the column wall. The motion is along the constant-depth contours, which are not closed in such a situation. We show from theoretical considerations that so long as the angle of the slice is bigger than the one-quarter power of the Ekman number, E, such an interior motion in the column does occur. In general, the motion consists of two eddies over the obstacle. A series of case study laboratory experiments is presented in support of the analysis, to show the effect of the slice orientation and magnitude on the flow over such a bump, and to illustrate the nature of the flows which are generated when inertial effects are dominant.

The motion of a rising disk in a rotating axially bounded fluid for large Taylor number

The motion of a disk rising steadily along the axis in a rotating fluid between two infinite plates is considered. In the limit of zero Rossby number and with the disk in the middle position, the boundary value problem based on the linear, viscous equations of motion is reduced to a system of dual-integral equations which renders ‘exact’ solutions for arbitrary values of the Taylor number, Ta, and disk-to-wall distance, H (scaled by the radius of the disk). The investigation is focused on the drag and on the flow field when Ta is large (but finite) for various H. Comparisons with previous asymptotic results for ‘short’ and ‘long’ containers, and with the preceding unbounded-configuration ‘exact’ solution, provide both confirmation and novel insights.In particular, it is shown that the ‘free’ Taylor column on the particle appears for H > 0.08 Ta and attains its fully developed features when H > 0.25 Ta (approximately). The present drag calculations improve the compatibility of the linear theory with Maxworthy's (1968) experiments in short containers, but for the long container the claimed discrepancy with experiments remains unexplained.

On the transition to columnar convection

Convection in a rotating annulus with no-slip sidewalls, stress-free ends, radial gravity, and sideways heating is considered. The transition from fully three-dimensional convection cells to Taylor columns with increasing rotation rate is studied and its dependence on the annulus parameters is established.

Axial drop motion in rotating fluids

A theoretical and experimental investigation of drop motion in rotating fluids is presented. The theory describing the vertical on-axis translation of an axisymmetric rigid body through a rapidly rotating low-viscosity fluid is extended to the case of a buoyant deformable fluid drop of arbitrary viscosity. In the case that inertial and viscous effects are negligible within the bulk external flow, motions are constrained to be two-dimensional in compliance with the Taylor–Proudman theorem, and the rising drop is circumscribed by a Taylor column. Calculations for the drop shape and rise speed decouple, so that theoretical predictions for both are obtained analytically. Drop shapes are set by a balance between centrifugal and interfacial tension forces, and correspond to the family of prolate ellipsoids which would arise in the absence of drop translation. In the case of a drop rising through an unbounded fluid, the Taylor column is dissipated at a distance determined by the outer fluid viscosity, and the rise speed corresponds to that of an identically shaped rigid body. In the case of a drop rising through a sufficiently shallow plane layer of fluid, the Taylor column extends to the boundaries. In such bounded systems, the rise speed depends further on the fluid and drop viscosities, which together prescribe the efficiency of the Ekman transport over the drop and container surfaces.A set of complementary experiments is also presented, which illustrate the effects of drop viscosity on steady drop motion in bounded rotating systems. The experimental results provide qualitative agreement with the theoretical predictions; in particular, the poloidal circulation observed inside low-viscosity drops is consistent with the presence of a double Ekman layer at the interface, and is opposite to that expected to arise in non-rotating systems. The steady rise speeds observed are larger than those predicted theoretically owing to the persistence of finite inertial effects.

The Annular Taylor Column

A study is made of the time evolution of the flow generated by an annulus (a disk with a hole in it) of inner, outer radii a and b (a ≪ b), impulsively set into motion and rising at an infinitesimal Rossby number along the axis of rotation of a uniformly rotating, unbounded mass of inviscid, incompressible fluid. The result is that a Taylor column in the form of an annular cylinder of inner, outer radii a and b, does evolve, with all the properties a Taylor column should possess. As a consequence, possibly the first engineering application of the Taylor column is suggested.

Ocean circulation at and near Cobb Seamount

This paper describes observations of the velocity field over and near Cobb Seamount, a shallow seamount near the bifurcation of the Subarctic Current into the California Current in the northeast Pacific Ocean. The background flow field is examined with surface drifter data acquired as part of the WOCE Surface Velocity Program. The likelihood that a Taylor Cap circulation will be observed at Cobb is then estimated. The actual circulation at Cobb is examined with current meters deployed on three separate visits to the site and surveys of the velocity field carried out using an RDI acoustic Doppler current profiler. The observations indicate that a recirculation around the seamount does exist but not fit well with the theory of formation of a stratified Taylor column. A divergent bottom Ekman layer is also observed, which might have important implications for the trapping and retention of fish larvae near Cobb Seamount.

The motion generated by a slowly rising disk in an unbounded rotating fluid for arbitrary Taylor number

The motion of a disk rising steadily parallel to the axis of rotation in a uniformly rotating unbounded liquid is considered. In the limit of zero Rossby number the linear viscous equations of motion are reduced to a system of dual integral equations which renders an ‘exact’ solution for arbitrary values of the Taylor number, Ta. The investigation is focused on the drag and the flow field. In the limits of small and large Ta the asymptotic results of the present formulation agree with – and extend – previous investigations by different approaches.A particular novel feature, for large Ta, is the contribution of the Ekman-layer flux to the outer motion. New insight into the structure of the Taylor column is gained; in particular, it is shown that the main part of the column is a ‘bubble’ of recirculating fluid, detached from the body and not communicating with the Ekman layer. However, it turns out that the essential discrepancy in drag between experiments (Maxworthy 1970) and previous theories cannot be attributed to the Ekman-layer suction effect.

Observation of oceanic structure around Tosa-Bae southeast of Shikoku

The hydrographic observations in the vicinity of a seamount, the Tosa-Bae, southeast of Shikoku have been carried out two times in summer of 1991 and 1992. The temperature, salinity fields are observed by CTD and velocity fields are measured by ADCP. Results of these observation are presented in this paper. It is shown that salinity maximum water at a depth of 100 m is confined to a southeastern are of the Tosa-Bae, however, salinity minimum water is found in northern side of the Tosa-Bae. This indicates the westward intrusion of less saline water over northern slope. A positive correlation is detected between the estimated Rossby height (fL/N) and the observed height of Taylor Column estimated from the vertical change in the isotherms and isohalines. Almost both heights give smaller value than representative depth of bottom topography of the Tosa-Bae, it is indicated that the topographic effect of the Tosa-Bae is not fully reached to the surface. From the correlations between the vertical difference of geostrophic flow and that of ADCP velocity, ageostrophic flow component is detected.

On the motion of a rigid cylinder in a rotating electrically conducting fluid

The flow structures generated and drag experienced by a rigid cylinder moving in an arbitrary direction through a rotating electrically conducting fluid in the presence of an applied magnetic field are investigated, with he aim of understanding better the nature of the small-scale flow in the core of the Earth which may be responsible for maintaining the geomagnetic field through dynamo action. Three cases are considered in the limit of small Rossby and magnetic Reynolds numbers. In the case of very weak rotation, the possible flow structures consist of a thin Hartmann layer and a long wake extending in the direction of the magnetic field, in which Lorentz and viscous forces balance, but only the long wake plays a dynamical role. The dominant drag force is experienced for motion that cuts magnetic lines of force. Motion of the cylinder parallel to its axis induces a much weaker drag, while that in the direction of the magnetic field induces none to dominant order. The cylinder also experiences weak lateral forces due to the Coriolis effect. In the case of weak rotation, the balance in the long wake is now magnetostrophic: between Lorentz and Coriolis forces. The drag is qualitatively identical to that in the first case, but the drag induced by motion parallel to the axis of the cylinder is increased, though still smaller than that for motions cutting magnetic lines of force. In the case of strong rotation, the flow structures consist of a thin Ekman layer and a foreshortened Taylor column extending in the direction of the rotation axis. In this column, the force balance is again magnetostrophic. Again only the large-scale structure plays a dynamical role. Motion of the cylinder perpendicular to its axis induces a larger drag than does motion parallel to its axis. The cylinder also experiences large lateral Coriolis forces.