Taylor Column Research Articles

Gyroscopic effects in a rotating sleeve hydrocyclone

In this short note, we give a simple explanation of a paradox observed in the rotating sleeve hydrocyclones based on the hypothesized existence of a Taylor column. A simple test to verify the existence of such a column is described. The effect of such a column upon the efficiency of the device is described, together with a suggested improvement of the design.

Frictional Taylor columns on the beta-plane

Abstract A one-layer quasi-geostrophic model is used to study Taylor columns on both the f-plane and the β-plane in the inviscid limit of the frictional problem. In this limit, the fluid is stagnant within the Taylor column and the velocity vanishes on its boundary. Ingersoll (1969) found an analytic solution for such a Taylor column for flow over a right circular cylinder on the f-plane. Under more general circumstances, an analytic solution is no longer possible. In this paper, solutions are found numerically by solving an integral equation for the values of the stream function on the boundary of the Taylor column, and then iteratively solving for the shape of the boundary. Ingersoll's solution is first extended by finding the shape of the Taylor column for flow over a cone on the f-plane where the Taylor column has a tear drop shape. Solutions are also found for westward and eastward flow over a cylinder on the β-plane. The Taylor column is approximately elliptical for westward flow with the major axis...

Asymptotic theory of thermal convection in rapidly rotating systems

An asymptotic theory of marginal thermal convection in rotating systems is constructed for the limit of rapid rotation. Many self-gravitating astronomical bodies, including the major planets, the Sun, and the Earth's liquid core, correspond to this limit. In the laboratory, an analogous system can be constructed with a very rapidly rotating apparatus, in which the centrifugal force plays the role of self-gravitation. The formulation is offered in such a way that both these geophysical systems and laboratory analogues are included as special cases. When the inclination of the outer boundaries relative to the equatorial plane is considered weak, the two types of system are identical at leading order. In this limit, the asymptotic analysis is profoundly simplified, because the system satisfies the Taylor-Proudman theorem to leading order. Nevertheless the system contains a very peculiar property: the mode defined by a conventional WKBJ theory implicitly assuming a locality of convection in the radial direction perpendicular to the axis of rotation cannot be accepted as a correct marginal mode, because a modulation equation gives an exponential growth in the radial direction, which contradicts an implicit initial assumption. The erroneous behaviour is traced to a spatial dispersion of thermal Rossby waves, which governs the marginal mode. The difficulty is resolved by extending the analysis to a complex plane of the radial coordinate of the point where convection amplitude attains its maximum. Such a complex radial distance is defined as the point where the wave dispersion disappears locally. The projection of the solution onto the real axis results in an inclination of the Taylor columns with respect to the radial direction. This is in good agreement with the most recent numerical studies. The isolation of convective Taylor columns in the radial direction weakens and the spiralling gets stronger as the Prandtl number decreases, as a result of the need to displace the critical radial distance further from the real axis.

A strong biological response to oceanic flow past Cobb Seamount

We report results of a CTD and chlorphyll a survey from Cobb Seamount, a shallow seamount in the northeast Pacific. Our results show a several-fold increasein the standing crop of chlorophyll a is centred over the seamount. Current meter and drifter data indicate an anticyclonic deflection of deep currents around consistent with a theoretical stratified Tylor cone. Cobb differs from other seamounts where similar phenomena have been reported (O wens and H ogg; 1980, Deep-Sea Research, 27, 1029–1045; Gould et al., 1981, Deep-Sea Research, 28, 409–440; Genin and Boehlert, 1985, Journal of Marine Research, 43, 907–924) in that its summit penetrates well into the euphotic zone. A Taylor column existing at such shallow depths could locally enhance primary production, providing a significant source of energy for higher trophic levels on the seamount. Indirect evidence for such a scenario comes from observations of a high biomass benthic community on Cobb Seamount.

The motion of an inviscid drop in a bounded rotating fluid

The motion of a buoyant inviscid drop rising vertically along the rotation axis of a rapidly rotating low viscosity fluid bounded above and below by rigid horizontal boundaries is considered in the case that the drop is circumscribed by a Taylor column that spans the entire fluid depth. Both the shape and steady rise speed of the drop are deduced as a function of the interfacial tension. The analysis demonstrates that the drop assumes the form of the prolate ellipsoidal figure of revolution which would arise in the absence of any relative motion in the surrounding fluid. The hydrodynamic drag on the drop follows simply from the analysis of Moore and Saffman [J. Fluid Mech. 31, 635 (1968)], who considered the equivalent motion of a rigid particle. The rise speed of a deformed inviscid drop is approximately one-half that of an identically shaped rigid particle; in particular, the rise speed of a spherical inviscid drop is 0.41 that of a rigid sphere.

Almost symmetric solitary eddies in a two-layer ocean

An asymptotic theory of two-dimensional planetary solitary eddies is presented. Previous studies in one-and-a-half layer models have discovered special classes of radially symmetric structure which are associated with eddies of permanent form. We generalize these studies by including an active lower layer and by considering the effects of azimuthal structure. Accordingly, we stress two main results; namely, (i) permanent-form two-layer eddies with essentially arbitrary radial structure exist, provided that the eddy includes a weak imbedded dipolar asymmetry and an appropriate counter-rotating deep flow, and (ii) fluid trapped under an eddy in Taylor columns can significantly affect eddy properties if the trapped fluid possesses non-trivial potential vorticity.The structural permanency in our solutions arises from a balance between nonlinear steepening, driven by the continuity equation, and planetary dispersion. The structural asymmetries affect eddy propagation, either by dipole interaction within the layer (as occurs in modons) or by pressure forces acting between layers. The primary role of the deep counter-rotating flow is to balance the net upper-layer transport. The interesting layer-layer interaction, however, involves higher-order dynamics and is sensitive to the continuity of the potential-vorticity field. In general, these eddies trap fluid both in the upper thermocline and in the lower layer.The dominance of oceanic anticyclones over cyclones is relatively well known. A main conclusion of this study is that the class of long-lived anticyclones is considerably broader than previously realized. This may help explain the observed bias toward anticyclonic eddies. A second conclusion is that estimates of material transport by eddies may need to account for the movement of fluid outside the main bowl of the eddies.

Bottom friction effects in rotating flow past shallow topography

Abstract Homogeneous rotating flow past an obstacle separates from the Taylor column for Rossby numbers, ϵ, larger than E ½, where E is the Ekman number. However, if the vertical scale of the obstacle is of order ϵ, we show here that, for ϵ = O(E ¼), the flow past a short right circular cylinder of height ϵμhis characterized by the values of E, ϵ/E ¼, and also α = μR/h, where his the container depth and Rits radius. Smooth and slightly distorted flow over the cylinder is replaced, for α > 1, by flow including a region of closed streamlines over one side of the cylinder, with vorticity in the eddy determined by the Prandtl-Batchelor Theorem; the eddy size and intensity grows for increasing α. Not only is there anti-cyclonic vorticity over the cylinder, but also small amounts of (mostly) cyclonic vorticity are present in the cylinder wake which exists unless α > 3.5911. That wake vorticity, decaying slowly with small “bottom friction”, contributes significantly to the net circulation in the flow. So, it develops that the far field in such a flow is a superposition of an inviscid vortex and a uniform current for l< α < 3.5911, with the magnitude of the anti-cyclone depending only on the value of α. Thus, two terms in the asymptotic expansion for the vorticity are required to obtain O(1) velocities. Numerical results for O(ϵ°) flow, obtained by integrating the Poisson equation for the streamfunction, are presented for a number of representative cases.

Differential Rotation as an Axisymmetric Resonant Mode of Convection

Recent results from helioseismology (see Goode, these Proceedings) have shown that the inferred contours of the solar angular velocity are more or less radial in the convection region, and the rotation becomes uniform below. These observations contradict the prevailing numerical models of Taylor columns which predict angular velocity contours parallel to the rotation axis of the Sun. Thus, an alternative explanation of solar differential rotation is called for.Presently, it is not feasible to construct a thermally-relaxed, dynamically self-consistent numerical model of the solar convection zone (see Chan and Serizawa, these Proceedings). It is then appropriate to explore simplified models that may shed some light. A number of analytical models have been proposed for the solar differential rotation, and the reader is referred to the book by Rüdiger (1989) for a comprehensive review of this subject. Here, we report on some recent development on the convective resonance model proposed by Chanet al.(1987; hereafter referred as CSM).

Occurrence of anticyclonic eddies on the Prince Edward Plateau (Southern Ocean): effects on phytoplankton biomass and production

Dimensional analysis suggests that mesoscale eddies observed at the Prince Edward Islands (47°S, 38°E) are unlikely to be the result of an island wake vortex shedding process. The analysis shows that appropriate conditions can exist for the formation of closed streamline, anticyclonic eddies (Taylor columns) over the plateau. Hydrographic observations on six surveys in the area show the repeated presence of anticyclonic eddies in the vicinity of the islands. These eddies appear to have some characteristics that are consistent with Taylor column phenomena, but the spatial resolution of the hydrographic data is not sufficient to draw conclusive results. Dense phytoplankton blooms are repeatedly found between the islands. A mechanism explaining these blooms in terms of the stability of the surface mixed layer and the availability of reduced forms of nitrogen is proposed. It is suggested that both water-column stability and available nutrient concentrations are locally enhanced by run-off retained by the eddy field.

Rapid formation of taylor columns: Obstacles against sidewalls

Abstract The problem of topographic forcing by an obstacle against the boundary of a rotating flow is considered in various parameter regimes. The timescale for the motion is the topographic vortex-stretching time, which is inversely proportional to the background rotation rate and the fractional height of the obstacle. For slow flows this time is short compared with the advection time and the governing equation of conservation of potential vorticity is linear. The final state satisfies the non-linear equation for the advection of potential vorticity, however, and so time dependence has given a specific solution to a non-linear problem. The presence of the sidewall causes a stagnant Taylor column to be set up far more rapidly than cases with no sidewall. It is shown that viscosity and mixing arrests the inviscid evolution at some stage, thus some fluid still crosses the obstacle in the steady state. These solutions suggest that experimental results on separation obtained by Griffiths and Linden (1983) can tentatively be ascribed to entrainment and expulsion of fluid through vertical shear layers at the edge of the topography.

Rotating stratified flow past a steep-sided obstacle: incipient separation

Many of the most interesting phenomena observed to occur in the flow of rotating and stratified fluids past obstacles, for example eddy shedding and wake unsteadiness, are due to separation of the boundary layer on the obstacle or its Taylor column. If the Rossby number of the flow lies between E½ and E (E is the Ekman number) and the Burger number is small, the structure of a viscous shear layer of width E⅙ on the circumscribing cylinder of an axisymmetric obstacle controls the inviscid flow. The surface boundary layer is not an Ekman layer, but a Prandtl layer, even at small Rossby numbers. As the slope of the obstacle at its base increases, the nature of the inviscid motion is altered substantially, in the rotation-dominated regime. We show that, for sufficiently large slopes, the flow develops a small region of non-uniqueness external to the column, simultaneously with the separation of the narrow band of fluid flowing round the base of the object.

Current-topography interactions at mid-ocean seamounts and the impact on pelagic ecosystems

Ocean currents impinging on topographic obstacles such as seamounts create a high level of variability in mesoscale physical oceanography. In the N Pacific, for example, the structure of the Kuroshio and its extension differ significantly E and W of the Emperor Seamount chain, and eddy fields detected downstream may be attributed to seamount effects. Nearfield effects of seamounts have been theoretically predicted for several decades but only recently has theory been confirmed by observation. Taylor columns, quasi-stationary eddies over seamounts, alter flow patterns and thus have impacts on both benthos on seamounts and on the biota in water overlying the seamount. SE Hancock Seamount, located at the N end of the Hawaiian Ridge (29°47′N; 179°04′E), has a summit depth of 265 m. This seamount is located near the subtropical front and is at the southerly extent of productive seamounts where trawl fisheries have existed in the past. The pelagic ecosystem in the upper 200 m over the seamount clearly differs from waters at control stations at distances of 10's of kilometers away as shown by plankton and midwater trawl hauls and hydroacoustic transects conducted during 1984 and 1985. Over the seamount, hydroacoustic transects show a significantly higher biomass of scatterers as compared to control stations. Sampling these scattering layers with small midwater trawls demonstrates high densities of a resident micronekton fauna dominated by the sternoptychid fish “Maurolicus muelleri” and the mysid “Gnathophausia longispina”; these taxa were virtually absent from the control stations, were oceanic micronekton, particularly larger forms, were generally in higher abundance than at the seamount stations. Similarly, ichthyoplankton abundance differs above the seamount and at reference stations. In summer sampling, larval fishes were less abundant over the seamount whereas in winter the abundance was greater there. The differences in distribution and abundance of both micronekton and ichthyoplankton are significant and consistently observed, suggesting that physical or biological processes at the seamount have important effects on the pelagic ecosystem. Hypotheses concerning current — topography interactions, exclusion of vertical migrators, and predation by resident micronekton and fishes can be used to explain the observed effects. Seamounts and other areas of complex topography are frequently sites of highly productive ecosystems; the S Emperor and N Hawaiian Ridge seamounts provide a good example, with a catch of approximately one million tons of boarfish in ten years. The interaction of ocean currents and complex topography may play an important role in this high productivity, as demonstrated in the high biomass of lower trophic levels in the seamount ecosystem. Interannual variability in the latitudinal position of the subtropical front and the strength of current flow over these seamounts may result in significant differences in mesoscale physical oceanography and therefore in the productivity of these ecosystems.

Coherent baroclinic eddies on a sloping bottom

A coherent and stable baroclinic eddy in a rotating fluid was produced on a sloping bottom by releasing a dome of salt water into the ambient fresh water. A strong cyclonic vortex is produced above the heavy dome. The entire eddy system moves ‘north-westward’ (with the up-slope direction designated ‘north’) as a ‘Taylor column’. The eddy system displays long lifetimes, but it is shown that a theory of isolated systems cannot account for the experimental observations. Instead, it is demonstrated that the vortex flow above the lens is along the lines of constant depth, producing a net pressure force on the lens, which approximately balances the buoyancy force. When Ekman friction is also included, it accounts for the northward motion of the dome.

Feedback between ice flow, barotropic flow, and baroclinic flow in the presence of bottom topography

Coupling between externally driven barotropic flow and locally driven baroclinic flow in the presence of an ice cover and topography is studied. The topography is a necessary ingredient in this coupling. This study shows that the observed mesoscale activity of the ice edge seen in satellite imagery does not necessarily reflect the mesoscale baroclinic activity in the ocean. Besides oceanic eddies, the ice cover can trace the topographic changes via the coupling to the barotropic flow. A two‐layer ocean model coupled to an ice model is constructed to simulate an ice‐ocean system with a varying bottom topography. In the absence of wind, forcing the ice cover reflects the externally driven barotropic ocean response, especially topographically forced Taylor columns by forming ice streamers or meanders. Some of these features propagate (advected with the ocean currents) as a whole downstream, creating an image of eddy propagation even though there is no baroclinic structure underneath. When downwelling favorable winds (ice on the left from the wind direction) are turned on, in addition to this background barotropic flow, the Ekman flow in the ocean (toward the open ocean) will enhance the meandering of the ice edge due to the barotropic flow. During upwelling favorable winds, the ice edge stays rather compact, including the case when a strong baroclinic, cyclonic vortex is developing beneath an ice meander supported by the Taylor column in the ocean.

Electrophoresis of gas bubbles in a rotating fluid

The electrophoretic velocity of a gas bubble is difficult to measure, since we must also contend with velocities due to buoyancy. One way to avoid this problem is to spin the electrophoretic cell about a horizontal axis. Centrifugal forces keep the bubble on the centreline of the cell. The price to be paid is the creation of Taylor columns which alter the hydrodynamic drag on the bubble. Here we modify two analyses by Moore & Saifman (1968, 1969) to include electrical effects. Motion of the body is assumed to be slow and steady, and the Ekman number small. The electrical double-layer thickness is small compared with the thickness of the Ekman layer. It is assumed that the presence of surfactants makes the gas-water interface rigid, and a no-slip boundary condition is applied. We predict that the electrophoretic velocity U should be proportional to e E ψ 0 ( a ν) −l (ν/Ω) ½ , where E is the applied electric field, e the permittivity of the suspending fluid, ψ 0 the ζ potential at the surface of the bubble, a the bubble radius, ν the fluid viscosity, ν the kinematic viscosity and Ω the rate of rotation. There is reasonable agreement with some, but not all, published experimental results.

Seasonality in currents of the Rockall Channel

SynopsisThough our knowledge of the circulation in this complex region is still incomplete, recent direct current measurements have identified four separate elements of the circulation which appear to undergo a seasonal variation of some sort. These are: (i) a summer-autumn maximum in the deep overflow of Norwegian Sea Deep Water across the Wyville-Thomson Ridge; (ii) an autumn minimum in the upper-ocean circulation around Rockall Bank, ascribed to Taylor Column processes; (iii) an autumn-winter maximum in the strength and breadth of the slope current along the European continental margin; (iv) a winter-spring maximum in eddy kinetic energy in the open waters of the Rockall Channel, and over the full depth range, as a function of windstress and stratification. The first three of these elements are of localised occurrence along the northern, western and eastern margins of the Channel and are described only briefly. The fourth process, encountered at a range of sites in the northeast Atlantic, is described in detail using a total data set of 68 instrument-years of direct current measurements recovered from the Rockall Channel in 1977–84. In the seasonally-varying 3–27 day (d) band of periods, eddy kinetic energies (kE) are shown to be depth-dependent in amplitude, but with little evidence of any significant phase-lag with either depth or location between the individual timeseries of kE estimates. These time-series demonstrate clearly and for the first time that the winterspring peaks in eddy kinetic energy lag the winter peaks in windstress by between 1 and 3 months. This phase-lag is explained as the cumulative result of wind forcing and eddy dissipation.

Dynamics of temperature and chlorophyll structures above a seamount: An oceanic experiment

Three hydrographic surveys comprised of densely spaced XBT and CTD stations were conducted over Minami-kasuga Seamount, in the northwest Pacific (21°36’N, 143O38’E). A cold dome, similar to a Taylor column, was observed above the seamount top during the first survey. Uplifted isotherms penetrated to the lower euphotic zone and were associated with higher chlorophyll concentrations. Vertical displacement of uplifted isotherms decayed with elevation above the seamount, so that both temperature and chlorophyll anomalies were undetectable at depths less than 80 m. Relatively high chlorophyll concentrations in a layer from 80 m to 100 m depth formed a distinctive deep chlorophyll maximum (DCM) which was less well defined away from the seamount. Calculations based on the observed chlorophyll increase and on estimated phytoplankton growth rate suggested a minimal residence time of the cold dome on the order of several days. Zooplankton densities were also higher over the seamount top, both within and above the cold dome. No cold dome, chlorophyll increase, or high zooplankton biomass were detected above the seamount on the second and third surveys, carried out 2 and 17 days later, respectively. Mixing and deflections of isotherms occurred within a “boundary zone” around the seamount slope during the first and third surveys. Our observations suggest that seamounts are a source of both biological and physical patchiness in the surrounding Ocean as features developed above them are swept away. The importance of the seamount-generated “experiment” is discussed in relation to field studies of the DCM. Specifically, our observations suggest that a sharp chlorophyll maximum can be formed by enhanced in situ growth following a sub-surface upwelling event.

Joint Vortices, Eastward Propagating Eddies and Migratory Taylor Columns

The behavior of an isolated pair of vortices consisting of two eddies situated on top of each other in a three-layer ocean is examined analytically. The amplitudes of both eddies are high and, consequently, the two eddies behave as one unit and migrate together in the ocean. For this reason, it is proposed to call the system joint vortices. The eddies are of equal or opposite sign; each vortex is situated in a different layer so that there are two active layers and one passive layer. Attention is focused on the behavior of joint vortices on a sloping bottom in the deep ocean and on a β plane in the upper ocean. That is, we consider deep joint eddies situated on an inclined floor in the lowest two layers of a three-layer ocean and upper joint eddies in the upper two layers. Special attention is given to the cases where one of the vortices is a lens-like eddy. Approximate solutions for slope (or β) induced drifts in the east-west direction are obtained. It is found that because of the high amplitudes and the resulting nonlinear coupling, the joint eddies have a mutual drift which is very different from the drift that each individual vortex would have. For example, while each individual vortex translates to the west in the absence of a conjugate vortex, the combined vortices may drift steadily to the east. This bizarre behavior stems from the presence of a “planetary lift” which is the oceanic equivalent of the side pressure force associated with the so-called Magnus effect. It is directed at 90° to the left of the drifting eddies. Other results of interest are: (i) Under some conditions, the westward drift of joint eddies consisting of two cyclonic vortices it much faster than the long-wave speed. Such fag drift contradict previously held contentions that the speed of cyclonic eddies cannot exceed the long wave speed. (ii) As it translates westward, an anticyclonic lens-like eddy can carry a Taylor column on top of it. Possible application of this theory to various eddies in the ocean is discussed.

Taylor column sidewall drag in a rotating cylinder

A time-dependent analysis is made of the inviscid, incompressible Taylor column generated by the uniform motion of a thin disk of radius a rising slowly along the vertical axis of rotation of a tall, vertical, rotating, liquid-filled right circular cylinder of radius b. It is shown analytically that the effect of the sidewalls of the cylinder on the Taylor column drag on the disk may be neglected if a/b&amp;lt;0.1. Even if a/b∼0.4, the increase in drag above unbounded Taylor column value is less than 10%.

Starting flow for an obstacle moving transversely in a rapidly rotating fluid

The initial-value problem for Taylor columns is considered for the oceanographically relevant case of slow flow over obstacles of small slope, and horizontal scale of order of the fluid depth or larger. In such flows depth variations cause, in the neighbourhood of the obstacle, a gradient of background potential vorticity. Topographic Rossby waves, forced in the starting flow, propagate across the gradient, cycling the obstacle in times of order of the topographic vortex-stretching time h/2Ωh0, where h is the fluid depth, Ω the background rotation rate and h0 the obstacle height. The linear inertialwave equation and the quasigeostrophic equations are related by considering the case where the inertial period is small compared with the topographic time, which is in turn small compared with the advection time.When viscosity is present the waves decay to a steady motion in a time of order of the viscous spin-up time. In inviscid flow the waves do not decay. The flow oscillates about steady, irrotational, zero-circulation flow. The drag and lift on the obstacle oscillate with almost constant frequency and amplitude equal to the Coriolis force on a body of fluid whose volume matches that of the obstacle. Particles above a right cylinder move in closed orbits of diameter 1/S, where S is the topographic parameter introduced by Hide (1961). Particles away from the cylinder move irrotationally, but asymmetrically, from upstream to downstream. A shear layer is present at the boundary of the cylinder throughout the motion. The initial vorticity distribution for flow over a paraboloid is everywhere finite. However, regions of positive and negative vorticity interlace ever more closely during the motion, causing at large time a similar shear layer at the column boundary. By this time the vorticity is increasing without bound above the obstacle and neglected nonlinear, horizontal viscous, or vertical effects are important.