Vertical Flow in the Southern Ocean Estimated from Individual Moorings

This study demonstrates that oceanic vertical velocities can be estimated from individual mooring measurements, even for nonstationary flow. This result is obtained under three assumptions: (i) weak diffusion (Péclet number ≫ 1), (ii) weak friction (Reynolds number ≫ 1), and (iii) small inertial terms (Rossby number ≪ 1). The theoretical framework is applied to a set of four moorings located in the Southern Ocean. For this site, the diagnosed vertical velocities are highly variable in time, their standard deviation being one to two orders of magnitude greater than their mean. The time-averaged vertical velocities are demonstrated to be largely induced by geostrophic flow and can be estimated from the time-averaged density and horizontal velocities. This suggests that local time-mean vertical velocities are primarily forced by the time-mean ocean dynamics, rather than by, for example, transient eddies or internal waves. It is also shown that, in the context of these four moorings, the time-mean vertical flow is consistent with stratified Taylor column dynamics in the presence of a topographic obstacle.

A bathtub vortex under the influence of a protruding cylinder in a rotating tank

Numerical simulations and laboratory experiments were jointly conducted to investigate a bathtub vortex under the influence of a protruding cylinder in a rotating tank. In the set-up, a central drain hole is placed at the bottom of the tank and a top-down cylinder is suspended from the rigid top lid, with fluid supplied from the sidewall for mass conservation. The cylinder is protruded to produce the Taylor column effect. The flow pattern depends on the Rossby number ($\mathit{Ro}= U/ fR$), the Ekman number ($\mathit{Ek}= \nu / f{R}^{2} )$ and the height ratio, $h/ H$, where $R$ is the radius of the cylinder, $f$ is the Coriolis parameter, $\nu $ is the kinematic viscosity of the fluid, $h$ is the vertical length of the cylinder and $H$ is the height of the tank. It is found appropriate to choose $U$ to be the average inflow velocity of fluid entering the column beneath the cylinder. Steady-state solutions obtained by numerically solving the Navier–Stokes equations in the rotating frame are shown to have a good agreement with flow visualizations and particle tracking velocimetry (PTV) measurements. It is known that at $\mathit{Ro}\sim 1{0}^{- 2} $, the central downward flow surrounded by the neighbouring Ekman pumping forms a classic one-celled bathtub vortex structure when there is no protruding cylinder ($h/ H= 0$). The influence of a suspended cylinder ($h/ H\not = 0$) leads to several findings. The bathtub vortex exhibits an interesting two-celled structure with an inner Ekman pumping (EP) and an outer up-drafting motion, termed Taylor upwelling (TU). The two regions of up-drafting motion are separated by a notable finite-thickness structure, identified as a (thin-walled) Taylor column. The thickness ${ \delta }_{T}^{\ast } $ of the Taylor column is found to be well correlated to the height ratio and the Ekman number by ${\delta }_{T} = { \delta }_{T}^{\ast } / R= {(1- h/ H)}^{- 0. 32} {\mathit{Ek}}^{0. 095} $. The Taylor column presents a barrier to the fluid flow such that the fluid from the inlet may only flow into the inner region through the narrow gaps, one above the Taylor column and one beneath it (conveniently called Ekman gaps). As a result, five types of routes along which the fluid may flow to and exit at the drain hole could be identified for the multi-celled vortex structure. Moreover, the flow rates associated with the five routes were calculated and compared to help understand the relative importance of the component flow structures. The weaker influence of the Taylor column effect on the bathtub vortex at $\mathit{Ro}\sim 1$ or even higher $\mathit{Ro}\sim 1{0}^{2} $ is also discussed.

The motion generated by a rising particle in a rotating fluid – numerical solutions. Part 2. The long container case

Numerical finite-difference results from the full axisymmetric incompressible Navier–Stokes equations are presented for the problem of the slow axial motion of a disk particle in an incompressible, rotating fluid in a long cylindrical container. The governing parameters are the Ekman number, E = ν*/(Ω*a*2), Rossby number, Ro = W*/(Ω*a*), and the dimensionless height of the container, 2H (the scaling length is the radius of the particle, a*; Ω* is the container angular velocity, W* is the particle axial velocity and ν* the kinematic viscosity). The study concerns the flow field for small values of E and Ro while HE is of order unity, and hence the appearance of a free Taylor column (slug) of fluid ‘trapped’ at the particle is expected. The numerical results are compared with predictions of previous analytical approximate studies. First, developed (quasi-steady-state) cases are considered. Excellent agreement with the exact linear (Ro = 0) solution of Ungarish & Vedensky (1995) is obtained when the computational Ro = 10−4. Next, the time-development for both an impulsive start and a start under a constant axial force is considered. A novel unexpected behaviour has been detected: the flow field first attains and maintains for a while the steady-state values of the unbounded configuration, and only afterwards adjusts to the bounded container steady state. Finally, the effects of the nonlinear momentum advection terms are investigated. It is shown that when Ro increases then the dimensionless drag (scaled by μ*a*W*) decreases, and the Taylor column becomes shorter, this effect being more pronounced in the rear region (μ* is the dynamic viscosity). The present results strengthen and extend the validity of the classical drag force predictions and therefore the issue of the large discrepancy between theory and experiments (Maxworthy 1970) concerning this force becomes more acute.

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.