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

Abstract

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.