Spin-Up

Benton, Edward R.; Clark, A

doi:10.1146/annurev.fl.06.010174.001353

Cited by 140 publications

(92 citation statements)

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“…Given the significance of spin-up to the dynamics controlling many atmospheric and oceanographic flows ͑in which the effects associated with the Earth's rotation are important and often dominant͒, a considerable amount of research has been dedicated to analyzing the spin-up problem for both homogeneous and stratified fluids, as well as for a range of flow geometries and configurations. Much of this previous work to date is described in the review articles by Benton and Clarke 1 and, more recently, by Duck and Foster. 2 This article further investigates the "double-diffusive" instability associated with the spin-up of a stably stratified fluid; a mechanism first identified by McInytre.…”

Section: Introductionmentioning

confidence: 99%

Instabilities in the spin-up of a rotating, stratified fluid

2010

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Theoretical analyses and laboratory experiments have been performed on the stability of a flow generated by the differential cyclonic corotation of a flat, rigid disk in a uniformly rotating, linearly stratified fluid contained within a cylindrical tank. The undisturbed fluid is stably stratified with salt (Schmidt number σ≈670) and the (vertical) axes of rotation of the disk and the fluid container are coincident. The theoretical analysis shows that when the interior flow satisfies gradient wind balance (or, alternatively, thermal wind balance), it is destabilized by the action of viscosity. In the experiments, the manifestation of the viscous overturning instability is seen to be the formation of steplike internal microstructures in the density field, observed as regularly spaced, curved ring-shaped sheets with associated localized sharp, vertical density gradients. A stability analysis of the flow shows that the instability criterion is dependent on local values of the vertical and radial gradients of zonal velocity and the background density field. These quantities are measured in the experiments using a combination of horizontal-plane particle image velocimetry and an array of traversing microconductivity probes. The stability criterion based on this linear analysis predicts that the interior of the fluid is unstable. Using the σ⪢1 condition, simple asymptotic expressions for the maximum growth rate and associated wave number have been derived from the cubic dispersion relation. The theoretically predicted length scales and e-folding times associated with the fastest growing modes are found to give excellent agreement with the corresponding values obtained from the laboratory experimental data.

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Section: Introductionmentioning

confidence: 99%

Instabilities in the spin-up of a rotating, stratified fluid

2010

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“…Accounting for these eruptions is an essential ingredient in getting the flow dynamics correct. A parametric restriction, in addition to (2), should be noted here. Application of the boundary condition on the sloping lower wall involves transferring the boundary condition to the flat coordinate plane, and corrections to that scale with α 2 .…”

Section: Introductionmentioning

confidence: 99%

Stratified spin-up in a sliced, square cylinder

Munro

Foster

2014

Physics of Fluids

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We previously reported experimental and theoretical results on the linear spin-up of a linearly stratified, rotating fluid in a uniform-depth square cylinder [M. R. Foster and R. J. Munro, "The linear spin-up of a stratified, rotating fluid in a square cylinder," J. Fluid Mech. 712, 7-40 (2012)]. Here we extend that analysis to a "sliced" square cylinder, which has a base-plane inclined at a shallow angle α. Asymptotic results are derived that show the spin-up phase is achieved by a combination of the Ekman-layer eruptions (from the perimeter region of the cylinder's lid and base) and cross-slopepropagating stratified Rossby waves. The final, steady state limit for this spin-up phase is identical to that found previously for the uniform depth cylinder, but is reached somewhat more rapidly on a time scale of order E −1/2 −1 /log (α/E 1/2 ) (compared to E −1/2 −1 for the uniform-depth cylinder), where is the rotation rate and E the Ekman number. Experiments were performed for Burger numbers, S, between 0.4 and 16, and showed that for S O (1), the Rossby modes are severely damped, and it is only at small S, and during the early stages, that the presence of these wave modes was evident. These observations are supported by the theory, which shows the damping factors increase with S and are numerically large for S O (1

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“…There are many physical and engineering applications for such flows, including turbomachinery, centrifuges, the dynamics of components of spacecraft and in astrophysics (a detailed discussion of the dynamics within the Sun's core can be found in Benton & Clark 1974). One of the earliest theoretical studies of this type, for homogeneous (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…The upper and lower Stewartson layers then collide to form a shear layer, directed towards the container centreline, leading to two meridional-plane circulation regions. An early review of work in this area is given in Benton & Clark (1974), whilst a more recent review is that of Duck & Foster (2001).…”

Section: Introductionmentioning

confidence: 99%

Spin-up problems of stratified rotating flows inside containers

Duck

2012

J. Fluid Mech.

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Rotating, stratified flows are important in a wide variety of both geophysical and engineering applications. Whilst 'steady state' flows of this type are generally very simple (in effect, rigid body rotation), the effect of abruptly altering (even a little) the rotation rate can induce significant temporal flow disruptions, made all the more complicated when the fluid is bounded inside a closed finite container, a problem studied both experimentally and theoretically by Foster & Munro (J.

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Spin-Up

Cited by 140 publications

References 0 publications

Instabilities in the spin-up of a rotating, stratified fluid

Instabilities in the spin-up of a rotating, stratified fluid

Stratified spin-up in a sliced, square cylinder

Spin-up problems of stratified rotating flows inside containers

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