Physics – Fluid Dynamics
Scientific paper
2003-12-22
Physics
Fluid Dynamics
28 pages, 15 figures. * New version including discussion of the recent work of Hollerbach, and much more. * A sign error in th
Scientific paper
We study the destabilization of a shear layer, produced by differential rotation of a rotating axisymmetric container. For small forcing, this produces a shear layer, which has been studied by Stewartson and is almost invariant along the rotation axis. When the forcing increases, instabilities develop. To study the asymptotic regime (very low Ekman number $E$), we develop a quasi-geostrophic two-dimensional model, whose main original feature is to handle the mass conservation correctly, resulting in a divergent two-dimensional flow, and valid for any container provided that the top and bottom have finite slopes. We use it to derive scalings and asymptotic laws by a simple linear theory, extending the previous analyses to large slopes (as in a sphere), for which we find different scaling laws. For a flat container, the critical Rossby number for the onset of instability evolves as $E^{3/4}$ and may be understood as a Kelvin-Helmoltz shear instability. For a sloping container, the instability is a Rossby wave with a critical Rossby number proportional to $\beta E^{1/2}$, where $\beta$ is related to the slope. We also investigate the asymmetry between positive and negative differential rotation and propose corrections for finite Ekman and Rossby numbers. Implemented in a numerical code, our model allows us to study the onset over a broad range of parameters, determining the threshold but also other features such as the spatial structure. We also present a few experimental results, validating our model and showing its limits.
Cardin Philippe
Schaeffer Nathanaël
No associations
LandOfFree
Quasi-geostrophic model of the instabilities of the Stewartson layer does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quasi-geostrophic model of the instabilities of the Stewartson layer, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quasi-geostrophic model of the instabilities of the Stewartson layer will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-618973