Abstract
The elliptical instability of a rotating stratified fluid is examined in the regime of a small Rossby number and order-one Burger number corresponding to rapid rotation and strong stratification. The Floquet problem describing the linear growth of disturbances to an unbounded, uniform-vorticity elliptical flow is solved using exponential asymptotics. The results demonstrate that the flow is unstable for arbitrarily strong rotation and stratification; in particular, both cyclonic and anticyclonic flows are unstable. The instability is weak, however, with growth rates that are exponentially small in the Rossby number. The analytic expression obtained for the growth rate elucidates its dependence on the Burger number and on the eccentricity of the elliptical flow. It explains, in particular, the weakness of the instability of cyclonic flows, with growth rates that are only a small fraction of those obtained for the corresponding anticyclonic flows. The asymptotic results are confirmed by numerical solutions of the Floquet problem.
Original language | English |
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Article number | 074104 |
Pages (from-to) | - |
Number of pages | 10 |
Journal | Physics of Fluids |
Volume | 21 |
Issue number | 7 |
DOIs | |
Publication status | Published - Jul 2009 |
Keywords / Materials (for Non-textual outputs)
- flow instability
- rotational flow
- stratified flow
- vortices
- BAROCLINIC INSTABILITY
- GRAVITY-WAVES
- BALANCE
- STABILITY
- FLOWS