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- W3200701601 abstract "We consider a uniform ellipsoid of potential vorticity (PV), where we exploit analytical solutions derived for a balanced model at the second order in the Rossby number, the next order to quasi-geostrophic (QG) theory, the so-called QG+1 model. We consider this vortex in the presence of an external background shear flow, acting as a proxy for the effect of external vortices. For the QG model the system depends on four parameters, the height-to-width aspect ratio of the vortex, $h/r$ , as well as three parameters characterising the background flow, the strain rate, $gamma$ , the ratio of the background rotation rate to the strain, $beta$ , and the angle from which the flow is applied, $theta$ . However, the QG+1 model also depends on the PV, as well as the Prandtl ratio, $f/N$ ( $f$ and $N$ are the Coriolis and buoyancy frequencies, respectively). For QG and QG+1 we determine equilibria for different values of the background flow parameters for increasing values of the imposed strain rate up to the critical strain rate, $gamma _c$ , beyond which equilibria do not exist. We also compute the linear stability of this vortex to second-order modes, determining the marginal strain $gamma _m$ at which ellipsoidal instability erupts. The results show that for QG+1 the most resilient cyclonic ellipsoids are slightly prolate, while anticyclonic ellipsoids tend to be more oblate. The highest values of $gamma _m$ occur as $beta to 1$ . For large values of $f/N$ , changes in the marginal strain rates occur, stabilising anticyclonic ellipsoids while destabilising cyclonic ellipsoids." @default.
- W3200701601 created "2021-09-27" @default.
- W3200701601 creator A5000824207 @default.
- W3200701601 date "2021-09-15" @default.
- W3200701601 modified "2023-10-18" @default.
- W3200701601 title "Balanced ellipsoidal vortex equilibria in a background shear flow at finite Rossby number" @default.
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- W3200701601 doi "https://doi.org/10.1017/jfm.2021.759" @default.
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