Abstract
It is shown how large-amplitude stability results for flows governed by potential-vorticity conservation can be obtained by geometric arguments using rearrangements of functions. The method allows for non-smooth solutions, and also gives a framework for the rigorous treatment of the effects of mixing by increasingly fine-scale filamentation. It is, thus, different from the energy-Casimir method. It is applied to the semi-geostrophic shear-flow problem in a channel, where the results can be compared with other methods. It is shown that, under the definitions used, there are no non-zonal nonlinearly-stable states in this problem. In the baroclinic case, it is shown how potential-vorticity conservation reduces the available energy for the transient flow. Copyright © 2003 Royal Meteorological Society
| Original language | English |
|---|---|
| Pages (from-to) | 1969-1988 |
| Number of pages | 20 |
| Journal | Quarterly Journal of the Royal Meteorological Society |
| Volume | 129 |
| Issue number | 591 |
| DOIs | |
| Publication status | Published - Apr 2003 |
Keywords
- Hamiltonian
- Potential vorticity
- Rearrangements