In chapter 1, some fundamental concepts about inertial instability in a general geophysical context are reviewed. The instability is described as a parcel instability, and an axisymmetric linear stability analysis is presented. The general form of the dispersion relation is discussed, and the linear instability problem is described in terms of a variational principle. In chapter 2, the special case of linear equatorial inertial instability is studied. Conditions leading to instability in the equatorial stratosphere and mesosphere are described, and some of the existing linear stability theory is reviewed. For the axisymmetric case, the theory is extended to demonstrate the scaling for the most unstable vertical wavenumber. The inability of the simple linear theory to satisfactorily explain the observations is discussed. In chapter 3, the linear instability of a more complicated equatorial flow with a 'slow' vertical variation is considered. The analysis uses a JWKB method, the results of which are compared with numerical simulations of the problem. The vertical variation leads to a reduction in the expected growth rate. There are also variations in the vertical wavenumber, although these do not seem to be sufficient to explain the large vertical scales present in observations. In chapter 4, a theory is presented for the weakly nonlinear evolution of axisymmetric inertial instability. In chapter 5, aspects of more strongly unstable flows are discussed, based on the results of numerical simulations of the axisymmetric instability.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:599728 |
| Date | January 2001 |
| Creators | Griffiths, S. D. |
| Publisher | University of Cambridge |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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