Willcocks, B.T. (2012) Instability and nonlinear equilibration of baroclinic flows. Doctoral thesis, UCL (University College London).
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Baroclinic instability, the fundamental mechanism underlying the generation of baroclinic eddies in the atmosphere and ocean is investigated in the two-layer, quasi-geostrophic model. The aim is to bridge the gap in understanding between analytical theories and high resolution numerical simulations of more realistic flows. In chapter 1 the physical motivation for the problems, two-layer model and numerical scheme are introduced. In chapter 2, the instability of a uniform flow profile without Ekman friction is investigated. The success of a weakly nonlinear theory due to Warn & Gauthier at finite criticality is assessed over the full parameter space. The relevance of nonlinear bounds on wave amplitude and perturbation energy due to Shepherd is also evaluated. Chapters 3 and 4 investigate the Holopainen instability, whereby a uniform flow profile, otherwise stable in frictionless flow, is destabilized by the addition of a small amount of Ekman friction. In chapter 3, the physical mechanisms of the baroclinic and Holopainen instabilities are contrasted in terms of potential vorticity disturbances. The instability of the Eady model is also discussed. In chapter 4, a weakly nonlinear theory due to Romea is shown to be accurate for flows unstable to the Holopainen instability and flows unstable to baroclinic instability in the presence of significant Ekman friction. An intermediate flow region is found where Warn & Gauthier’s theory is accurate at early times, but the final state is well predicted by Romea’s theory. The equilibration of an unstable baroclinic jet is investigated in chapter 5. A predictive theory due to Esler based on global constraints is extended to test two new hypotheses, which are also shown to be successful in predicting the equilibrated flow profile of initially symmetric jets. The theory is adapted to include asymmetric initial jets where each hypothesis is found to have limited quantitative success.
|Title:||Instability and nonlinear equilibration of baroclinic flows|
|Open access status:||An open access version is available from UCL Discovery|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics|
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