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Title: A discontinuous Galerkin finite element method for quasi-geostrophic frontogenesis
Author: Lindley, Jorge Vicente Malik
ISNI:       0000 0004 7227 8917
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2017
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In this thesis, a mixed continuous and discontinuous Galerkin finite element method is developed for the three-dimensional quasi-geostrophic equations, and is used to investigate the role that weather front formation plays in the transfer of energy to small scales that would produce a k. 5=3 energy spectrum as observed in the atmosphere. The quasi-geostrophic equations are used for computational efficiency and are found to be sufficient for producing simple fronts. Discontinuous Galerkin finite elements are used for the potential vorticity as continuous Galerkin methods perform poorly with advection dominated problems. The less dynamical vertical direction is discretised with finite difference to simplify the finite element method in the horizontal. Streamfunction boundary values are derived for free-slip boundary conditions in the three-dimensional model. The scheme is verified with numerical tests and is shown to converge at optimal rates until free-slip boundaries are introduced. Conservation of energy and enstrophy are shown numerically. Using the numerical method, a channel model simulation suggests that the bend up of fronts produced by a meandering zonal jet could be a viable mechanism for producing a k.5=3 regime.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics