John Thuburn

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A numerical scheme applicable to arbitrarily structured C-grids is presented for the nonlinear shallow-water equations. By discretizing the vector invariant form of the momentum equation, the relationship between the nonlinear Coriolis force and the potential vorticity flux can be used to guarantee that mass, velocity and potential vorticity evolve in a(More)
Inertio-gravity mode and Rossby mode dispersion properties are examined for discretizations of the linearized rotating shallow water equations on a regular hexagonal C-grid in planar geometry. It is shown that spurious non-zero Rossby mode frequencies found by previous authors in the f-plane case can be avoided by an appropriate discretization of the(More)
A C-grid staggering, in which the mass variable is stored at cell centers and the normal velocity component is stored at cell faces (or edges in two dimensions) is attractive for atmospheric modeling since it enables a relatively accurate representation of fast wave modes. However, the discretization of the Coriolis terms is non-trivial. For constant(More)
The advection schemes used in numerical models of chemistry and transport •t fixed resolution must unavoidably c•use the models to misrepresent the transport in some w•y. This c•n include f•ilure to establish or preserve the functional relations between long-lived chemical tracers that •re often observed in the •tmosphere. We show that linear functionM(More)
The atmospheric heat transport on Earth from the Equator to the poles is largely carried out by the mid-latitude storms. However, there is no satisfactory theory to describe this fundamental feature of the Earth's climate. Previous studies have characterized the poleward heat transport as a diffusion by eddies of specified horizontal length and velocity(More)
6 We describe discretisations of the shallow water equations on the sphere using the framework of finite element exterior calculus, which are extensions of the mimetic finite difference framework presented in Ringler, Thuburn, Klemp, and Skamarock (Journal of Computational Physics, 2010). The exterior calculus notation provides a guide to which finite(More)
Accurate simulation of atmospheric flow in weather and climate prediction models requires the discretization of the governing equations to have a number of desirable properties. Although these properties can be achieved relatively straightforwardly on a latitude-longitude grid, they are much more challenging on the various quasi-uniform spherical grids that(More)
In this paper we examine the influence of periodic islands within a time periodic chaotic flow on the evolution of a scalar tracer. The passive scalar tracer is injected into the flow field by means of a steady source term. We examine the distribution of the tracer once a periodic state is reached, in which the rate of injected scalar balances advection and(More)