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- Leon Barry, George C Craig, John Thuburn
- Nature
- 2002

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)

- T. D. Ringler, John Thuburn, Joseph B. Klemp, William C. Skamarock
- J. Comput. Physics
- 2010

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)

- John Thuburn, T. D. Ringler, William C. Skamarock, Joseph B. Klemp
- J. Comput. Physics
- 2009

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)

- John Thuburn
- J. Comput. Physics
- 2008

The advection schemes used in numerical models of chemistry and transport at xed resolution must unavoidably cause the models to misrepresent the transport in some way. This can include failure to establish or preserve the functional relations between long-lived chemical tracers that are often observed in the atmosphere. We show that linear functional… (More)

- John Thuburn
- J. Comput. Physics
- 2008

The rationale for designing atmospheric numerical model dynamical cores with certain conservation properties is reviewed. The conceptual difficulties associated with the multiscale nature of realistic atmospheric flow, and its lack of time-reversibility, are highlighted. A distinction is made between robust invariants, which are conserved or nearly… (More)

- John Thuburn, Colin J. Cotter
- SIAM J. Scientific Computing
- 2012

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)

- Colin J. Cotter, John Thuburn
- J. Comput. Physics
- 2014

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)

The advection of a tracer field in a fluid flow can create complex scalar structures and increase the effect of weak diffusion by orders of magnitude. One tool to quantify this is to measure the flux of scalar across contour lines of constant scalar. This gives a diffusion equation in area coordinates with an effective diffusion that depends on the… (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)