Type: Seminar

Distribution: World

Expiry: 23 Mar 2010

Auth: pamelag(.ampgrad;1539.16000)@p80724.pc.maths.usyd.edu.au

Quasigeostrophic shallow-water flow on the beta plane typically involves turbulent motion and the formation of jets, which can be modelled by considering inviscid flow in a channel. I will present a review of the use of Chebyshev spectral methods for the solution of the stream-function vorticity formulation of flow in a channel, periodic in the streamwise direction and with Dirichlet boundary conditions on the channel wall. The vorticity equation is handled with standard pseudo-spectral techniques, while Poisson’s equation for the streamfunction is solved by transforming in both x and y and deriving a recursion relation for the Chebyshev coefficients in y. The recursion relation can be expressed as a quasipentadiagonal matrix equation, which may be solved in O(N) operations. Example flows used to test convergence and accuracy of the scheme will be discussed.

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