*PEQUOD solves the multi-layer quasi-geostrophic equations in a rectangular domain. The model has two primary modes of operation: basin mode and channel mode. Typically, the basin mode is used as a simple model for a wind driven double gyre, with energy input to the system via upper layer wind forcing. The channel mode is used as a simple model for baroclinic zonal jet formation, with the energy input to the system via lateral buoyancy forcing.
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*The quasi-geostrophic potential vorticity equation (1) is solved subject to forcing and dissipation
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*where is the quasi-geostrophic potential vorticity (hereafter referred to as the "potential vorticity").The LHS in equation (1) is the material derivative, and is any forcing and dissipation. Equation (1) is then represented in a vertically layered form, which leads to a series of decoupled Helmholtz equations.
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*In PEQUOD two separate finite-difference approaches may be used to solve the layered quasi-geostrophic potential vorticity equation, however, this work will only be concerned with the CABARET approach. For the advection of relative potential vorticity, the scheme consists of three steps: predictor, extrapolator and corrector. The predictor and extrapolator step are performed using centred differencing in space. The extrapolator step is performed using upwinding of the advection term with a non-Total Variation Diminishing (TVD) flux limiter to bound the approximation. This scheme is second order accurate provided the method used to compute the fluxes is (at least) second order accurate.
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*Potential vorticity inversion for to yield the stream function is performed via the resulting linear elliptic problem being inverted using a direct solver. A discrete sine transform [7] is performed in the meridional direction, yielding a series of sparse one-dimensional Helmholtz problems in the zonal direction that can, for example, be inverted via Gaussian elimination. An inverse discrete sine transform of the resulting solutions of the one-dimensional problems completes the inversion.
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Phil Ridley 2012-10-01