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An analytically integrated finite volume pressure gradient discretization for avoiding thermobaric instabilities in layered ocean models.
Alistair Adcroft, Robert Hallberg, Matthew Harrison
Princeton University
(Abstract received 07/18/2007 for session X)
ABSTRACT
The use of a realistic equation of state in isopycnal models can lead to spurious thermobaric instability unless steps are taken to treat the compressibility of sea-water carefully (Sun et al., JPO 1999; Hallberg, Ocean. Mod. 2005). We re-visit the problem in the context of the finite volume formulation of the pressure gradient force and note that in this frame work the Montgomery formulation is no longer advantageous. We find that an analytic treatment of terms in the finite volume discretization i) properly represents compressibility, ii) avoids the spurious thermobaric instability, and iii) minimizes any pressure gradient errors that would normally occur when not using the Montgomery formulation in layered models. In the limit of purely isopycnal layers and an equation of state that excludes thermobaricity, this analytically integrated finite volume discretization is mathematically identical to the Montgomery potential formulation, suggesting that there is no disadvantage to using the new discretization in all situations.
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2007 LOM Workshop, Bergen, Norway, August 20-22, 2007