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Helen Warn

Abstract

A model consisting of two layers of inviscid, constant-density fluid in stable stratification on a rotating gravitating sphere is linearized about a basic state consisting of a steady zonal flow with arbitrary latitudinal variation in the upper layer, balanced geostrophically by mean free surface and interfacial slopes. Normal modes solutions are assumed and a Galerkin procedure employed to obtain approximate solutions to the resulting eigenproblem for various basic state wind profiles. Baroclinically unstable modes for the basic states of constant angular rotation in the upper layer and of jet-type wind profiles are compared with the results of mid-latitude β-plane studies. In general, it is found that the spherical model produces modes with growth rates in reasonable agreement to those predicted by β-plane theory, but for the parameter ranges consistent with the model their growth rates are somewhat smaller than those suitable for typical mid-latitude storms.

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Pierre Koclas, Andrew Staniforth, and Helen Warn

Abstract

A frontogenesis model is formulated using the inviscid, adiabatic, Boussinesq, hydrostatic primitive equations and bilinear finite elements. Results of integrations of the model for a horizontal deformation flow are compared with the analytic solution obtained (using the “cross-front geostrophic approximation”) by Hoskins and Bretherton. For sufficient resolution the numerical solutions are almost identical to the analytic one in the region near the front, even though the front is well developed and only five hours away from becoming discontinuous at the surface. A substantial improvement in computational efficiency is achieved by using variable resolution away from the front instead of uniform resolution everywhere: as much as a factor of 25 reduction in CPU time and a factor of 5 reduction in storage requirements are observed. Contrary to the recent findings of Aksel et al., no difficulties are encountered in the application of open boundary conditions and neither is resolution limited by the use of finite elements rather than finite differences. Indeed, the variable-resolution feature of bilinear finite elements is a decided advantage for many meteorological problems because of the computational economics that may be realized.

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