Building upon previous work (e.g., Farrell (1982), Grotjahn et al (1995)) in the initial-value analysis of the early stages of cyclogenesis we examine the problem in multiple dimensions. By contrasting the differences between the various models of baroclinic instability with one and two dimensional zonal flows we assess the efficacy of modal and nonmodal growth.
Calculations are performed using a quasi-geostrophic, linearized, initial-value model. The domain is a Cartesian, periodic channel. This model is spectral in the horizontal, uses second order finite differences in the vertical and integration through time uses the third-order Adams-Bashforth scheme. Model formulation ranges from the Eady(1949) model to one with variable Coriolis and realistic profiles of static stability.
Diagnostic tools assess the relative importance of modal and nonmodal growth. We present the following norms: potential enstrophy, total energy and RMS amplitude. Calculation of the projection onto the set of normal and continuum modes will be presented to help describe the emergence of the normal mode at the end of the integration.
During model testing we find the growth rate spectra to be sensitive to vertical resolution in combination with the zonal velocity profile. It is found that for certain, not unrealistic, zonal velocity profiles, growth rates at large wavenumbers can be exaggerated if too small (though relatively large) of a vertical resolution is used. In some cases, the maximum growth rate shifts to significantly larger wavenumbers.
Most initial-value studies of this type examine the growth in one dimension. This assumes that the interaction is aligned along the jet axis and that the perturbations interact in the most constructive manner. In the atmosphere the upper level trough often approaches an existing lower level feature along a path that is displaced (meridionally) from the low level feature. We therefore consider various displacements of the upper and lower level features. For all initial conditions we examine, it is found that all diagnostics show a reduction in nonmodal growth and, the time needed for the field to asymptote to normal mode form is extended when compared to the one dimensional case.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics