The adjoint method for finding optimal or singular modes is employed for studying the finite time stability of steady, tw0-dimensional atmospheric fronts as represented by the uniform potential vorticity semigeostrophic model.
The most unstable singular models over a given period of time are computed for a wide range of scalar products. The reference scalar products are relevant to physical space and include total, kinetic, or potential energy; geopotential variance; and enstrophy.
A front inspired by observations from FRONTS 87 and including a surface potential temperature anomaly is examined first through the usual linear results. The validity of the linear approximation is considered as a function of amplitude. The modes are also integrated in nonlinear simulations and their life cycles am shown.
Results indicate that each norm and wave has its own preferred spatial scale. This severely restricts the concept of scale selection. Energy and geopotential variance modes increase mostly by improving the energy collection by barotropic processes. Enstrophy modes favor baroclinic processes. The linear approximation is more restrictive for the former than for the latter. In the nonlinear regime, the enstrophy mode exhibits faster deepening rates and larger vertical velocities.
Similar conclusions arise for the Hoskins-Bretherton deformation front in the same range of wavelengths, although this front is stable in the sense of Charney and Stern. The discussion examines the scale selection process inherent to the different scalar products.