## Abstract

An efficient solution procedure is developed for a nonseparable semigeostrophic Eady problem on a semi-infinite *f* plane. A model is designed to study the effects of meridionally isolated jets and tropopause morphology on baroclinic instability. Potential vorticity (PV) is assumed to be piecewise constant and discontinuous at the tropopause, whose height is allowed to vary with latitude. The computational domain is discretized in a stretched coordinate to maintain adequate resolution in the vicinity of the tropopause and axis of the jet. The basic state is numerically inverted from the two PV values with the specification of only the meridional profiles of potential temperature (PT) at the surface and (unspecified) tropopause height. The nonseparable eigenvalue problem about this basic state is solved for the discrete (zero-PV) normal modes. Since continuum modes are not sought, the size of the problem is reduced greatly, keeping the storage and CPU requirements moderate even at relatively high spatial resolutions.

This model is used to investigate changes in the zonal-mean state and the stability thereof, in response to arrangements of the zonal-mean PT at the surface and tropopause. In particular, (a) partial mixing of surface PT and (b) appearance of a local minimum of PT on the tropopause are considered as models of baroclinic adjustment and tropopause folds, respectively. The former renders the mean flow more barotropic and shifts up the zonal scale of baroclinic instability. The latter gives rise to a markedly dipped tropopause that is barotropically unstable at various ranges of wavenumbers. The resultsâ€™ implications on the life cycle simulations and roll-up of stratospheric intrusions are discussed.

*Corresponding author address:* Dr. Noboru Nakamura, Department of the Geophysical Sciences, University of Chicago, 5734 S. Ellis Avenue, Chicago, IL 60637.

Email: nnn@bethel.uchicago.edu