The Baroclinic Instability of Highly Structured One-Dimensional Basic States

Abstract

The baroclinic instability of highly structured one-dimensional basic states is studied using a frictionless, adiabatic, quasi-geostrophic model on a ?-plane. Square-root-pressure coordinates are used at 48 levels in the vertical, and calculations are made for the upper boundary conditions ?? = 0 and ?? = 0. Many properties of the unstable waves are considered: instability source, wavelength, growth rate, phase velocity, steering levels and the vertical structure of their amplitude, phase, meridional entropy transport and potential-to-kinetic-energy conversion. The highly structured basic states have zonal velocities and static stabilities obtained from one month averaged data for latitudes 25?65°N and for months (January, April, July and October) which represent seasonal extremes and transitions. The long-wave modes discovered by Green (1960) are shown to have several interesting properties. Doubling times are moderately short (?1 week). Pressure amplitudes, kinetic energy destruction and meridional entropy transport are particularly strong in the lower stratosphere (relative to other levels). Their kinetic energy is generated in the troposphere. Their entropy transports are countergradient in the lower stratosphere when a reversed shear exists in that region. Quasi-geostrophic, potential vorticity, meridional gradient profiles (q?y) for the one-month averaged data possess a considerable number of zeros (Fullmer, 1982). These zeros and their associated negative q?y regions have a substantial effect on the unstable mode spectrum. Some modes? growth rates are drastically reduced when a particular negative q?y region is removed. New modes (distinct from those discovered by Charney, Eady and Green) exist only when certain negative q?y regions are present. Some of the new modes are examples of in-situ stratospheric baroclinic instability. The unstable mode spectrum is also shown to be sensitive to small changes in the unperturbed state. It is shown that only those changes which drastically alter the negative regions and associated zeros of the q?y profile result in a substantial change in the unstable mode spectrum.