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20-layer model amplitude ATMOSPHERIC DEVELOPMENT atmospheric instability Baer baroclinic initial value BAROCLINIC INSTABILITY baroclinic stability barotropic instability basic state parameters Colorado State University constant static stability continuity equation continuous model continuous spectrum convergence cyclone development dashed line discussed eigenvalues eigenvectors exact solution expansion coefficients Fig.l finite difference model function of pressure geostrophic growth rate initial value formulation initial value problem INSTABILITY AND ATMOSPHERIC inverse static stability linear zonal wind lines in Fig long waves matrix Meteor non-geostrophic effects normal mode solutions numerical model obtained ordinary differential equations perturbation kinetic energy perturbation tendency phase speed quasi-continuous spectrum quasi-geostrophic atmosphere shear shown in Fig solved spectral model spectral prediction equations square root stability problem static stability shown streamfunction system of equations T. J. Simons Tellus trigonometric truncation errors turbations unstable mode unstable waves wave of wavenumber wavelength of 4000 wavespeed Wiin-Nielsen wind shear zonal flow zonal wind profile