Eddy Heat Fluxes and Stability of Planetary Waves. Part I

Abstract

The stability of baroclinic Rossby waves in a zonal shear flow is examined. The model used is a linear, quasi-geostrophic, two-level, adiabatic and frictionless midlatitude ?-plane model. The perturbations consist of truncated zonal Fourier harmonics. There are two important zonal scales in the stability problem: the basic wave scale and the radius of deformation. The former occurs as an explicit scale while the latter is the natural response scale of a perturbed baroclinic zonal flow. The ratio of these two scales, together with two nondimensional parameters which describe the amplitudes of the barotropic and baroclinic components of the basic wave, constitute the three parameters in our parameter study of the stability problem. Parameter space is partitioned according to the dominant energy source for instability: the Lorenz and Kim regimes are characterized by significant horizontal and vertical shears of the basic wave, respectively, while the Phillips regime is characterized by a strong zonal flow. A fourth regime, the mixed-wave regime, where the horizontal and vertical shears of the basic wave are comparable and both large, is also identified. Growth rates, spectra and energetics are examined for the most unstable mode in each regime. When the basic wave scale is larger than the radius of deformation, higher harmonics of the basic wavenumber are excited; when the two scales are comparable, only the perturbation zonal flow and basic wave harmonic components have significant amplitude. Away from the Phillips regime, the most unstable mode has a nonzero meridional wavenumber.