Cyclone Development along Weak Thermal Fronts

Abstract

The properties of wavelike eddies imbedded in zonal flows containing vertical and horizontal shear are examined via an analytical model of a midlatitude cyclone. The model combines and extends some work by several previous investigators. Perturbation methods are used to formulate and solve this model. A transformation to geostrophic coordinates is employed that includes some ageostrophic effects and additional ageostrophic terms are retained after scaling the primitive equations. The zonal flows are chosen to model conditions observed in the atmosphere during incipient wave-cyclone development. Solutions grow due to barotropic and (primarily) baroclinic instability of the zonal flow. The stability, structure and energetics of some solutions are discussed. The lowest order solutions are in basic agreement with several previous studies. The effects of the intensity and vertical structure of the prescribed model thermal front are examined in a consistent fashion. As. the intensity of the front increases, the growth rate increases for most wavenumbers. As the meridional width of the east-west aligned frontal zone diminishes, 1) the most unstable wavelength shifts to shorter wavelengths, 2) the fastest moving wave shifts to longer wavelengths and 3) the meridional scale of the eddy decreases proportionally. The amplitude is increased in the vicinity of the front. The phase of the eddy pressure field is changed by the front in two ways: 1) barotropically unstable horizontal tilts are introduced and 2) the westward tilt with height is decreased in the upper region and increased in the lowest part by the horizontal shear. The energy conversions in these experiments reveal that the two instability mechanisms inhibit each other. This occurs because the two mechanisms are not independent. The ageostrophic terms 1) introduce meridional asymmetry into the solution, 2) reduce the growth rate and phase, speed and 3) tend to form a jet in a mean zonal flow that is initially only a function of height. Like the ageostrophic terms, the nonlinear distortion caused by the coordinate transformation improves the comparison between the model solutions and observed cyclones.