Wave - Cisk in a Baroclinic Basic State

Prefrontal squall lines are mesoscale convective systems that often cannot be linked to any preexisting organizing mechanism. This suggests the possibility that they are self-forced disturbances, driven by a cooperative interaction between convective and larger scales. To investigate this hypothesis, a wave-CISK model is developed for two-dimensional disturbances in a baroclinic basic state with constant vertical wind shear. The governing equations are the linearized Boussinesq equations for an inviscid and hydrostatic fluid on an f-plane. The model domain is infinite in the horizontal and consists of two layers in the vertical, representing the troposphere and the stratosphere. The model troposphere has constant static stability and wind shear, and the stratosphere has a larger static stability and no wind shear. The convective heating is confined to the troposphere. Normal mode solutions are assumed and the convective heating is parameterized in the standard CISK fashion: its vertical structure is specified, and it is set proportional to the low level vertical velocity. The model allows for arbitrary orientations of the disturbance axis. Results show the existence of two modes: large scale Eady modes, which are amplified slightly by heating, and smaller scale wave-CISK modes. The Eady modes are found to have their largest growth rates on the baroclinic axis, i.e. with the disturbance axis perpendicular to the shear vector. Wavelengths of maximum growth are on the synoptic scale (on the order of 3600 km). The wave-CISK modes have their maximum growth rates near the symmetric axis, i.e. with disturbance axes approximately parallel to the shear vector. For heating amplitudes that are not unrealistically large, wavelengths of maximum growth are finite and on the mesoscale (on the order of 500 km). Sensitivity experiments for these wave-CISK modes show that the value of the maximum growth rate and the wavelength of maximum growth are not very sensitive to the form of the vertical heating profile, while other characteristics of the fastest growing mode are. In particular, the orientation of the disturbance axis depends on the heating profile: for maximum heating in the middle troposphere the disturbance axis is rotated 20*-30* clockwise from the symmetric axis, implying upshear propagation, while for higher levels of maximum heating the disturbance is more nearly aligned with the shear vector or rotated slightly in the opposite direction. If low level cooling is included in the heating profile, disturbance axes are rotated further counterclockwise. The phase speeds of the fastest growing modes are larger for higher levels of maximum heating, due to the basic state shear component in the direction of propagation. Variations of the heating amplitude, the stratospheric static stability, and the bulk Richardson number show a tendency for a clockwise rotation as the heating amplitude and the stratospheric stability are decreased, and the Richardson number is increased. The growth rate and the wavenumber of the fastest growing mode are found to decrease with decreasing static stability of the stratosphere, and to be approximately proportional to the magnitude of the basic state wind shear. Comparisons with observations of squall lines in the atmosphere show some aspects of the solution, such as its vertical structure, to be in qualitative agreement. The orientation angle of the fastest growing mode, however, is near to observed values only if heating profiles with heating maxima at upper levels and cooling at lower levels are used. Predicted phase speeds of these modes are too high by a factor of two to five. The wave-CISK theory, at least in its current formulation, is thus unable to account for the observed characteristics of squall lines. Thesis Supervisor: Dr. Kerry A. Emanuel Title: Assistant Professor of Meteorology