Abstract
The linear stability of two atmospheric flows is examined, with basic-state data taken from environments where comma clouds were observed to form. The basic states each feature a baroclinic zone associated with an upper-level jet, with conditional instability on the north side. The semigeostrophic approximation is used, along with a simple parameterization for cumulus heating, and the eigenvalue problem is solved using a Chebyshev spectral method. The instabilities can be regarded as resulting from the interaction of potential-vorticity anomalies from three sources: advection along isentropic surfaces of the basic-state potential-vorticity (PV) gradient. advection of the surface potential temperature gradient (which is equivalent to a PV gradient in a thin layer at the surface), and potential vorticity generated by release of latent heat.
It is found that for the comma clouds the instability is a baroclinic interaction of upper- and lower-level PV anomalies. However, heating is an important source of potential vorticity in these modes, and substantially influences their structure. This is reflected in a tendency for the surface depression to be confined to the heating region on the cold-air side of the jet, particularly in one of the cases where the surface temperature gradient was very weak. It also results in a shorter wavelength due to a reduced vertical scale as the midtropospheric PV anomaly associated with the upper part of the heating region becomes stronger than the anomaly produced at the PV gradient at the tropopause.
The solutions am also compared with observations of the systems early in their development. For both cases the confined low-level structure associated with heating is found to match the observed cyclogenesis closely in both position and extent. The predicted wavelengths and phase speeds are also consistent with observations, although precise comparison is difficult with the available data.
