NONLINEAR EVOLUTION OF ORDINARY FRONTAL WAVES INDUCED BY LOW-LEVEL POTENTIAL VORTICITY ANOMALIES

Linear, semi-geostrophic (SG) theory reveals the instability of steady fronts with low-level potential vorticity anomalies. Joly and Thorpe (1990) have shown in this context the most unstable normal modes to ha ve sub-synoptic wavelengths. The present study uses a primitive equati on (PE) model to construct, at these wavelengths and along the same fr onts, the PE normal modes and extends the evolution to the nonlinear r egime. It is shown that PE normal modes have a structure similar to th e original SG modes at the same given wavenumber. In the nonlinear exp eriments, two different kinds of behaviour are found, depending on the initial wavelength of the perturbation, the frontal baroclinicity and the width of the potential vorticity anomaly. The first kind, and mai n finding of this study, is characterized by the inability of a barotr opically unstable mode (in the energy sense) to lead to large pressure falls in the vortex. Such a mode, with its wavelength smaller than th e Rossby radius, is successful in breaking the frontal flow but satura tes within two days. The other occurs when the wavelength is larger th an the Rossby radius. Then, it is shown that the initially significant barotropic contribution to the growth vanishes and the wave enters a phase of classical baroclinic growth. It is only when this second phas e occurs that the frontal change in structure is accompanied by signif icant deepening of the surface low. It saturates in a way similar to l arger-scale baroclinic waves, by increasing the upper-level jet and sh ear.