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. Joy and Thorpe (1990) have shown in this context the most unstable normal modes to have sub‐synoptic wavelenghts. The present study uses a primitive equation (PE) model to construct, at these wavelenghts and along the same fronts, the PE normal modes and extends the evolution tot he nonliner regime. IT is shown that PE normal modes have a structure similar to the original SG modes at the same given wavenumber. In the nonlinear experiments, two different kinds of behaviour are found, depending on the initial wavelenght of the perturbation, the frontal baroclinicity and the width of the potential vorticity anomaly. The first kind, and main finding of this study, is characterized by the inability of a barotropically unstable mode (in the energy sense) to lead to large pressure falls in the vortex. Such a mode, with its wavelenght smaller than the Rossby radius, is successful in breaking the frontal flow but saturates within two days. The other occurs when the wavelengh is larger than 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 phase occurs that the frontal change in structure is accompanied by significant deepening of the surface low. IT saturates in a way similar to larger‐scale baroclinic waves, by increasing the upper‐level jet and shear.