Midlatitude Rossby wave forcing of equatorial Kelvin waves

Observations strongly suggest that convectively coupled Kelvin waves can be generated by extratropical wave activity. This mechanism is particularly efficient over Australia, where wave activity appears immediately after the extratropical Rossby waves propagate into the region during the Austral winter. This interaction occurs where the zonal wind is strongly sheared both in the meridional and vertical directions.

In order to understand this phenomenon the authors study the linear primitive equations in the presence of barotropic and baroclinic shear and the dispersion characteristics of the sheared Matsuno modes are calculated. Depending on the shear strength, the waves are stable or unstable and can be categorized into three groups. First there are the classical Matsuno modes modified by shear. Second there are extratropical "free" Rossby waves. Third, there are Rossby waves meridionally confined to the shear layer - these latter modes can be unstable, or stable and part of the continuous spectrum. In examples where the zonal winds are barotropically and baroclinically stable, we show that a continuous spectrum of Rossby waves exists. If the zonal winds are strong enough, the Rossby waves in the continuous spectrum have an equatorial signature exactly like the Matsuno Kelvin wave - despite the fact that, in these examples, the Matsuno Kelvin wave also exists on its own and that all modes are stable. For stronger shears, these continuous spectrum modes become unstable. Although the appear similar to Sakai's Rossby/Kelvin instability, their existence arises from a completely different phenomenon. The Sakai instability requires the frequency of a stable equatorial Rossby mode to coincide with the stable Kelvin wave frequency in order for the two modes to create a stable/unstable pair. Our results show that unstable Rossby waves need only have their frequencies Doppler shifted to that of the Kelvin wave frequency by the underlying shear in order that they acquire a Kelvin-like component - the Matsuno Kelvin wave remains stable for these values of shear. We conclude that a Kelvin-like signature is a ubiquitous feature of equatorial waves in shear, irrespective of whether or not the shear is unstable.