On the Self-Organisation of Baroclinic Waves into Wave Packets

A linear, wave-mean flow model based on the quasi-geostrophic, two-layer model is designed to investigate the stability of zonally uniform baroclinic wavetrains. In the linear model the mean flow is specified, and includes a component proportional to the local wave amplitude squared. It is shown that the linear model may be tuned so that the baroclinic waves behave in a similar way to those in a fully turbulent two-layer flow. However, the linear model can be analysed asymptotically, and expressions can be derived for the growth rates of sideband disturbances to the uniform wavetrain. It is then shown that the length scale of the fastest growing sideband mode is a good predictor of the length scale of wave packets in the model.