We discuss the nonlinear dynamics and routes to chaos of baroclinic waves as found in a laboratory experiment, the baroclinic annulus, and in Direct Numerical Simulation (DNS). Thermal convection in a rapidly rotating fluid subject to differential heating occurs in many systems, ranging from the atmosphere to roating machinery. Our focus is the transition sequence from a steady wave to chaotic mixed-mode vacillations via amplitude vacillation. The main techniques used are phase space reconstruction and a phase coherence measure of the different waves to estimate the strength of the nonlinear wave-wave interactions. While experimental evidence tends to show the onset of amplitude vacillation and further bifurcations towards a mode transition to next-lower mode, recent numerical solutions have shown vacillation and modulated vacillation before a mode transition to the next-higher mode. These apparently inconsistent results will be discussed in detail.
