Thermal Rossby waves driven by centrifugal buoyancy in a rotating cylindrical fluid gapbecome unstable right at the onset of convection when the Prandtl number is small. TheBenjamin–Feir–Newell instability leads to modulated thermal Rossby waves which can also bedescribed by a generalized Ginzburg–Landau equation. A resonance instability occurs at afinite distance in Rayleigh number from the neutral curve. It leads to two independent wavepatterns propagating past each other and finally gives rise to vacillations of the amplitudeof convection. Most of these features can be described to a good approximation by a systemof three coupled amplitude equations. Time integrations based on a Galerkin expansion showtransitions to chaotic convection at higher Rayleigh numbers.