Nonlinear convection in rotating systems: Slip-stick three-dimensional traveling waves

We investigate convection in a fluid channel uniformly heated from below and rotating about a vertical axis. When the width of the channel is moderate, convective instabilities are characterized by two three-dimensional traveling waves having the same frequency and wave number but traveling in opposite directions with different spatial structures. This Rapid Communication demonstrates that neither the progradely nor the retrogradely traveling wave is physically realizable in the vicinity of the instability threshold. The nature of convection is marked by nonlinear interactions of the two oppositely traveling three-dimensional waves which interfere strongly, leading to either vacillating or stationary convective flows