Nonlinear traveling waves in rotating Rayleigh-Bénard convection: Stability boundaries and phase diffusion

We present experimental measurements of a sidewall traveling wave in rotating Rayleigh-Bénard convection. The fluid, water with Prandtl number about 6.3, was confined in a 1-cm-high cylindrical cell with radius-to-height ratio $\Gamma =5.\mathrm{}$ We used simultaneous optical-shadowgraph, heat-transport, and local temperature measurements to determine the stability and characteristics of the traveling-wave state for dimensionless rotation rates $60<\mathrm{}\Omega <420.\mathrm{}$ The state is well described by the one-dimensional complex Ginzburg-Landau (CGL) equation for which the linear and nonlinear coefficients were determined for $\Omega =274.\mathrm{}$ The Eckhaus-Benjamin-Feir-stability boundary was established and the phase-diffusion coefficient and nonlinear group velocity were determined in the stable regime. Higher-order corrections to the CGL equation were also investigated.