Oscillatory Convection As Traveling Waves

Recently, Cross suggested (1) that the traveling wave states which we observe (2) at the onset of convection in ethanol-water mixtures can be explained in detail in terms of the linear properties of the traveling waves. For a state with zero net growth, the finite reflectivity r at the cell boundaries requires waves which grow as they move. Consequently, he predicts that r should be related to the observed growth length l of the waves, and that the onset Rayleigh number will be shifted by an amount Delta Epsilon Alpha Gamma-1, where Gamma is the aspect ratio. We describe experimental results which support this picture. Our direct measurements of l(Psi,Gamma) and Delta Epsilon(Psi,Gamma) agree reasonably well with this theory. Finally, we have directly observed the linear propagation and reflection of pulses of traveling waves launched from one end of the cell, as well as the collision of two counterpropagating pulses without distortion.