Formation Process of the Traveling-Wave State with a Defect in Binary Fluid Convection

We give results of simulations on the transient evolution from conduction to an ex tended traveling wave (ETW) state containing a sink defect slightly above the onset of the subcritical instability for a binary fluid mixture with the separation ratio '¢ = -0.47 con fined in a rectangular cell of aspect ratio r = 46. The simulation was performed using the two-dimensional full fluid equations of motion. We find that the system starting from a conduction state first experiences a linear stage with independently counterpropagating wave (CPW) packets and then develops a modulated traveling wave (MTW) and a traveling wave (TW) containing transient sink and source defects. It then ultimately evolves into a TW with a stable sink defect similar to those observed in experiments. For our parameters, the system evolves into the nonlinear regime as the lateral concentration profile becomes a trapezoidal, strongly non-harmonic shape in the localized regions. Comparisons with other calculations and experiments are presented.