Abstract
We study the mathematical structure of localized convection cell solutions in a binary fluid mixture. These solutions are not observed in Rayleigh-Bénard convection in a pure fluid in which the concentration field is homogeneous. In particular, a solution representing time-periodic traveling localized convection cells (periodic traveling pulse, PTP) has not been obtained even numerically because this solution requires two unknown variables to be determined: group velocity and temporal period in the comoving frame with the group velocity. We have applied an integrated numerical method to obtain the PTP solution as well as the steady, periodic, and traveling solutions. Therefore, we can treat all classes of solvable solutions under the integrative framework. By using this method, a global bifurcation structure containing a variety of solutions including PTPs is obtained and the phase dependence of the collision of counter-propagating PTPs is investigated in detail.
