DYNAMICS OF CURVED DOMAIN BOUNDARIES IN CONVECTION PATTERNS

Curved domain boundaries (DB's) between locally stable convection patt erns are studied near the onset of convection, within the framework of the Newell-Whitehead-Segel theory [J. Fluid Mech. 38, 279 (1969); 38, 203 (1969)]. We consider the case where there exists a Lyapunov funct ional. By means of asymptotic methods, the equations of motion for DB' s are derived, and their solutions are obtained. It is shown that the behavior of a DB depends strongly on the difference between Lyapunov f unctional's densities of the coexisting patterns. In the case of a non zero difference, the normal velocity depends on the orientation of the DB, and caustics can be produced in a finite time. In the case of zer o difference, the normal velocity depends on both orientation and dist ortion of the DB, and the DB tends typically to straighten after a lon g time.