Transitions between roll patterns in thermal convection.

Current theories of pattern formation predict the existence of 'phase grain boundaries' across which the orientation of the wave number of convective rolls changes abruptly. However, the usual assumption of slow variation is violated by these solutions. By restricting attention to near the critical Rayleigh number Ra-c for linear onset of convection, a rational weakly nonlinear theory may be envisaged. This might have either smoothly varying solutions, or discontinuous 'outer solutions' matched by an inner transition region. We find smooth steady solutions, with just two participating modes; but we show that there exists no weakly nonlinear solution of near-discontinuous type. To elucidate the evolution of an initially discontinuous state, we solve an associated linear time-dependent problem. Our results show that, sufficiently close to Ra-c, steady transitions between differing roll orientations must take place gradually, rather than abruptly; and that predictions of abrupt transitions from model equations, which are not rigorously validated, may mislead. (C) 2000 The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.