2001/03/01 by Denis Boyer, Jorge Viñals · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Fluid Dynamics and Thin Films #Nonlinear Dynamics and Pattern Formation #Theoretical and Computational Physics #cond-mat.soft
paper · pdf · doi:10.1103/physreve.63.061704
16 pages, 5 figures
arxiv created 2001/03/01 · openalex publication_date 2001/05/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the motion of a grain boundary that separates two sets of mutually perpendicular rolls in Rayleigh-Bénard convection above onset. The problem is treated either analytically from the corresponding amplitude equations, or numerically by solving the Swift-Hohenberg equation. We find that if the rolls are curved by a slow transversal modulation, a net translation of the boundary follows. We show analytically that although this motion is a nonlinear effect, it occurs in a time scale much shorter than that of the linear relaxation of the curved rolls. The total distance traveled by the boundary scales as epsilon(-1/2), where epsilon is the reduced Rayleigh number. We obtain analytical expressions for the relaxation rate of the modulation and for the time-dependent traveling velocity of the boundary, and especially their dependence on wave number. The results agree well with direct numerical solutions of the Swift-Hohenberg equation. We finally discuss the implications of our results on the coarsening rate of an ensemble of differently oriented domains in which grain-boundary motion through curved rolls is the dominant coarsening mechanism.