Fronts, Domain Growth and Dynamical Scaling in a d=1 non-Potential System

TL;DR

This paper investigates the non-relaxational dynamics of front motion and domain growth in a one-dimensional non-potential system modeling Rayleigh-Benard convection with rotation, revealing a nearly logarithmic to linear coarsening transition.

Contribution

It provides a detailed classification of front families and demonstrates that a scaling description of coarsening applies even in non-potential, non-relaxational systems.

Findings

Front velocities and shapes are characterized.

Coarsening follows a nearly logarithmic growth law initially.

A crossover to linear growth occurs influenced by non-potential effects.

Abstract

We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial dependent terms have been added. As long as the angular velocity is different from zero, there is no known Lyapunov potential for the dynamics of the system. As a consequence the system follows a non-relaxational dynamics and the asymptotic state can not be associated with a final equilibrium state. When the rotation angular velocity is greater than some critical value, the system undergoes the Kuppers-Lortz instability leading to a time dependent chaotic dynamics and there is no coarsening beyond this instability. We have focused on the transient dynamics below this instability, where the dynamics is still non-relaxational. In this regime the dynamics is governed by a non-relaxational motion of fronts separating dynamically equivalent homogeneous states. We classify the families of fronts that occur in the dynamics, and calculate their shape and velocity. We have found that a scaling description of the coarsening process is still valid as in the potential case. The growth law is nearly logarithmic with time for short times and becomes linear after a crossover, whose width is determined by the strength of the non-potential terms.