Numerical study of pattern formation following a convective instability in non-Boussinesq fluids

TL;DR

This paper numerically investigates pattern formation in non-Boussinesq fluids following convective instability, reproducing experimental features and analyzing pattern transitions, nucleation, and front velocities using a generalized Swift-Hohenberg model.

Contribution

It introduces a generalized two-dimensional Swift-Hohenberg model to simulate pattern formation in non-Boussinesq fluids, aligning with experimental observations and theoretical predictions.

Findings

Reproduces experimental convection patterns such as hexagons, rolls, and spirals.

Analyzes transitions and competition among different patterns.

Finds front velocities consistent with marginal stability theory.

Abstract

We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced by using a generalized two-dimensional Swift-Hohenberg equation. The formation of hexagonal patterns, rolls and spirals is studied, as well as the transitions and competition among them. We also study nucleation and growth of hexagonal patterns and find that the front velocity in this two dimensional model is consistent with the prediction of marginal stability theory for one dimensional fronts.