Near-onset dynamics in natural doubly diffusive convection

TL;DR

This paper investigates the initial onset and evolution of convection patterns in doubly diffusive systems, revealing coexistence of steady states and complex dynamics like traveling waves across various parameters.

Contribution

It provides a comprehensive analysis of the primary bifurcation and nonlinear dynamics in doubly diffusive convection for all Lewis and Prandtl numbers.

Findings

Large-amplitude steady convection can coexist with conduction.

Traveling waves and periodic orbits are identified as unstable states.

Convection patterns depend on the Lewis and Prandtl numbers.

Abstract

Doubly diffusive convection is considered in a vertical slot where horizontal temperature and solutal variations provide competing effects to the fluid density while allowing the existence of a conduction state. In this configuration, the linear stability of the conductive state is known, but the convection patterns arising from the primary instability have only been studied for specific parameter values. We have extended this by determining the nature of the primary bifurcation for all values of the Lewis and Prandtl numbers using a weakly nonlinear analysis. The resulting convection branches are extended using numerical continuation and we find large-amplitude steady convection states can coexist with the stable conduction state for sub- and supercritical primary bifurcations. The stability of the convection states is investigated and attracting travelling waves and periodic orbits are identified using time-stepping when these steady states are unstable.