Towards Convectons in the Supercritical Regime: Homoclinic Snaking in Natural Doubly Diffusive Convection

TL;DR

This paper investigates the existence and behavior of localized convective states called convectons in doubly diffusive convection, especially in regimes where the primary bifurcation is supercritical, revealing complex structures influenced by inertia at low Prandtl numbers.

Contribution

It demonstrates that convectons persist in supercritical regimes without bistability, expanding understanding of localized convection patterns in doubly diffusive systems.

Findings

Convectons exist beyond subcritical regimes into supercritical regimes.

Secondary branches exhibit homoclinic snaking behavior.

Inertia effects become significant at low Prandtl numbers.

Abstract

Fluids subject to both thermal and compositional variations can undergo doubly diffusive convection when these properties both affect the fluid density and diffuse at different rates. A variety of patterns can arise from these buoyancy-driven flows, including spatially localised states known as convectons, which consist of convective fluid motion localised within a background of quiescent fluid. We consider these states in a vertical slot with the horizontal temperature and solutal gradients providing competing effects to the fluid density while allowing the existence of a conduction state. In this configuration, convectons have been studied with specific parameter values where the onset of convection is subcritical, and the states have been found to lie on a pair of secondary branches that undergo homoclinic snaking in a parameter regime below the onset of linear instability. In this paper, we show that convectons persist into parameter regimes in which the primary bifurcation is supercritical and there is no bistability, despite coexistence between the stable conduction state and large-amplitude convection. We detail this transition by considering spatial dynamics and observe how the structure of the secondary branches becomes increasingly complex owing to the increased role of inertia at low Prandtl numbers.