Three-dimensional convectons

Part of the applied mathematics seminar series.

Doubly diffusive convection arises frequently in natural phenomena and industrial processes, and occurs in systems characterised by competing fields that diffuse at different rates. Well-known examples are provided by thermohaline convection and the salt-finger instability. Recent work has led to the realisation that subcritical instabilities can lead to stable but spatially localised convection. In this talk, I will introduce the basic ideas behind spatial localisation using a model system, the Swift--Hohenberg equation. I will then turn to three-dimensional thermohaline convection where a salt-water mixture is confined between vertical walls maintained at different temperatures and salinities. For this configuration, I will present spatially localised solutions consisting in spots of convection embedded in a background conduction state. I will also provide a brief overview of the numerical methods used.