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Applied Math Colloquium

Friday, January 31st, 2014, 11:30 AM
Cullimore Lecture Hall, Lecture Hall II
New Jersey Institute of Technology

Spatial localization in three-dimensional doubly diffusive convection

Cedric Beaume

University of California, Berkeley

Abstract

Doubly diffusive convection arises frequently in natural phenomena and industrial processes, and occurs in systems characterized 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 realization that subcritical instabilities of this type can lead to stable but spatially localized convection. In this talk, I will introduce the basic ideas behind spatial localization 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 concentrations. For this configuration, I will present spatially localized solutions consisting in spots of convection embedded in a background conduction state. I will then discuss the properties of these unusual solutions and interpret the results in terms of the Swift--Hohenberg model. I will also provide a brief overview of the numerical methods used.