Transport & mixing
Large-scale random flows. The distribution of atmospheric greenhouse gases and oceanic plankton species in the ocean are characterised by fine-scale, strongly inhomogeneous, complex structures that characterise the corresponding tracer fields. These structures are beautiful and striking physical phenomena; they can also have a large-scale impact on the climate of our planet. Alexandra’s research has focused on employing analytical and numerical methods (dynamical systems, analytical bounds, stochastic and data-driven Lagrangian modelling) to obtain reduced descriptions that yield predictions, in a number of idealised and environmental situations where the underlying flow is predominantly large-scale and random.
Past collaborations: Prof. Peter H. Haynes (University of Cambridge), Dr Bernard Legras (ENS, Paris).
Porous media. Structural inhomogeneities in porous media can strongly impact on the transport of constituents evolving therein. Using the theory of large deviations together with multiscale and matched asymptotics, Alexandra’s research has developed a new range of simplified models that capture the evolution of the constituent concentration after long times, when the spatial scale of the concentration fields is much larger than that of the medium. Explicit results provide new insight into the way media with complex network geometries and obstacles affect the distribution of low scalar concentrations where classical predictions (obtained via the method of homogenisation) fail.
Current collaborations: Yahya Farah (EPSRC funded PhD student), Dr Daniel Loghin (University of Birmingham), Prof. Jacques Vanneste (University of Edinburgh).
Reactive front propagation
Cut-off reactions. Reactive fronts arise in a wide range of applications in mathematical chemistry and biology. They describe the spatial invasion of chemical or biological reactions and are usually established as a result of the interaction between molecular diffusion, local growth, and saturation. Their propagation can be strongly affected by a reaction that is effectively deactivated at points where the concentration lies below a threshold cut-off value. Such reactions are motivated by applications in combustion or systems of interacting particles in which case the cut-off value may be viewed as the effective mass of a single particle. Using a combination of classical analysis and asymptotic methods, Alexandra's research determines the long-time behaviour of the reactive front and approximates it in the limit of small and large cut-off values.
Current collaborations: Prof. Dave Needham (University of Birmingham), Dr Alex D. O. Tisbury (EPSRC funded PhD student).
Periodic flows. In a wide range of environmental systems and engineering applications, the propagation of reactive fronts can be greatly facilitated by advection which typically increases the effective area of the reaction. A new range of simplified models developed in Alexandra's research explain the role of stagnation points in slowing down the propagation of fronts, elucidate differences between alternative models of reaction and determine their impact in a variety of periodic flows.
Current collaborations: Prof. Dave Needham (University of Birmingham), Prof. Jacques Vanneste (University of Edinburgh).