Applied Interdisciplinary Mathematics

Density stratification and interaction with boundaries can add a considerable layer of complexity to the dynamics of fluids, even in the simplest setups: for instance, moving rigid or deformable bodies, vortex rings, jets and waves may drag ambient fluids into regions where buoyancy forces can arise, thus creating strong flows unless mitigated by mixing or viscosity. The interplay between these components can give rise to critical phenomena, whereby different time evolutions and outcomes can be expected when crossing sharp parametric thresholds. This talk will present an overview of our theoretical, computational, and experimental studies on a class of such problems, focusing on the associated transport, mixing and interaction with structures and boundary geometries. The main examples will be drawn from the settling of rigid spheres and the rising of jets or plumes in stratified waters, and from the dispersion of solutes in microfluidic ducts and pipes. Speaker(s): Roberto Camassa (University of North Carolina, Chapel Hill)