Nonlinear interactions between random waves and vortices

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BuhlerDMS-1009213 The investigator undertakes a theoretical and numericalstudy of nonlinear interactions between waves and vortices inproblems spanning several subject areas, namely atmosphere andocean fluid dynamics, small-scale engineering applied to particlemixing, and the dynamics of rotating superfluids in quantummechanics. Project topics include energy exchanges betweenrandom waves and vortices in the ocean, the role of wave-inducedvortex structures for particle dispersal in the deep ocean, thedesign and dynamics of small-scale engineering devices to modelthe acoustic mixing of immersed particles, and the peculiar fluiddynamics that attends the quantum-mechanical interactions betweenwaves and point vortices in rotating superfluids. A common themeof these problems is that they involve huge separations of scalebetween different dynamical components of the flows. Suchseparations present mathematical difficulties and makestraightforward numerical simulations impractical. The investigator takes up several problems that involveanalysis of the interactions between waves and vortices in fluidflows: ocean fluid dynamics relevant to climate dynamics,small-scale fluid engineering applied to acoustic mixing, androtating superfluids in condensed matter physics. The ocean is avast environment in which a multitude of dynamical componentssuch as waves and currents interact, and these interactionseventually determine the present ocean state and also its futuredevelopment. Our ability to predict ocean dynamics hingesdelicately on our ability to understand and to model theseinteractions, because a direct computer simulation far exceedsour computational resources and will do so for decades to come. This is so because different dynamical components of the flowsoccur at vastly different scales of length or time. Theinvestigator mathematically and computationally studies theinteractions between waves and vortices, using modernmathematical theory to simplify and thereby to reduce thecomplexity of the interactions that must be modelled on acomputer. Similar scale-separated interactions among dynamicalcomponents of flows are studied in other complex systems oftechnological relevance, such as non-invasive particle mixingtechniques using wave engineering, and the detailed study ofsuperfluid behaviour that has recently become possible usingbreakthroughs in laboratory technology.