Nonlinear interactions between random waves and vortices

New York University, New York NY

Investigators

Abstract

Buhler DMS-1009213 The investigator undertakes a theoretical and numerical study of nonlinear interactions between waves and vortices in problems spanning several subject areas, namely atmosphere and ocean fluid dynamics, small-scale engineering applied to particle mixing, and the dynamics of rotating superfluids in quantum mechanics. Project topics include energy exchanges between random waves and vortices in the ocean, the role of wave-induced vortex structures for particle dispersal in the deep ocean, the design and dynamics of small-scale engineering devices to model the acoustic mixing of immersed particles, and the peculiar fluid dynamics that attends the quantum-mechanical interactions between waves and point vortices in rotating superfluids. A common theme of these problems is that they involve huge separations of scale between different dynamical components of the flows. Such separations present mathematical difficulties and make straightforward numerical simulations impractical. The investigator takes up several problems that involve analysis of the interactions between waves and vortices in fluid flows: ocean fluid dynamics relevant to climate dynamics, small-scale fluid engineering applied to acoustic mixing, and rotating superfluids in condensed matter physics. The ocean is a vast environment in which a multitude of dynamical components such as waves and currents interact, and these interactions eventually determine the present ocean state and also its future development. Our ability to predict ocean dynamics hinges delicately on our ability to understand and to model these interactions, because a direct computer simulation far exceeds our computational resources and will do so for decades to come. This is so because different dynamical components of the flows occur at vastly different scales of length or time. The investigator mathematically and computationally studies the interactions between waves and vortices, using modern mathematical theory to simplify and thereby to reduce the complexity of the interactions that must be modelled on a computer. Similar scale-separated interactions among dynamical components of flows are studied in other complex systems of technological relevance, such as non-invasive particle mixing techniques using wave engineering, and the detailed study of superfluid behaviour that has recently become possible using breakthroughs in laboratory technology.