The dynamics of buoyant vortices

点击翻译按钮获取中文摘要

The goal of this project is to carry out a systematic study of vortical flows incorporating buoyancy effects, including the effects of gravity, density differences and surface tension. Explicit calculations of the motion of vortices in the presence of density differences and surface tension will develop understanding of fundamental fluid processes. Potential applications include a number of technological and geophysical situations, such as volcano vortex rings, cavitation, and flows around helicopter rotors and wind turbins. The project brings together researchers with complementary skills and experience in vortex dynamics and variable-density flows, and begins a new collaborative effort with scientists in Japan, Spain and Great Britain. In addition to outreach, during a series of workshops, the PI and teachers will develop a curriculum unit focusing on the calculus relevant to physical principles, illustrated by examples from the proposed work and fluid mechanics more generally. Four sub-projects will be investigated. First, the stability of vortex filaments will be examined in the presence of density variations. The case of rings and helices will be examined, since for these geometries solutions are known for the basic state. Second, an asymptotically consistent model for the evolution of a thin-core vortex filament with density variations will be developed and implemented. A formulation based on a force balance allows buoyancy and surface tension forces to be incorporated in a natural manner. Third, contour dynamics methods for axisymmetric vortex rings with density differences will be developed. This leads to the evolution of a vortex sheet on the boundary generated by baroclinic torques. Fourth, a new approach to contour dynamics applicable to helical vortices will be introduced and implemented, giving new exact solutions to the problem. The sub-projects are independent but related: each gives insight into features of the full problem. The outcome should include advances in the understanding of vortical fluid flow, including new solutions, and in new reduced models of such flows.