The dynamics of buoyant vortices

该项目的目标是对包含浮力效应的涡旋流进行系统研究，包括重力、密度差和表面张力的影响。在存在密度差和表面张力的情况下，对涡旋运动的明确计算将有助于对基本流体过程的理解。潜在的应用包括许多技术和地球物理情况，如火山漩涡环、空化、直升机旋翼和风力涡轮机周围的流动。该项目汇集了在涡旋动力学和变密度流方面具有互补技能和经验的研究人员，并与日本、西班牙和英国的科学家开始了新的合作努力。除了拓展外，在一系列讲习班期间，PI和教师将开发一个课程单元，重点关注与物理原理相关的微积分，并通过拟议工作中的例子和更普遍的流体力学来说明。将调查四个子项目。首先，涡流细丝的稳定性将在密度变化的情况下进行检验。圆环和螺旋的情况将被研究，因为这些几何形状的解是已知的基本状态。其次，建立并实现了随密度变化的薄芯涡丝演化的渐近一致模型。基于力平衡的配方允许浮力和表面张力以自然的方式结合。第三，发展具有密度差的轴对称涡环的轮廓动力学方法。这导致了斜压转矩在边界上产生涡片的演化。第四，介绍并实现了一种适用于螺旋涡的轮廓动力学的新方法，给出了问题的新的精确解。子项目是独立但相关的：每个子项目都提供了对整个问题特征的洞察。结果应包括对涡旋流体流动的理解方面的进展，包括新的解决方案，以及这种流动的新的简化模型。

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.