Nonlinear interactions between random waves and vortices

BuhlerDMS-1009213 该研究员对波和涡旋之间的非线性相互作用进行了理论和数值研究，这些问题跨越了几个学科领域，即大气和湍流流体动力学，应用于粒子混合的小规模工程，以及量子力学中旋转超流体的动力学。 项目主题包括海洋中随机波浪和漩涡之间的能量交换、波浪诱导的漩涡结构对深海中颗粒扩散的作用、模拟浸没颗粒声混合的小型工程设备的设计和动力学，以及旋转超流体中波浪和点漩涡之间量子力学相互作用的特殊流体动力学。 这些问题的一个共同的主题是，它们涉及到巨大的规模分离之间的不同动态组件的流动。 这样的分离带来了数学上的困难，使得直接的数值模拟变得不切实际。 研究者着手解决几个问题，包括分析流体流动中波和涡之间的相互作用：与气候动力学相关的海洋流体动力学，应用于声混合的小尺度流体工程，凝聚态物理中的旋转超流体。 海洋是一个巨大的环境，在这个环境中，波浪和海流等多种动力要素相互作用，这些相互作用最终决定了海洋的现状和未来发展。 我们预测海洋动力学的能力微妙地取决于我们理解和模拟这些相互作用的能力，因为直接的计算机模拟远远需要计算资源，而且在未来几十年内都将如此。之所以如此，是因为不同的流动动力学成分发生在截然不同的长度或时间尺度上。 研究人员在数学和计算上研究波和涡之间的相互作用，使用现代数学理论来简化，从而减少必须在计算机上模拟的相互作用的复杂性。 在其他复杂的技术相关系统中，也研究了类似的流动动态成分之间的尺度分离相互作用，例如使用波动工程的非侵入性粒子混合技术，以及最近使用实验室技术突破而成为可能的超流行为的详细研究。

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.