Nonlinear Dynamical Systems Methods for Turbulence

NSF奖摘要- DMS-0102940数学科学：湍流的非线性动力系统方法摘要DMS-0102940 Haller湍流的数学，“经典物理学最后一个未解决的问题”，传统上是统计的性质。 这种方法导致长期预测的通用流体流动的整体性能。 与此相反，许多技术和地球物理混合问题，如燃料和空气在燃烧室中的混合，或在墨西哥湾的石油泄漏的蔓延，需要详细的有限时间湍流mixing.This项目的预测关注的有限时间混合理论的进一步发展和新的应用。 这种新的非线性理论使人们能够分析具体的数值或实验速度场，并隔离流中负责混合或缺乏混合的全局结构。 该项目将涉及这些新技术的应用及其在全球环流模型、涡旋分解和合并、海洋漂流物数据分析、燃烧室混合增强和连续铸钢方面的推广。

NSF Award Abstract - DMS-0102940Mathematical Sciences: Nonlinear Dynamical Systems Methods for Turbulence AbstractDMS-0102940HallerThe mathematics of turbulence, the "last unsolved problem of classical physics," has traditionally been statistical in nature. This approach leads to long-term predictions of the bulk properties of generic fluid flows. In contrast, many technological and geophysical mixing problems, such as mixing of fuel and air in a combustor, or the spread of an oil spill in the Gulf of Mexico, call for detailed finite-time predictions on turbulent mixing.This project is concerned with further development and novel applications of the recent theory of finite-time mixing. This new nonlinear theory enables one to analyze concrete numerical or experimental velocity fields and isolate global structures in the flow that is responsible for mixing or lack thereof. The project will involve applications of these new techniques and their extensions to global circulation models, vortex breakdown and merger, ocean drifter data analysis, mixing enhancement in combustors, and continuous steel casting.