Nonlinear Dynamical Systems Methods for Turbulence

美国国家科学基金会奖摘要-DMS-0102940数学科学：湍流的非线性动力系统方法摘要DMS-0102940哈勒湍流数学是“经典物理中最后一个未解的问题”，传统上是统计性质的。这种方法导致了对一般流体流动的整体性质的长期预测。相比之下，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，或墨西哥湾漏油的扩散，都需要对湍流混合进行详细的有限时间预测。该项目涉及最近有限时间混合理论的进一步发展和新的应用。这一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，并分离出流动中导致混合或缺乏的整体结构。该项目将涉及这些新技术的应用及其在全球环流模式、涡旋分解和合并、大洋漂流数据分析、燃烧室混合增强以及连续铸钢方面的应用。

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.