Transport and Wave Propagation in Turbulence

这个项目涉及标量、矢量和波在发展湍流中的输运。 该项目的第一部分涉及湍流速度的统计建模和标量（例如温度）波动统计分析方法。 湍流速度的一个特征是存在大范围的尺度。 这在温度波动中引起类似的宽范围尺度，从而在局部波动中引起类似的宽范围尺度，例如折射率。 湍流空气折射率的研究是数学分析和技术应用的一个重要挑战性问题。 该项目的第二部分讨论了大气湍流中波动的统计特性。 特别是，该项目侧重于几个制度，其中简化的波的描述可以推导出，其中一些是众所周知的广泛适用。 它们包括抛物线近似、白噪声近似和辐射传输极限。 我们的目标是制定一个数学框架，以严格和统一的方式研究各种近似。 在各种近似的解决方案的细节将进行调查，通信和成像systems.Understanding的标量和波传输通过大气湍流的设计提供指导是必不可少的许多重要应用，包括热量和污染物的传输，激光和无线通信，遥感和成像。 例如，在声波或光波在大气中传播的情况下，波速经历由小尺度温度和湿度波动决定的随机波动。 这个计画发展一个统一的数学架构来解决标量输运和波在紊流介质中的传播问题。 研究结果将有助于光通信和成像技术的改进。

This project concerns the transport of scalars, vectors, and waves in developed turbulence. The first part of the project deals with the statistical modeling of turbulent velocity and methods of analyzing the statistics of scalar (for example, temperature) fluctuations. A characteristic feature of turbulent velocity is the presence of a wide range of scales. This induces a similarly wide range of scales in fluctuations of temperature and hence in the local fluctuations of, for example, the refractive index. The study of the refractive index in the turbulent air is an important challenging problem for mathematical analysis as well as technological applications. The second part of the project addresses the statistical properties of wave motion in atmospheric turbulence. In particular, the project focuses on several regimes where simplified description of waves can be derived, some of which are known to be widely applicable. They include the parabolic approximation, the white-noise approximation, and the radiative transfer limit. The goal is to formulate a mathematical framework to study the various approximations in a rigorous and unified way. The details of the solutions in the various approximations will be investigated, providing guides for the design of communications and imaging systems.Understanding of scalar and wave transport through atmospheric turbulence is essential for many important applications, including heat and contaminant transport, laser and wireless communications, remote sensing, and imaging. In the case of sound or optical wave propagation in the atmosphere, for instance, the wave speed undergoes random fluctuations determined by small-scale temperature and humidity fluctuations. This project develops a unified mathematical framework to address problems of scalar transport and wave propagation through turbulent media. The results of the research will contribute to the improvement of optical communications and imaging technologies.