Extraction of the Essential Dynamics of Turbulent Flows and its Use for Predictive Purposes

本研究是基于涡流拉伸与相空间中畸变体元的几何性质之间的数学类比。后者可以用奇异吸引子及其指数增长率来描述。这些都涉及到分形。本文的研究是为了确定这种类比是否可以用来表示湍流涡度动力学的分形描述。研究者之前能够建立分形和湍流能量之间的联系。涡度的情况与湍流的物理机制更相关，因此可能会产生比目前可用的更简洁和紧凑的湍流动力学描述。

This research is based on mathematical analogy between vortex stretching and the geometric properties of distorted volume elements in phase space. The latter can be described by strange attractors and their exponential growth rates. These are known to involve fractals. The research is to establish whether this analogy can be used to show fractal descriptions of turbulent vorticity dynamics. The investigator was able previously to establish a connection between fractals and turbulent energy. The vorticity case is much more relevant to the physical mechanisms of turbulence, thus a much more concise and compact description for turbulence dynamics than presently available may result.