Dynamic and Geometric Complexity
Complex fluid flow and heat/mass transfer problems encountered in natural and human-made environments are characterized by both geometric and dynamic complexity. For example, the geometric configuration of a jet engine, a heart, or a crystal growth device is irregular; to analyze the heat and fluid flow in these devices, geometric complexity is a major issue. From the analytical point of view, dynamic complexity is a well-established characteristic of fluid dynamics and heat/mass transfer. The combined influence of dynamic and geometric complexities on the transport processes of heat, mass, and momentum is the focus of the present work. A computational framework, including both numerical and modeling approaches, will be presented to tackle these complexities. In this chapter, we will first present basic background to help identify the issues involved and to highlight the state of our current knowledge.
Dynamic complexity results from the disparities of the length, time, and velocity scales caused by the presence of competing mechanisms, such as convection, conduction, body forces, chemical reaction, and surface tension; these mechanisms are often coupled and nonlinear. A case in point is the classical boundary layer theory originated by Prandtl (Schlichting 1979, Van Dyke 1975), whose foundation is built on the realization that the ratio of viscous and convective length and time scales can differ by orders of magnitude for high Reynolds number flows.