Abstract
Publisher Summary This chapter focuses on vorticity dynamics on boundaries. One of the central problems in vorticity and vortex dynamics is the interaction of vorticity field and boundaries. The boundary can be a rigid wall, a flexible solid wall, or an interface of two different fluids. Boundaries are the most basic source of vorticity (in particular, the unique source for incompressible flow of a homogeneous fluid in a conservative external body-force field), and the whole life of a vortex usually begins at a boundary. Due to the continuous creation of vorticity from boundaries, a bounded vortical flow is much more complicated than an unbounded flow, in particular in the regions near the boundary. This chapter presents a unified general theory of the vorticity dynamics on various boundaries for viscous compressible flows and then reviews its applications to specific problems mainly confined to incompressible flows. Two types of boundaries are considered in the chapter: a solid boundary, either rigid or flexible; and an interface of two immiscible fluids. Both are regarded as sharp material surfaces. Some other boundaries, such as a porous wall, regrettably are omitted, though they are also important in practice. The chapter also briefly reviews the development of boundary vorticity dynamics.
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