Vorticity and Vortex Dynamics in Complex Turbulent Flows

Abstract

Some of the basic principles of vortex dynamics arc reviewed in this paper and applied to calculating and understanding various kinds of turbulent flows. After setting out the basic equations and boundary conditions, the different principles are illustrated for special eases where different simplifications are justified. The displacement of two-dimensional vorticity is applied to two-dimensional shear flows over slender shapes (such as humps or hills on surfaces where the ‘triple-deck’ method is explained in terms of vorticity). The general changes of vorticity and velocity are related to the movement of fluid-line elements. A new geometrical proof for the changes in velocity is given. These concepts are applied to distorted turbulent flows (isotropic and anisotropic) and shear flows. Recent results on the forces on and motions of finite fluid volumes in rotational, non-uniform flows are reviewed and it is shown that the inertial or added mass effects are generally of greater importance than the distortion of the vorticity field. This gives some new insight into Prandtl’s mixing length theory. A simple class of interaction between vortices is reviewed to illustrate how the interactions differ depending on the relative strengths of the vortices. Finally, some new ideas are reviewed on vorticity shed from surfaces and how this interacts with vorticity advected onto a body from upstream.