Turbulence and the dynamics of coherent structures. II. Symmetries and transformations

Introduction. The accurate determination of coherent structures depends upon having a sufficiently large database. As we will see in this part, symmetry considerations can considerably extend the amount of available data. In addition, a priori consideration of symmetries can be significant in designing numerical or physical experiments. In the following we outline, on a case by case basis, and sometimes only in brief, the effect of such deliberations for a number of standard geometries. We then show how such data can be transformed for use in related geometries.