Vortices are important because they are an intrinsic feature of the most damaging storms that occur on earth: hurricanes and tornadoes. Also, vortices are an interesting example of nonlinear interaction between a rotating flow and the structure that spontaneously develops due to the dynamic constraint imposed by the Proudman–Taylor theorem.

This chapter begins in the following section with a survey of various types of vortices and a brief discussion of their dynamics. The equations governing axisymmetric vortices are introduced in § 28.2, then two simple vortices are investigated in § 28.3. These simple vortices are the basis for the more realistic models that are developed in § 28.4. Finally in § 28.5 we briefly discuss hurricanes and consider their efficiency in converting heat to kinetic energy.

Survey of Vortices

A vortex is a swirling mass of fluid; it is a three-dimensional structure in which fluid flows roughly symmetrically about an axis. There are many kinds of atmospheric vortices, ranging in size and strength from the flow at a street corner that rustles leaves around in a circle to hurricanes that devastate coastlines. On the other hand, only one type of vortex occurs in water: the whirlpool.

Vortices may be categorized as either barotropic or baroclinic. These two types are discussed in the following subsections.

Barotropic Vortices

Barotropic vortices arise as a nonlinear consequence of the instability of a basic-state shear. They often are abetted by topography and are distinguished from baroclinic vortices by the lack of a source of energy other than the kinetic energy of the flow. A familiar example of a barotropic vortex is that generated as wind blows past a building. A down-wind corner of the building is a singular point in the flow-field, where flow separation occurs, with a weak vortex forming in the lee of the building.

Whirlpools – vortices in water – commonly form in rivers and near narrow channels that have strong tidal flows by the same mechanism: flow separation at an irregular boundary, with the whirlpool being a region of strong re-circulation in the lee of the obstacle; they rarely occur in open waters.