A vortex is a rotating region of fluid such as, for example, a tornado or a whirlpool. These vortices are generally created at a moving boundary due to the shear resulting from the no slip condition, but can also result from thermal circulation. In general, vortices move with the fluid and are dispersed by the action of viscosity. One feature of vortices is that their axes can only terminate at solid boundaries, though they can form closed toroidal loops. Properties of vortices are discussed in Paterson (1983) and Kay and Nedderman (1985).
Two simple examples of vortices are the free vortex and the forced vortex. A free vortex is one in which the azimuthal component of velocity, vф, is inversely proportional to the distance from the axis of rotation, i.e., vф ∞ 1/r. In this case, the vorticity is zero everywhere as is illustrated in Figure 1a which shows a fluid element moving in such a flow. Of course, in practice, such a flow cannot exist exactly as it would imply an infinite velocity at the axis. Figure 1b shows the case of a forced vortex, for which vф ∞ r. This type vortex has the property that the vorticity is constant everywhere and equal to twice the angular velocity. Real vortices can often be represented approximately by an inner core which is a fixed vortex, and an outer region where the velocity profile is as for a free vortex—this is known as a Rankine vortex.
An example of a situation in which vortices are generated is that of flow past a cylinder. Figure 2a shows the presence of two counter rotating vortices behind the cylinder. At higher flow speeds, the vortices become detached and leave the cylinder. This is known as vortex shedding and vortices depart from alternate sides of the cylinder, producing a von Kármán vortex street. A schematic illustration of the streamlines (in a frame of reference moving with the mean fluid flow) is given in Figure 2b.
Vortices are also shed from aerofoils. In this case, the vortices combine to form two trailing vortices, which extend from the ends of the aerofoil. This is an important effect in maintaining the lift on an aeroplane. (See also Crossflow.)
Further information on vortices can be found in Massey (1989) and Acheson (1990).
Acheson, D. J. (1990) Elementary Fluid Dynamics, Oxford University Press, New York.
Kay, J. M. and Nedderman, R. M. (1985) Fluid Mechanics and Transfer Processes, Cambridge University Press, Cambridge.
Massey, B. S. (1989) Mechanics of Fluids, Van Nostrand Reinhold, London.
Paterson, A. R. (1983) A First Course in Fluid Dynamics, Cambridge. University Press, Cambridge.