McKay, Donald. "Front matter" Multimedia Environmental Models ...

no currents or eddies. In practice, of course, the environment is rarely stagnant, there
being currents and eddies induced by the motion of wind, water, and biota such as
fish and worms. This turbulent motion, illustrated in Figure 7.3, also promotes mixing
by conveying an element or eddy of fluid from one region to another. The eddies
may vary in size from millimetres to kilometres, and a large eddy may contain a
fine structure of small eddies. Intuitively, it is unreasonable for an eddy to penetrate
an interface, thus in regions close to interfaces, eddies tend to be damped, and only
slippage parallel to the interface is possible. There may, therefore, be a thin layer
of relatively quiescent fluid close to the interface that can be referred to as a laminar
sublayer. In this layer, movement of solute to and from the interface may occur only
by molecular diffusion.
Under certain conditions, eddies in fluids may be severely damped, or their
generation may be prevented. This occurs in a layer of air or water when the fluid
density decreases with increasing height. This may be due to the upper layers being
warmer or, in the case of sea water, less saline. An eddy that is attempting to move
upward immediately finds itself entering a less dense fluid and experiences a hydrostatic
“sinking” force. Conversely, a companion eddy moving downward experiences
a “floating” force, which also tends to restore it to its original position. This inherent
resistance to eddy movement damps out most fluid movement, and stable, stagnant
conditions prevail. Thermoclines in water and inversions in the atmosphere are
examples of this phenomenon. These stagnant or near-stagnant layers may act as
diffusion barriers in which only molecular diffusion or slight eddy diffusion can
occur. Conversely, situations in which density increases with height tend to be
unstable, and eddy movement is enhanced and accelerated by the density field.
An attractive approach is to postulate the existence of an eddy diffusivity, or a
turbulent diffusivity, B T, which is defined identically to the molecular diffusivity,
B M. The flux equation within a phase then becomes
©2001 CRC Press LLC
N = –A(B M + B T)dC/dy
The task is then to devise methods of estimating B T for various environmental
conditions. We expect that, in many situations, such as in winds or fast rivers, B T
Figure 7.3 The nature of turbulent or eddy diffusion in which chemical is conveyed in eddies
within a fluid to a surface.