To develop a further understanding of the significance of (11.21), we approximate the Reynolds stress through the eddy-viscosity hypothesis

(12.1)

The eddy viscosity is scaled with a characteristic velocity scale and a characteristic length scale, which gives.

(12.2)

We further assume that is nearly independent of , then

(12.3)

It is to be remembered that equation (12.2) is a scaling law, not quite an equation. Because of the fact that (equation 11.16), the above relation may be written as

(12.4)

We now turn to the estimation of the order of magnitude of the terms on the rhs of equation (11.21). We assume that the transport of mean vorticity is similar to that of the mean momentum. Thus

(12.5)

We are unable to use a similar approach to estimate since for this flow. However, by comparing (12.1), (12.3) and (12.5)

(12.6)

Thus is associated with a change of length scale. It is usually called the vortex stretching force and is associated with the change in the size of eddies.

The relative contributions of and depend on the kind of flow considered. If "l" is approximately constant across the flow, vortex stretching is negligible. In such a situation vorticity transport dominates. Jets and wakes are the examples.

On the otherhand if "l" changes with , vorticity transport alone is inadequate to explain the transport stress.