Effect of straining on an isolated wake

The effect of an external straining flow on a laminar wake caused by other bodies is illustrated with linearised calculations (see Fig. 7.2b). Consider a point source of momentum in a planar linear straining flow, 

Equation (7.12) admits similarity solutions of the form oj(r,y) = Q(r)m(y) where y = y/Y(r) (see Hunt Eames [294]) and the characteristic vorticity and lengthscales 

In the absence of strain (P = 0), Q = Qo is conserved. But straining flows may either reduce or increase the volume flux (for p 0, 0 respectively). For fi 0, the reduction of the volume flux generates a flow equivalent to a line distribution of sources of strength m = -d 2/dx( 0) contributing a dipole component to the flow, in addition to that described by (7.7). The flow induced by the wake is 

The total dipole strength induced by a rigid body in a straining flow is approximately the sum of (7.7) and (7.17). The relationship between drag and volume flux is now no longer valid for when the wake vorticity is partially or completely annihilated, and is now determined by the local strain rate through 

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