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Figure 16.6 Contours of the ratio of distorted kinematic Reynolds stre ss u 1 u 3 and
the free-stream value for flow upstream of the shaded circular cylinder. u 1 /u 2
=
9,
u 3 /u 2
u 2
=
4 , with
the free-stream value of u 1 u 3 .From Wyngaard ( 1981 ).
probe to be vertically symmetric about its horizontal midplane. He showed also that
the flow-blocking effect due to probe bulk causes the scalar flux to be overestimated,
but this can be minimized in an array with minimal stagnation loss in streamwise
speed at the flux-measurement point.
16.3.2 Conserved scalars
Conserved scalar fields are also affected by flow distortion, but in ways that depend
on the nature of the velocity field. We'll consider three limits here.
16.3.2.1 Steady laminar flow
A conserved scalar C is released at a variable rate from a source in a steady,
divergence-free, laminar velocity field. We measure the scalar downstream with a
sensor that induces flow distortion. How does this influence the measured C signal?
We assume that in the flow-distortion process we can neglect molecular diffusion,
so we can write
DC
Dt =
∂C
∂t +
U j C ,j
=
0 ,
(16.92)
 
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