Reply by Author to P. Bradshaw and V.C. Patel

Abstract

RADSHAW and PateFs comments are most cogent. The comparison of hypotheses for the mean velocity profile in turbulent axisymmetric flow along a cylinder given in Ref. 1, though correct, did not include the general hypothesis discussed by Bradshaw or, otherwise viewed, failed to define the most likely form of the hypothesis.! It is this modified hypothesis cited by Bradshaw (hereafter called the localsimilarity hypothesis), apart from inessential complications, that was applied to cylindrical flows in Refs. 2 and 3. As defined in Ref. 1, the derivative hypothesis corresponded, in the logarithmic range, to a ratio of shear stress to eddy viscosity given by (i/p)/e = Av^/y(l + y/a). Though, as stated by Bradshaw, this hypothesis corresponds to his Eq. (6) with T = rw/(l + y/a)2,it likewise corresponds—perhaps more sensibly though equally invalidly—to T = iw/(l+y/a) but with e = Ky(iw/p)1/2 instead of e = Ky(i/p)1/2, i.e., with the eddy velocity scale assumed equal to its value at the wall instead of proportional to local shear-stress velocity. The local-similarity hypothesis, we note, implies an eddy viscosity given by