Comments on ''three-dimensional effects in viscous wakes.'

T note clarifies a definition used by Steiger and Bloom to characterize viscous wake dimensions In Ref 1 and earlier publications, 3 an Oseen approximation of the boundary-layer equations was used to calculate the asymptotic wake growth Physically, the analysis would be expected to be more exact in the far downstream region of the wake, but several predictions of Ref 1 are unrealistic in this region This problem is discussed first Then a numerical example is presented in which four undetermined constants of the analysis are evaluated from data of an incompressible, turbulent wake The following is a definition of a viscous layer thickness used in Ref 1: in the plane z = 0, y = 5i; and in the plane y = 0, z = 62 when u = 0 99 ue These definitions are introduced at Eq (26) The viscous wake width in the y = 0 plane has been calculated from Eq (33b) (corrected for typographical error) and is shown in Fig 1 as a function of the transformed axial coordinate s The round-off error introduced by u = 0 99 ue causes the wake widths 52 for all eccentricities e to approach — • oo The error introduced in Ref 1 by the term ln{lOO[(^e — Uo)/ue]} in Eqs (26a, 29, 30, 33a, 33b, 34, and 40) and in Fig 4 is appreciable for all values of s The equation numbers and nomenclature are those of Ref 1 To avoid this numerical problem, it is preferable to define the wake dimensions in terms of the defect velocity u — ue — u That is, in the plane z = 0, y = 81; and in the plane y = 0, z = 52 when u = 0 01 (ue — UQ), where UQ is the local wakecenterline velocity Then in all of the equations just mentioned the correct logarithmic term becomes simply In {100} With this correction, the predicted asymptotic wake characteristics are in accord with data for incompressible, turbulent wakes Furthermore, the algebraic complexity of the analysis is reduced Equation (27) (for pe = p = const) can now be combined with Eqs (33b, 38, and 39) to yield an explicit relation between the wake dimension 52 and the

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