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This paper presents the in-line force coefficients for circular cylinders in planar oscillatory flows of small amplitude. The results are compared with the theoretical predictions of Stokes (1851) and Wang (1968). For two-dimensional, attached- and laminar-flow conditions the data are, as expected, in good agreement with the Stokes–Wang analysis. The oscillatory viscous flow becomes unstable to axially periodic vortices above a critical Keulegan–Carpenter number K ( K = U m T / D , U m = the maximum velocity in a cycle, T = the period of flow oscillation, and D = the diameter of the circular cylinder) for a given β (β = Re / K = D 2 / vT , Re = U m D / v , and v = the kinematic viscosity of fluid) as shown experimentally by Honji (1981) and theoretically by Hall (1984). The present investigation has shown that the Keulegan—Carpenter number at which the drag coefficient Cd deviates rather abruptly from the Stokes—Wang prediction nearly corresponds to the critical K at which the vortical instability occurs.
Turgut Sarpkaya (Tue,) studied this question.