Unsteady Boundary Layers : 3rd Report, Boundary Layer on a Circular Cylinder in Rotational Oscillation

A method of calculating the fluctuating boundary layer on a circular cylinder, performing rotational oscillation in a uniform flow, is presented. Two-dimensional, laminar flow of an incompressible fluid is assumed. Equation of motion is linearized on the assumption that the velocity fluctuation in the boundary layer is small. The frequency of the fluctuation is also assumed rather low, thus retaining terms up to the first order in frequency. By extending the Blasius'series method to unsteady flow, solutions are expressed as linear combinations of a family of universal functions. As an example, the torque fluctuation of the cylinder is calculated. Streamline patterns near the separation point of the boundary layer are calculated, by observation of which a new criterion of the separation of the unsteady boundary layer is proposed. It is based on the asymptotic behavior, at a large distance from the solid wall, of the streamlines.