回転円柱を過ぎる粘性流体の流れ

抄録

Two-dimensional flow of an incompressible viscous fluid past a rotating circular cylinder placed symmetrically in a uniform flow is considered theoretically using Oseen's approximation for small values of Reynolds numbers. The expansion formulae for the stream function and the vorticity are obtained up to the fourth power, O(Re⁴), of the Reynolds number and it is shown that the flow patterns calculated by these expansion formulae agree even in the neighborhood of an object with those as predicted by the numerical solutions to the Navier-Stokes equations in the range of the small Reynolds numbers. Furthermore, flow near a circular cylinder is investigated in detail. The expansion formulae for the lift, the moment and the pressure distributions on a circular cylinder are obtained up to O(Re²), O(Re³) and O(Re²), and it is confirmed that the results of these expansion formulae agree with those of the numerical solutions to the Navier-Stokes equations.