Analysis of Linear Viscous Flow with a Free Surface in a Circular Cylinder Subjected to Small-Amplitude Circular Oscillations

Abstract

A fluid flow with a free surface inside a circular cylinder subjected to horizontal, circular oscillation was analyzed theoretically and numerically under the assumption of small-amplitude oscillation and high Reynolds number. It was shown that the nature of the oscillatory flow is of a standing-wave type when projected onto the axial plane and of a progressive-wave type when projected onto the azimuthal plane. The Stokes drift motion in the azimuthal direction and the steady streaming velocity at the edge of the bottom- and side-wall boundary layers are then used in the numerical computation for the steady axisymmetric recirculatory flow outside the boundary layers. We have found that the solutions can be well predicted by asymptotic analysis for the full Navier–Stokes equations in the low streaming-Reynolds-number limit. A simple experiment on flow visualization revealed a good agreement in the surface flow pattern on the bottom wall. It also provided steady recirculatory flows that were not much different from the numerical results on the whole.