Solution for spin-up from rest of liquid with a free surface

Abstract

The problem of spin-up from rest of a liquid in a partially filled circular cylinder is considered, The Ekman number of the system, E = nu/Omega R(2), is much smaller than unity. Numerical solutions to the governing Navier-Stokes equations have been secured, The numerical results provide descriptions of the evolving free surface shape, as well as the time-dependent three-component (u, v, w) velocity field. Particular attention is given to the task of verifying the capabilities of the earlier analytical models. Numerical results for four prototypical flow configurations are examined. For all four cases, close agreement is noted in the free surface contour and azimuthal velocity field between the present numerical results and the predictions of the analytical model. Utilizing the numerical data, time-dependent meridional flowfields are depicted. These are consistent with the fundamental notions embedded in the analytical model, The present numerical study is supportive of the basic contentions of the model.