E. Minkov et al., The motion generated by a rising particle in a rotating fluid - numerical solutions. Part 1. A short container, J FLUID MEC, 413, 2000, pp. 111-148
Numerical finite-difference results of the full axisymmetric incompressible
Navier-Stokes equations are presented for the problem of the slow axial mo
tion of a disk particle in an incompressible, rotating fluid in a cylindric
al container. The governing parameters are the Ekman number, E, the Rossby
number, Ro, and the dimensionless height of the container, H (with respect
to the diameter of the particle). The study concerns small values of E, Ro,
and HE-1/2 and compares the numerical results with predictions of previous
analytical (mostly approximate) studies. Special attention is focused on t
he drag force. First, developed (quasi-steady state) cases are considered.
Excellent agreement with the exact linear (Ro = 0) solution of Ungarish & V
edensky (1995) is obtained when the computational Ro = 10(-4). The effects
of the nonlinear momentum advection terms are analysed and shown to be prop
ortional to RoE(-1/2) Next, the time-development for both (a) impulsive sta
rt and (b) start under a constant axial force are considered, and good qual
itative agreement with previous analytical results (including the appearanc
e of oscillations in case (b)) is indicated.