Axisymmetric damped natural frequencies in a slowly spinning cylindrical container filled with viscous liquid

The axisymmetric fundamental natural damped frequency of the free surface in a slowly rotating cylindrical container is determined for incompressible viscous liquid. It was found that with increasing liquid height ratio h/a oscillation frequencies and decay magnitude both exhibit increased values. The influence of the surface tension parameter σ* = σa/qv2 shows for increasing magnitude increasing oscillation frequencies and decreasing decay magnitudes. For increasing Bond number Bo the oscillation frequency increases while the decay magnitude decreases. The effect of increasing the spin parameter ω0 = Ω0a2/v is manifested by an increase of the oscillation frequency and decay magnitude, i.e. for faster spin a liquid disturbance decays faster with larger oscillation frequency.