  We demonstrate dynamic stabilisation of axisymmetric Fourier modes
susceptible to the classical Rayleigh-Plateau (RP) instability on a liquid
cylinder by subjecting it to a radial oscillatory body force. Viscosity is
found to play a crucial role in this stabilisation. Linear stability
predictions are obtained via Floquet analysis demonstrating that RP unstable
modes can be stabilised using radial forcing. We also solve the linearised,
viscous initial-value problem for free-surface deformation obtaining an
equation governing the amplitude of a three-dimensional Fourier mode. This
equation generalises the Mathieu equation governing Faraday waves on a cylinder
derived earlier in Patankar et al. (2018), is non-local in time and represents
the cylindrical analogue of its Cartesian counterpart (Beyer & Friedrich 1995).
The memory term in this equation is physically interpreted and it is shown that
for highly viscous fluids, its contribution can be sizeable. Predictions from
the numerical solution to this equation demonstrates RP mode stabilisation upto
several hundred forcing cycles and is in excellent agreement with numerical
simulations of the incompressible, Navier-Stokes equations.
