We study the mechanisms of centrifugal instability and its eventual self-limitation, as well as regenerative instability on a vortex column with a circulation overshoot (potentially unstable) via direct numerical simulations of the incompressible Navier–Stokes equations. The perturbation vorticity (
${\boldsymbol{\omega} }^{\prime } $
) dynamics are analysed in cylindrical (
$r, \theta , z$
) coordinates in the computationally accessible vortex Reynolds number,
$\mathit{Re}({\equiv }\mathrm{circulation/viscosity} )$
, range of 500–12 500, mostly for the axisymmetric mode (azimuthal wavenumber
$m= 0$
). Mean strain generates azimuthally oriented vorticity filaments (i.e. filaments with azimuthal vorticity,
${ \omega }_{\theta }^{\prime } $
), producing positive Reynolds stress necessary for energy growth. This
${ \omega }_{\theta }^{\prime } $
in turn tilts negative mean axial vorticity,
$- {\Omega }_{z} $
(associated with the overshoot), to amplify the filament, thus causing instability. (The initial energy growth rate (
${\sigma }_{r} $
), peak energy (
${G}_{\mathit{max}} $
) and time of peak energy (
${T}_{p} $
) are found to vary algebraically with
$\mathit{Re}$
.) Limitation of vorticity growth, also energy production, occurs as the filament moves the overshoot outward, hence lessening and shifting
$\vert {- }{\Omega }_{z} \vert $
, while also transporting the core
$+ {\Omega }_{z} $
, to the location of the filament. We discover that a basic change in overshoot decay behaviour from viscous to inviscid occurs at
$Re\sim 5000$
. We also find that the overshoot decay time has an asymptotic limit of 45 turnover times with increasing
$\mathit{Re}$
. After the limitation, the filament generates negative Reynolds stress, concomitant energy decay and hence self-limitation of growth; these inviscid effects are enhanced further by viscosity. In addition, the filament transports angular momentum radially inward, which can produce a new circulation overshoot and renewed instability. Energy decays at the
$\mathit{Re}$
studied, but, at higher
$\mathit{Re}$
, regenerative growth of energy is likely due to the renewed mean shearing. New generation of overshoot and Reynolds stress is examined using a helical (
$m= 1$
) perturbation. Regenerative energy growth, possibly resulting in even vortex breakup, can be triggered by this new overshoot at practical
$\mathit{Re}$
(
${\sim }1{0}^{6} $
for trailing vortices), which are currently beyond the computational capability.