Axial velocity deficit is a source of instability in vortices that may otherwise be stable. Temporal large‐eddy simulation is performed to study the response of vortices with axial velocity deficits to random and controlled disturbances at high Reynolds numbers. The qvortex [Batchelor, J. Fluid Mech. 20, 321 (1964)] is used as a model of such vortices. When the vortex is linearly unstable, the disturbances grow and result in the appearance of large‐scale helical sheets of vorticity. Later, these large‐scale helical structures break up into small‐scale filaments. Associated with the formation of the large‐scale structures is a redistribution of both angular and axial momentum between the core and the surroundings. The redistribution weakens the axial velocity deficit in the core while strengthens the rigid‐body‐like rotation of the core. The emerging mean velocity profiles drive the vortex core to a stable configuration. The vortex eventually returns to a laminar state, with an insignificant decay in the tangential velocity, but with a much weakened axial velocity deficit. A direct numerical simulation obtained at a lower Reynolds number confirms the above conclusions.