Turbulence generated by large-scale motions during structure formation affects the evolution of the thermal and non-thermal components of the intracluster medium. As enstrophy is a measure of the magnitude of vorticity, we study the generation and evolution of turbulence by analysing the Lagrangian history of enstrophy. For this purpose, we combine cosmological simulations carried out with the ENZO code with our Lagrangian post-processing tool CRATER. This way we are able to quantify the individual source terms of enstrophy in the course of the accretion of groups on to galaxy clusters. Here, we focus on the redshift range from z = 1 to z = 0. Finally, we measure the rate of dissipation of turbulence and estimate the resulting amplification of intracluster magnetic fields. We find that compressive and baroclinic motions are the main sources of enstrophy, while stretching motions and dissipation affect most of the ensuing enstrophy evolution. The rate of turbulent dissipation is able to sustain the amplification of intracluster magnetic fields to observed levels.