This study describes high-resolution numerical simulations of the evolution of an aircraft contrail and its transition into a contrail-cirrus. The contrail is modeled as a vortex pair descending in a stratified atmosphere where turbulent fluctuations are sustained in the late regime of diffusion. The focus of this study is laid on the three-dimensional vortex dynamics – including vortex instability and turbulence – and on the interaction between dynamics and microphysics and its role in determining the growth and the distribution of ice crystals. The results show the feasibility of three-dimensional simulations of the entire lifetime of a contrail until its transformation into a contrail-cirrus in supersaturated conditions. In particular, it is shown that the contrail-cirrus optical depth is maintained as the cloud expands, in agreement with available observations.