We have used 2D numerical simulations to study the evolution of galaxy cluster cooling flows undergoing a rotational perturbation. We show that such rotations in the intracluster medium may arise from cluster/subcluster mergers. Our galaxy cluster initial conditions involve spherically symmetric, steady-state cooling flows with varying mass-dropout strengths. The rotational perturbation serves to break the symmetry for each of the initial cooling flows, resulting in the formation of thin, gaseous disc-like structure extending radially out to ~10 kpc. Disc-like structure formed for low mass-dropout strength simulations appears to contain cooling condensations whereas disc-like structure in higher mass-dropout strength simulations appears smooth. This is due to the influence of mass-dropout on the degree of cooling, which serves to reduce the strength of thermal instabilities by the removal of `cold' gas from the flow. Morphological comparisons of the disc-like structure formed in our simulations are made to structure observed in the X-ray emitting gas of A4059. Comparisons of the gas dynamics within the disc-like structure are also made to the solid-body rotation profile observed from emission-line gas within the central galaxy of Hydra A. The influence of grid effects on the simulations is also discussed.