As part of a series of papers aimed at understanding the evolution of the Milky Way ’ s Central Molecular Zone ( CMZ ) , we present hydrodynamical simulations of turbulent molecular clouds orbiting in an accurate model of the gravitational potential extant there . We consider two sets of model clouds differing in the energy content of their velocity fields . In the first , self–virialised set , the turbulent kinetic energies are chosen to be close in magnitude to the clouds ’ self–gravitational potential energies . Comparison with isolated clouds evolving without an external potential shows that the self–virialised clouds are unable to withstand the compressive tidal field of the CMZ and rapidly collapse , forming stars much faster and reaching gas exhaustion after a small fraction of a Galactocentric orbit . In the second , tidally–virialised , set of simulations , the clouds ’ turbulent kinetic energies are in equilibrium with the external tidal field . These models are better supported against the field and the stronger turbulence suppresses star formation . Our results strongly support the inference that anomalously low star formation rates in the CMZ are due primarily to high velocity dispersions in the molecular gas . The clouds follow open , eccentric orbits oscillating in all three spatial coordinates . We examine the consequences of the orbital dynamics , particularly pericentre passage , by performing companion simulations of clouds on circular orbits . The increased tidal forces at pericentre produce transient accelerations in star formation rates of at most a factor of 2.7 . Our results demonstrate that modelling star formation in galactic centres requires the inclusion of tidal forces .