  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.
