Nulling interferometry, a powerful technique for high-resolution imaging of the close neighbourhood of bright astrophysical objets, is currently considered for future space missions such as Darwin or the Terrestrial Planet Finder Interferometer (TPF-I), both aiming at Earth-like planet detection and characterization. Ground-based nulling interferometers are being studied for both technology demonstration and scientific preparation of the Darwin/TPF-I missions through a systematic survey of

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... mstellar dust disks around nearby stars. In this paper, we investigate the influence of atmospheric turbulence on the performance of ground-based nulling instruments, and deduce the major design guidelines for such instruments. End-to-end numerical simulations allow us to estimate the performance of the main subsystems and thereby the actual sensitivity of the nuller to faint exozodiacal disks. Particular attention is also given to the important question of stellar leakage calibration. This study is illustrated in the context of GENIE, the Ground-based European Nulling Interferometer Experiment, to be installed at the VLTI and working in the L band. We estimate that this instrument will detect exozodiacal clouds as faint as about 50 times the Solar zodiacal cloud, thereby placing strong constraints on the acceptable targets for Darwin/TPF-I.