  Numerical simulations of atmospheric turbulence and AO wavefront correction
are performed to investigate the timescale for fringe motion in optical
interferometers with spatial filters. These simulations focus especially on
partial AO correction, where only a finite number of Zernike modes are
compensated. The fringe motion is found to depend strongly on both the aperture
diameter and the level of AO correction used. In all of the simulations the
coherence timescale for interference fringes is found to decrease dramatically
when the Strehl ratio provided by the AO correction is <~30%. For AO systems
which give perfect compensation of a limited number of Zernike modes, the
aperture size which gives the optimum signal for fringe phase tracking is
calculated. For AO systems which provide noisy compensation of Zernike modes
(but are perfectly piston-neutral), the noise properties of the AO system
determine the coherence timescale of the fringes when the Strehl ratio is
<~30%.
