  Visibility scintillation resulting from wave propagation through the
turbulent ionosphere can be an important sources of noise at low radio
frequencies ($\nu\lesssim 200$ MHz). Many low frequency experiments are
underway to detect the power spectrum of brightness temperature fluctuations of
the neutral-hydrogen $21$-cm signal from the Epoch of Reionization (EOR:
$12\gtrsim z\gtrsim 7$, $100\lesssim \nu \lesssim 175$ MHz). In this paper, we
derive scintillation noise power-spectra in such experiments while taking into
account the effects of typical data processing operations such as
self-calibration and Fourier synthesis. We find that for minimally redundant
arrays such as LOFAR and MWA, scintillation noise is of the same order of
magnitude as thermal noise, has a spectral coherence dictated by stretching of
the snapshot $uv$-coverage with frequency, and thus is confined to the well
known wedge-like structure in the cylindrical ($2$-dimensional) power spectrum
space. Compact, fully redundant ($d_{\rm core}\lesssim r_{\rm F} \approx 300$ m
at $150$ MHz) arrays such as HERA and SKA-LOW (core) will be scintillation
noise dominated at all baselines, but the spatial and frequency coherence of
this noise will allow it to be removed along with spectrally smooth
foregrounds.
