  The sensitivity and the frequency bandwidth of third-generation
gravitational-wave (GW) detectors are such that the Newtonian noise (NN)
signals produced by atmospheric turbulence could become relevant. We build
models for atmospheric NN that take into account finite correlation times and
inhomogeneity along the vertical direction, and are therefore accurate enough
to represent a reliable reference tool for evaluating this kind of noise. We
compute the NN spectral density from our models and compare it with the
expected sensitivity curve of the Einstein Telescope (ET) with the xylophone
design. The noise signal decays exponentially for small values of the frequency
and the detector's depth, followed by a power-law for large values of the
parameters. We find that, when the detector is built at the earth's surface,
the NN contribution in the low-frequency band is above the ET sensitivity curve
for strong wind. Building the detector underground is sufficient to push the
noise signal under the ET sensitivity curve, but the decrement is close to
marginal for strong wind. In light of the slow decay with depth of the NN,
building the detector underground could be only partially effective as passive
noise mitigation.
