  We assess the dominant low-redshift anisotropic signatures in the
distance-redshift relation and redshift drift signals. We adopt
general-relativistic irrotational dust models allowing for gravitational
radiation -- the `quiet universe models' -- which are extensions of the silent
universe models. Using cosmological simulations evolved with numerical
relativity, we confirm that the quiet universe model is a good description on
scales larger than those of collapsing structures. With this result, we reduce
the number of degrees of freedom in the fully general luminosity distance and
redshift drift cosmographies by a factor of $\sim 2$ and $\sim 2.5$,
respectively, for the most simplified case. We predict a dominant dipolar
signature in the distance-redshift relation for low-redshift data, with
direction along the gradient of the large-scale density field. Further, we
predict a dominant quadrupole in the anisotropy of the redshift drift signal,
which is sourced by the electric Weyl curvature tensor. The signals we predict
in this work should be tested with present and near-future cosmological
surveys.
