  Astronomical observations suggest that the Universe may be anisotropic on the
largest scales. In order to model this situation, we develop a new approach to
cosmology that allows for large-scale anisotropy to emerge from the growth of
non-linear structure. This is achieved by decomposing all relevant fields with
respect to a preferred space-like direction, and then averaging the resulting
scalar quantities over spatial domains. Our approach allows us to derive a set
of large-scale effective field equations that govern the dynamics of any
emergent large-scale anisotropy, and which (up to back-reaction terms) take the
form of the field equations of the locally rotationally symmetric Bianchi
cosmologies. We apply our approach to the dust-filled Farnsworth solutions,
which are an interesting set of exact cosmological models that allow for both
anisotropic expansion and large-scale bulk flow.
