  At equilibrium, the structure and response of ordered phases are typically
determined by the spontaneous breaking of spatial symmetries. Out of
equilibrium, spatial order itself can become a dynamically emergent concept. In
this article, we show that spatially anisotropic viscous coefficients and
stresses can be designed in a far-from-equilibrium fluid by applying to its
constituents a time-modulated drive. If the drive induces a rotation whose rate
is slowed down when the constituents point along specific directions,
anisotropic structures and mechanical responses arise at long timescales. We
demonstrate that the viscous response of such anisotropic driven fluids can
acquire a tensorial, dissipationless component called anisotropic odd (or Hall)
viscosity. Classical fluids with internal torques can display additional
components of the odd viscosity neglected in previous studies of quantum Hall
fluids that assumed angular momentum conservation. We show that these
anisotropic and angular momentum-violating odd-viscosity coefficients can
change even the bulk flow of an incompressible fluid by acting as a source of
vorticity. In addition, shear distortions in the shape of an inclusion result
in torques.
