  We present a hydrodynamic model of spreading epithelial monolayers as polar
viscous fluids, with active contractility and traction on the substrate. The
combination of both active forces generate an instability that leads to
nonlinear traveling waves, which propagate in the direction of polarity with
characteristic time scales that depend on contact forces. We show that a
viscous fluid model explains a variety of observations on the slow dynamics of
epithelial monolayers, in particular those that had been interpreted before as
signatures of elasticity. The non-elastic nature of the waves can be tested on
the basis of simple predictions of the model. Our theoretical framework
provides new insights such as the interpretation of plithotaxis as a result of
a strong flow-polarity coupling, and the quantification of collective
force-transmission of cells in terms of the non-locality of interactions. In
addition, we study the nonlinear regime of those waves deriving an exact map of
the model into the Complex Ginzburg-Landau equation, which provides a complete
classification of possible nonlinear scenarios. In particular, we predict the
transition to different forms of weak turbulence, which in turn could explain
the very unstable and irregular dynamics often observed in epithelia.
