  Collective cell migration plays a crucial role in many developmental
processes that underlie morphogenesis, wound healing, or cancer progression. In
such coordinated behaviours, cells are organised in coherent structures and
actively migrate to serve different biological purposes. In some contexts,
namely during epithelial wound healing, it is well known that a migrating
free-edge monolayer develops finger-like instabilities, yet the onset is still
under debate. Here, by means of theory and numerical simulations, we shed light
on the main mechanisms driving the instability process, analysing the linear
and nonlinear dynamics of a continuum compressible polar fluid. In particular,
we assess the role of cell polarisation, substrate friction, and contractile
stresses. Linear theory shows that it is crucial to analyse the perturbation
transient dynamics, since we unravel a plethora of crossovers between different
exponential growth rates during the linear regime. Numerical simulations
suggest that cell-substrate friction could be the mechanism responsible for the
formation of complex finger-like structures at the edge, since it triggers
secondary fingering instabilities and tip-splitting phenomena. Finally, we
obtain a critical contractile stress that depends on cell-substrate friction
and the initial-to-nematic length ratio, characterising an active
wetting-dewetting transition. In the dewetting scenario, the monolayer retracts
and becomes stable without developing finger-like structures.
