  Viscous fingering patterns form in confined geometries at the interface
between two fluids as the lower-viscosity fluid displaces the one with higher
viscosity. Previous studies have examined the most unstable wavelength of the
patterns that form using both linear-stability analysis and the dynamics of
finger growth in the nonlinear regime. Interesting differences in dynamics have
been seen between rectilinear and radial geometries as well as between fluid
pairs that are immiscible (with interfacial tension) or miscible (with
negligible interfacial tension). This paper reports measurements of how all of
these systems transition from the linearly unstable regime to their late time,
nonlinear dynamics. In all four cases there is a region of stable or slow
growth characterized by an onset length scale before fingers enter the
late-time regime. For immiscible fluids in a rectilinear geometry this onset
length is consistent with linear-stability analyses. All other cases are not
adequately described by existing theory. In radial geometries, the onset length
predicted from theory is an order of magnitude smaller than what is
experimentally observed and has the incorrect scaling with dimensionless
numbers. For miscible fluids in a rectilinear geometry the onset length is
related to the development of steady-state structures within the confining
dimension and cannot be explained by quasi-two dimensional theories. By
combining the onset length with the finger growth rate measured after onset,
the global patterns that form well into the late-time dynamics can be
predicted.
