  A comprehensive and detailed overview of the flow topology over a cambered
NACA 65(1)-412 airfoil at Re = 20,000 is presented for angles of attack ranging
from 0{\deg} to 10{\deg} using high-order direct numerical simulations. It is
shown that instabilities bifurcate the flow and cause it to change at a
critical angle of attack from laminar separation without reattachment over a
laminar separation bubble at the trailing edge to a bubble at the leading edge.
The transition of the flow regimes is governed by the Karman vortex shedding of
the pressure side boundary layer at the trailing edge, Kelvin-Helmholtz
instabilities within the separated shear layer on the suction side, as well as
three-dimensional instabilities of elliptic flow within the vortex cores and
hyperbolic flow in the shear layer between subsequent Karman vortices. As the
suction side shear layer transitions and reattaches, the interaction of the two
and three-dimensional instabilities results in three-dimensional tubular
structures and large-scale turbulent puffs. The formation and shifting of the
laminar separation bubble defines the far-wake topology several chord-lengths
behind the airfoil and is accompanied by a sudden increase of the lift force
and decrease in the drag that underscores the sensitive nature of low-Reynolds
number airfoil aerodynamics. Lift and drag polars are presented for direct
numerical simulations, wind tunnel experiments, and simplified numerical
procedures where incorrect prediction of the force coefficients is caused by
the failure to correctly model the low-pressure region at the trailing edge
that is caused by the time-dependent generation of the Karman vortices.
