  Invariant solutions of shear flows have recently been extended from spatially
periodic solutions in minimal flow units to spatially localized solutions on
extended domains. One set of spanwise-localized solutions of plane Couette flow
exhibits homoclinic snaking, a process by which steady-state solutions grow
additional structure smoothly at their fronts when continued parametrically.
Homoclinic snaking is well understood mathematically in the context of the
one-dimensional Swift-Hohenberg equation. Consequently, the snaking solutions
of plane Couette flow form a promising connection between the largely
phenomenological study of laminar-turbulent patterns in viscous shear flows and
the mathematically well-developed field of pattern-formation theory. In this
paper we present a numerical study of the snaking solutions, generalizing
beyond the fixed streamwise wavelength of previous studies. We find a number of
new solution features, including bending, skewing, and finite-size effects. We
show that the finite-size effects result from the shift-reflect symmetry of the
traveling wave and establish the parameter regions over which snaking occurs. A
new winding solution of plane Couette flow is derived from a strongly skewed
localized equilibrium.
