  Plane Couette flow transitions to turbulence for Re~325 even though the
laminar solution with a linear profile is linearly stable for all Re (Reynolds
number). One starting point for understanding this subcritical transition is
the existence of invariant sets in the state space of the Navier Stokes
equation, such as upper and lower branch equilibria and periodic and relative
periodic solutions, that are quite distinct from the laminar solution. This
article reports several heteroclinic connections between such objects and
briefly describes a numerical method for locating heteroclinic connections.
Computing such connections is essential for understanding the global dynamics
of spatially localized structures that occur in transitional plane Couette
flow. We show that the nature of streaks and streamwise rolls can change
significantly along a heteroclinic connection.
