  The recent theoretical discovery of families of travelling wave solutions in
pipe flow at Reynolds numbers lower than the transitional range naturally
raises the question of their relevance to the turbulent transition process.
Here a series of numerical experiments are conducted in which we look for the
spatial signature of these travelling waves in transitionary flows. Working
within a periodic pipe of 5D (diameters) length, we find that travelling waves
with low wall shear stresses (lower branch solutions) are on a surface which
separates initial conditions which uneventfully relaminarise and those which
lead to a turbulent evolution. Evidence for recurrent travelling wave visits is
found in both 5D and 10D long periodic pipes but only for those travelling
waves with low-to-intermediate wall shear stress and for less than about 10% of
the time in turbulent flow. Given this, it seems unlikely that the mean
turbulent properties such as wall shear stress can be predicted as an expansion
over the travelling waves in which their individual properties are
appropriately weighted. Rather, further dynamical structures such as periodic
orbits need to be isolated and included in any such expansion.
