  The recent theoretical discovery of finite-amplitude travelling waves in pipe
flow has re-ignited interest in the transitional phenomena that Osborne
Reynolds studied 125 years ago. Despite all being unstable, these waves are
providing fresh insight into the flow dynamics. Here we describe two new
classes of highly-symmetric travelling waves (possessing rotational,
shift-&-reflect and mirror symmetries) and report a new family of
mirror-symmetric waves which is the first found in pipe flow not to have
shift-&-reflect symmetry. The highly-symmetric waves appear at lower Reynolds
numbers than the originally-discovered non-mirror-symmetric waves found by
Faisst & Eckhardt 2003 and Wedin & Kerswell 2004 and have much higher wall
shear stresses. The first M-class comprises of the various
discrete-rotationally-symmetric analogues of the mirror-symmetric wave found in
Pringle & Kerswell (2007) and have a distinctive double layer structure of fast
and slow streaks across the pipe radius. The second N-class has the more
familiar separation of fast streaks to the exterior and slow streaks to the
interior and looks the precursor to the class of non-mirror-symmetric waves
already known.
