Exact coherent states of attached eddies in channel flow

Exact coherent states in shear flows take the form of a travelling wave, and their unstable manifolds are believed to form a skeleton for the dynamics of turbulence. We present a new set of exact coherent states that we have numerically continued up to Re=30000, and which show several properties associated with Townsend's attached eddy hypothesis. These states are wall-attached, show self-similar scaling with spanwise wavelength, and asymptotic scaling with wall-units as Re is increased. For large Re these states appear via a saddle-node bifurcation with spanwise wavelength $L_z^+\approx 50$ and phase speed $c^+\approx 11$. These results suggest that as Re is increased, new sets of self-sustaining structures are born in the near-wall region, while those that emerged earlier continue into self-sustaining structures in the logarithmic region.