  Channel flow, the pressure driven flow between parallel plates, has exact
coherent structures that show various degrees of localization. For states which
are localized in streamwise direction but extended in spanwise direction, we
show that they are exponentially localized, with decay constants that are
different on the upstream and downstream side. We extend the analysis of Brand
and Gibson [J. Fluid Mech. 750, R1 (2014)] for stationary states to the case of
advected structures that is needed here, and derive expressions for the decay
in terms of eigenvalues and eigenfunctions of certain second order differential
equations. The results are in very good agreement with observations on exact
coherent structures of different transversal wave lengths.
