Strongly nonlinear three-dimensional interactions between a roll-streak structure and a
Tollmien-Schlichting wave in plane Poiseuille flow are considered in this study. Equations
governing the interaction at high Reynolds number originally derived by Bennett, Hall
& Smith (J. Fluid Mech, vol. 223, 1991, pp. 475–495) are solved numerically. Travelling
wave states bifurcating from the lower branch linear neutral point are tracked to finite
amplitudes, where they are observed to localize in the spanwise direction. The nature of
the localization is analysed in detail near the relevant spanwise locations, revealing the
presence of a singularity which slowly develops in the governing interaction equations
as the amplitude of the motion is increased. Comparisons with the full Navier-Stokes
equations demonstrate that the finite Reynolds number solutions gradually approach the
numerical asymptotic solutions with increasing Reynolds number.