Secondary perturbations of Benjamin waves

The evolution of small two-dimensional perturbations of boundary flow in the region preceding the laminar-turbulent transition zone is investigated using a four-deck asymptotic model. It is assumed that the main flow is a two-dimensional boundary layer flow distorted by a wave of finite amplitude that is periodic in time and with a longitudinal coordinate. The problem is reduced to investigating the solutions of a linearized Benjamin-Ono equation, which describes secondary perturbations of a periodic Benjamin wave. The explicit expressions obtained for the structure of the perturbations confirm the neutral stability of the main flow with respect to two-dimensional perturbations. An exact solution of the problem of the passage of a Tollmien-Schlichting wave through a region perturbed by a solitary Benjamin wave is constructed by analysing the stability of the periodic.