Parametric oscillations and the transition to turbulence in laminar flows

A new type of analytic expansion for use in stability calculations is presented and applied to the question of the stability of laminar solutions of the Navier-Stokes equation. This leads in a natural way to a model of the transition from laminar to turbulent flow as an effect of parametric instabilities. The parametric instabilities occur because of the symmetry breaking involved in the presence of a Tollmien-Schlichting wave. Recent experiments and numerical simulations are then shown to be in accordance with this model