A bypass scenario of laminar-turbulent transition in the wind-driven free-surface boundary layer
Résumé
The work is concerned with the theoretical and experimental study of laminar-turbulent transition in the wind induced boundary layer in water beneath the free surface. The mechanism of this transition has not been identified yet and the present work is aimed to fill this gap. The experiments in the wave tank showed that the first perturbations which emerge out of natural primordial noise are long compared to the boundary layer thickness, then they gradually grow, become more nonlinear until suddenly a strong localised instability occurs. This instability results in almost immediate breakdown of the laminar boundary layer and formation of localised 3D turbulent spots. The spots slowly expand downstream forming turbulent streaks having the shape of upstream pointed arrowheads marked by the wind generated capillary-gravity waves on the water surface. The streaks merge further downstream creating basin-wide turbulence zone. The notable feature of the observed transition is that there is no universal critical Reynolds number, although the results are reproducible for the same values of wind. The critical distance Xc where the turbulent spots first appear is found to be inversely proportional to the wind stress at the surface. The theoretical study begins with the classical linear stability analysis carried out within the framework of Orr-Sommerfeld equation with the appropriate boundary conditions. In contrast to classical wall boundary layers, there are no linearly unstable modes. An analysis of weakly-nonlinear evolution of decaying perturbations under some unrestrictive assumptions suggests an unusual bypass scenario based on the explosive transverse instability of solitary waves as a plausible mechanism for the transition.