Non-linear interactions of localized disturbances. A new route to turbulence
Résumé
The transition scenario related to the disturbance growth on time scales significantly shorter than typical Tollmien-Schlichting (TS) waves that ‘by-passes’ the spatial and temporal development of the two-dimensional disturbances and their inherent secondary instabilities is the subject of this investigation. The set-up of three-dimensionality leads to the achievement of finite amplitudes and of the non-linear effects. They can mainly be generated by local surface irregularities such as roughness. This scenario has been investigated in detail in the past both in internal and external flows for single localized perturbations. It is well known since a while that there is a large structural similarity between a turbulent spot and developed turbulence in wall layers. One of the key problems in wall turbulence is the generation of Reynolds stress producing eddies. There are a multitude of different hypothesis and conjunctures advanced so far, but most of them are contradictory with observed experimental results. The destabilization caused by large scale eddies is for example contradictory with the observed bursting behavior whose frequency scales with inner rather than the outer variables. The regeneration process in the wall turbulence, and in parallel, the development of turbulent structures through by-pass mechanism should be related in some way to the preexisting structures themselves. The aim of the present investigation is to study the interaction between the localized perturbations to determine whether they rapidly trigger the transition under some circumstances, or not. This aspect has not been investigated before to our knowledge. We show through direct numerical simulations of high spatial and temporal resolution that the genesis of new quasi-streamwise vortices depends upon the capability of the primary structures to regenerate streamwise dependent intense wall normal vorticity. The DNS shows that the impingement of sweep flow caused by a parent structure razes rapidly one of the high speed streak. This leads to a local asymmetry between the streamwise evolutions of wall normal vorticity resulting in a secondary vorticity layer, which, in return is tilted by the shear and regenerates new quasi-streamwise structures. The bypass transition resulting from this process is significantly more rapid compared to the effect of localized single disturbances. [abstract only; no pdf]