Investigation of the Dynamics of Near-Wall Turbulence Using Nonlinear Time Sequence Analysis

It is widely accepted that the wall turbulent flows are globally high dimensional (e.g. Keefe, Kim & Moin 1992). Therefore the system is not globally treatable either theoretically or in experiments and, at best, we can only focus our study on the main features of the dynamics. Fortunately this approach is not in actual fact restrictive, since it is also naturally suggested by the presence of coherent structures which, in a certain sense, constitute the skeleton of the near-wall turbulence. Because of their coherency and simplicity in relation to the rest of the dynamics, it is likely that in phase space such organized flow structures correspond to distinct and fairly simple orbits that, at random intervals, leave and suddenly reconnect to the large dimensional part of the attractor (Newell et al., 1988). In particular, in the low dimensional model of Aubry et al. (1988), the bursting phenomenon is shown to correspond in phase space to heteroclinic excursions (see also Sanghi & Aubry, 1993, and references therein). These theoretical studies, as well as certain ad hoc simplified numerical simulations (Hamilton et al. 1995), can capture the main features of the near-wall dynamics and are very important for highlighting the physical origin of the bursting process. However, they still have too little contact with the real turbulence. From the experimental and numerical point of view, the bursting process is quantitatively studied by means of conditional sampling techniques (e.g. Luchik & Tiederman, 1987), that unfortunately suffer from a certain subjectivity in the choice of the threshold values.