Effects of unsteadiness in transitional shear-flows: Application to a wake flow

In recent years, results from experimental and numerical investigations suggest that large scale dynamics plays a dominating role in transitional shear-flows. Many authors (Karniadakis et Al., 1992, Williamson et Al., 1993) have clearly shown that large scale structures can result from the instability of the mean velocity profile. These structures undergo deterministic evolution strongly affected by reciprocal non-linear interactions. In this context a dynamical system approach is a suitable tool to model large scale dynamics in transitional shear-flows because it is able to encode these deterministic processes. A dynamical system is presented, describing the local time evolution of large scale motions for a general three-dimensional disturbance superimposed to the basic velocity field. In this paper the model was applied to a two-dimensional cylinder wake in an unsteady mean flow. At this purpose a extension of the mathematical model was performed in order to achieve information on the effects of unsteadiness of the basic flow in transitional wake dynamics. Flow visualizations and velocity measurements were also carried out in a hydraulic tunnel. This produced useful information to select the main features of the large scale motion in the cylinder wake. A low dimensional system, obtained as a truncated form of the proposed model, was used to describe the dynamical behaviour of the wake. A good agreement was found between the experimental and numerical results. The role of a low frequency basic flow noise in the wake dynamics was described, thus confirming other authors findings (Miksad et Al., 1992).