Self-sustained oscillations of a confined jet: a case study for the non-linear delayed saturation model

Abstract

This paper is concerned with a dominant feature of transitional separated flows, namely their ability to develop and maintain self-sustained oscillations. Experiments performed with an axisymmetric confined jet exhibit very nicely the low frequency, large amplitude oscillation of the reattachment point. The unsteadiness of the reattachment process of the flow at the confining walls is discussed by focusing on the role of the permanent backflow in the recirculation bubble. It is conjectured that this convective backflow may lead to a non-linear retarded action of the turbulent downstream flow on the upstream shear layer instability. This crucial ingredient -the time lag- is implemented in a new formalism referred to as the Non-Linear Delayed Saturation Model (NLDS), whose features are precisely discussed in connection with the flow. The observed oscillation frequencies of the reattachment point compare well with the predictions of the model. Although the validity of the model is demonstrated with regard to the confined jet case, it is clear that the NLDS concept may represent a paradigm for unstable separated reattaching flows (flow over backward facing steps, blunt bodies, channel protrusions,…).