Journal of Fluids and Structures 25 (2009) 654–665 Physics of temporal forcing in wakes B. Thiria, J.E. Wesfreid Physique et Me´canique des Milieux He´te´roge`nes, Ecole Supe´rieure de Physique et Chimie Industrielles de Paris (PMMH UMR 7636 CNRS-ESPCI-P6-P7), 10 rue Vauquelin, 75231 Paris, Cedex 5, France Received 6 November 2008; accepted 7 April 2009 Abstract In this paper, we review some recent results concerning the physics of forcing in open flows. First, we recall some properties of global modes in wakes, showing their shapes and their dependence on the Reynolds number and underline the importance of the mean flow correction induced by the fluctuations. Second, we show how a local temporal forcing can affect these properties, always through the modification of the mean flow, until the wake reaches a critical transition even far from the threshold. At last, we address some conjectures about an extended model suitable for describing the dynamics of forced wakes. r 2009 Elsevier Ltd. All rights reserved. Keywords: Global instability; Forced wake; Mean flow correction 1. Introduction The wake of a cylinder is one of the most well-known cases of hydrodynamical instability studies in open flows. The phenomenon is elegant and looks simple: the geometry is basic, can generally be considered as a 2-D case, and it has, in the supercritical regime, a single well-defined frequency that depends on the Reynolds number. Besides, its main properties (drag, pressure, global mode characteristics, etc.) have been covered by a large literature (experimental, numerical and theoretical). In fact, this case is commonly considered as a basic case for the understanding of more complex situations involving bluff bodies moving in a fluid. As simple as it seems, the cylinder wake, or Be ´ nard–von Karman instability (BvK) is still one of the greatest interest for the wake community, and periodically feeds knowledges on fluid mechanics. In particular, some recent works focused on studying bluff body wakes under forcing conditions. This issue has been highlighted by the recent increasing of studies on flow control. By definition, the control of a flow involves an external perturbation (in time or space) which enables the changing of some of the flow characteristics in order to optimize specific values (such as drag, lift, base pressure, shear layer or vortex strength), thus naturally providing forced flows. More generally, flows under forcing conditions can be found in most of the real cases. For instance, once the structure giving rise to instability starts to vibrate itself, it acts like a temporal forcing which modifies the flow dynamics. Here again, physics of forcing can take place in all the fluid–structures interactions situations. Many studies have dealt with periodic forcing of wakes and how this forcing affect properties such as forces, structures, etc. Among these works, one can underline on the one hand, those conducted by Tokumaru and Dimotakis (1991), Dalton and Xu (2001), Protas and Wesfreid (2002) or Thiria et al. (2006) in the case of a cylinder performing rotary oscillations, many works on in-line oscillations [see extensive review ARTICLE IN PRESS www.elsevier.com/locate/jfs 0889-9746/$ - see front matter r 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfluidstructs.2009.04.002