Theor. Comput. Fluid Dyn. DOI 10.1007/s00162-014-0321-x ORIGINAL ARTICLE A. Inasawa · J. M. Floryan · M. Asai Flow recovery downstream from a surface protuberance Received: 12 March 2013 / Accepted: 11 February 2014 © Springer-Verlag Berlin Heidelberg 2014 Abstract A single roughness element and the beginning/end of a roughness patch represent common surface protuberances. The flow recovers from disruptions caused by such protuberances either by returning to its original state or by approaching a new state downstream from a protuberance. Understanding of the recov- ery process is important in the determination of the sensitivity of the laminar–turbulent transition to surface protuberances. The beginning/end of a roughness patch has been modeled as a small-height channel expan- sion/contraction, while a rectangular protuberance has been used in the analysis of disruptions caused by a single roughness element. The recovery process has been studied using semi-analytical methods, direct numer- ical simulations as well as experiments. The size of the recovery zone has been measured using two types of criteria, one based on the properties of the stationary flow and the other one based on the characteristics of the linear instability. It has been found that the flow remains stationary without any unsteady separation at the subcritical Reynolds number Re = 5000 of interest. The effects of the step persist very far in the downstream direction; for the step height of 1 % of the channel half-height, the two-dimensional TS wave reaches asymp- totic form at about 500 channels half-heights (50,000 step’s heights) downstream from the step. The length of the recovery zone is reduced by an order of magnitude if the channel returns to its upstream form downstream from the protuberance, as demonstrated through analysis of a single roughness element. Smoothing of the downstream side of the protuberance eliminates flow separation but does not affect the flow characteristics. Keywords Flow instabilities · Surface roughness · Shear layers 1 Introduction It is acknowledged that surface roughness plays an important role in the onset and evolution of the laminar- turbulent transition process, as well as in the determination of the structure of turbulent flows. Its role has been studied since the very beginning of modern fluid mechanics, e.g., Hagen [1], Darcy [2], Reynolds [3]. This work is focused on the elucidation of one of the roles that surface roughness may play in promoting flow instability. The geometry of surface roughness is recognized as one of the significant factors. The number of geometric variations is uncountable but has been traditionally divided into three classes [4], i.e., isolated two-dimensional Communicated by M.R. Malik. A. Inasawa · M. Asai Department of Aerospace Engineering, Tokyo Metropolitan University, Asahigaoka 6-6, Hino, Tokyo 191-0065, Japan J. M. Floryan (B ) Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada E-mail: mfloryan@eng.uwo.ca