European Journal of Mechanics / B Fluids 68 (2018) 167–183 Contents lists available at ScienceDirect European Journal of Mechanics / B Fluids journal homepage: www.elsevier.com/locate/ejmflu Systematic study of distributed excitation of unsteady Görtler modes by freestream vortices Vladimir I. Borodulin, Andrey V. Ivanov, Yury S. Kachanov *, Dmitry A. Mischenko Khristianovich Institute of Theoretical and Applied Mechanics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, 630090, Russia article info Article history: Received 3 April 2017 Received in revised form 9 November 2017 Accepted 25 November 2017 Available online 5 December 2017 Keywords: Laminar boundary layer Concave wall Görtler instability Distributed vortex receptivity Excitation of Görtler modes Distributed receptivity coefficients abstract The paper is devoted to experimental investigation of an efficient mechanism of distributed excitation of nonstationary Görtler vortices in a boundary layer on concave wall due to scattering of three-dimensional, streamwise oriented freestream vortices on natural two-dimensional base-flow nonuniformity associated with the boundary layer growth. The investigations are performed in a broad range of disturbance frequencies and spanwise wavenumbers. The measurements have shown that the distributed receptivity mechanism is able to modify significantly the disturbance growth rates. This mechanism is found to be able to compete successfully with the linear instability mechanism. It is found that at relatively low frequencies and not too large freestream disturbance amplitudes, the Görtler modes’ development is dominated basically by the corresponding linear instability mechanism. Meanwhile, this mechanism becomes weaker with growth of frequency and, simultaneously, the distributed receptivity mechanism gets stronger. This leads to enhancement of role of the latter in amplification of Görtler instability modes, and at high frequencies the role of the distributed receptivity mechanism becomes very important and often even decisive one. Based on deep processing of the experimental data, quantitative values of the distributed linear receptivity coefficients are obtained for the case of excitation of unsteady Görtler modes and estimated for the case of steady Görtler vortices by means of extrapolation to the zero frequency. A complementary experiment devoted to investigation of the problem of linear unsteady Görtler instability is performed for the particular conditions of the distributed receptivity experiments. All main stability characteristics are obtained and compared with calculated ones. In general, the experimental informa- tion presented in this paper can be used for verification of various instability and vortex receptivity theories. © 2017 Elsevier Masson SAS. All rights reserved. 1. Introduction The process of the laminar–turbulent transition occurred in laminar boundary-layer flows at not too high amplitudes of exter- nal perturbations is divided traditionally into three main stages: (a) stage of excitation of boundary-layer disturbances, character- ized by the base-flow receptivity to various external perturba- tions, (b) stage of linear flow instability, and (c) stage of nonlinear disturbance development, breakdown of laminar regime and final formation of turbulent flow. The present experiments are devoted to investigation of the first stage indicated above in the case of a boundary layer growing on a concave wall. The study of this flow is of particular importance due to its instability to some specific, three-dimensional disturbances representing a system of counter- rotating, streamwise vortices, called Görtler vortices, which can be * Corresponding author. E-mail address: kachanov@itam.nsc.ru (Y.S. Kachanov). either stationary or nonstationary. This kind of instability is caused by centrifugal forces, which action is essentially nonuniform in the wall-normal direction due to presence of a strong wall-normal mean-velocity gradient. Görtler instability is a subject of inten- sive experimental, theoretical, and numerical investigations (see e.g. [1–5] for review). The Görtler instability is widespread in boundary layers at sub-, super-, and hypersonic speeds [6,7]. Boundary layer over curved surfaces are very often present in various aerodynamic devices and vehicles, such as blades of turbines and compressors [8,9], airfoils [10,11], heat transfer enhancements [12,13], et al. It turned out also that the Görtler instability is able to appear in many other near-wall flows having curved streamlines and cross-flow velocity gradients, for instance in wall jets over both concave and convex surfaces, flows in curved channels, flows between rotating cylinders and spheres, free shear layers at boundaries of underex- panded supersonic jets [14] etc. Due to these circumstances, the importance of investigation of this kind of instability is difficult to overestimate. https://doi.org/10.1016/j.euromechflu.2017.11.008 0997-7546/© 2017 Elsevier Masson SAS. All rights reserved.