The onset of transition in the boundary layer over a grooved surface is studied by introducing the presence of grooves into the standarde 9 model with the aid of a previously obtained equivalent boundary condition. Under conditions of self-similarity and smallness of the grooves, Tollmien-Schlichting waves are found to be excited at a slightly smaller Reynolds number and Görtler vortices at a slightly larger one than on a smooth surface.
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Walsh, M.J., Riblets. In: Bushnell, B. and Hefner, J. (eds),Viscous Drag Reduction in Boundary Layers. Progress in Aeronautics and Astronautics, Vol. 123 (1990) pp. 204–261.
Luchini, P., Effects of riblets on the growth of laminar and turbulent boundary layers. In:7th European Drag Reduction Meeting, Berlin, September (1992).
Chu, D.C. and Karniadakis, G.Em., A direct numerical simulation of laminar and turbulent flow over riblet-mounted surfaces.J. Fluid Mech. 250 (1993) 1–42.
Carpenter, P.W. and Garrad, A.D., The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 1. Tollmien-Schlichting instabilities.J. Fluid Mech. 155 (1985) 465–510.
Carpenter, P.W. and Garrad, A.D., The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 2. Flow-induced surface instabilities.J. Fluid Mech. 170 (1986) 199–232.
Luchini, P., Asymptotic analysis of laminar boundary-layer flow over finely grooved surfaces.Europ. J. of Mechanics B/Fluids 14 (1995) 169–195.
Richardson, S., A model for the boundary conditions of porous materials.J. Fluid Mech. 49 (1971) 327–336.
Richardson, S., On the no-slip boundary condition.J. Fluid Mech. 59 (1973) 707–719.
Bechert, D.W. and Bartenwerfer, M., The viscous flow on surfaces with longitudinal ribs.J. Fluid Mech. 206 (1989) 105–129.
Bechert, D.W., Bartenwerfer, M. and Hoppe, G., Turbulent drag reduction by nonplanar surfaces — A survey on the research at TU/DLR Berlin. In: Gyr, A. (ed.),Proc. IUTAM Symposium on Structure of Turbulence and Drag Reduction, Zürich, 25–28 July 1989. Berlin: Springer-Verlag (1990) pp. 525–543.
Luchini, P., Pozzi, A. and Manzo, F., Resistance of a grooved surface to parallel flow and crossflow.J. Fluid Mech. 228 (1991) 87–109.
Grek, G.R., Kozlov, V.V. and Titarenko, S.V., An experimental study on the influence of riblets on transition. Part I: Effects on the linear development of Tollmien-Schlichting waves. In:8th European Drag Reduction Meeting, Lausanne, 23–24 September (1993).
Grek, G.R., Kozlov, V.V. and Titarenko, S.V., An experimental study on the influence of riblets on transition. Part II: Effects on the development of A-vortices on ribbed surfaces. In:8th European Drag Reduction Meeting, Lausanne, 23–24 September (1993).
Kozlov, V.V., Private communication.
Smith, A.M.O. and Gamberoni, N., Transition, pressure gradient and stability theory. Douglas Aircraft Report ES-26388 (1956).
Van Ingen, J.L., A suggested semi-empirical method for the calculation of the boundary-layer transition region. Delft University of Technology, Aero. Eng. Report VTH-74 (1956).
White, F.M.,Viscous Fluid Flow. New York: McGraw-Hill (1991).
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Luchini, P., Trombetta, G. Effects of riblets upon flow stability. Appl. Sci. Res. 54, 313–321 (1995). https://doi.org/10.1007/BF00863516