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An experimental investigation of an unsteady adverse pressure gradient turbulent boundary layer: embedded shear layer scaling

  • D. M. Schatzman (a1) and F. O. Thomas (a2)


An experimental investigation of an unsteady adverse pressure gradient turbulent boundary layer is described. It is demonstrated that the local flow physics is largely dominated by an inflectional instability which gives rise to an embedded shear layer contained within the boundary layer. Experimental measurements are presented which are fully consistent with the presence of clockwise spanwise-oriented coherent vorticity within the embedded shear layer. Using embedded shear layer scaling parameters in the form of the shear layer vorticity thickness and the velocity defect at the upper inflection point, both the mean and the phase-averaged boundary layer velocity profiles exhibit similarity in both space and time over a large wall-normal extent. In a similar manner, the profiles of the streamwise-component turbulence intensity and Reynolds stress also exhibit similarity when scaled with the embedded shear layer parameters. The embedded shear layer scaling of previously published adverse pressure gradient turbulent boundary layer measurements confirms its generic applicability in a wide range of flow-field geometries and extending to high Reynolds numbers.


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Antonia, R. A. & Krogstad, P. A. 1992 Scaling the bursting period in turbulent rough wall boundary layers. Exp. Fluids 15 (1), 8284.
Bourassa, C. & Thomas, F. O. 2009 An experimental investigation of a highly accelerated turbulent boundary layer. J. Fluid Mech. 634, 359404.
Carr, L. W.1981 A compilation of unsteady turbulent boundary layer experimental data. NACA Tech. Mem. 81317.
Castillo, L. & George, W. K. 2001 Similarity analysis for turbulent boundary layer with pressure gradient: outer flow. AIAA J. 39 (1), 4147.
Coles, D. E. & Hirst, E. A. 1969 Computation of turbulent boundary layers – 1968. In AFOSR-IFP-Stanford Conference. Stanford University.
Corke, T. C., Enloe, C. L. & Wilkinson, S. P. 2010 Dielectric barrier discharge plasma actuators for flow control. Annu. Rev. Fluid Mech. 42, 505529.
Corke, T. C., Post, M. L. & Orlov, D. M. 2009 Single dielectric barrier discharge plasma enhanced aerodynamics: physics, modeling and applications. Exp. Fluids 46, 126.
Covert, E. E. & Lorber, P. F. 1984 Unsteady turbulent boundary layers in adverse pressure gradients. AIAA J. 22, 2228.
Dengel, P. & Fernholz, H. H. 1990 An experimental investigation of an incompressible turbulent boundary layer in the vicinity of separation. J. Fluid Mech. 212, 615636.
Despard, R. A. & Miller, J. A. 1971 Separation in oscillating laminar boundary-layer flows. J. Fluid Mech. 47, 2131.
Drazin, P. G. 2002 Introduction to Hydrodynamic Stability. Cambridge University Press.
Harun, Z., Monty, J. P. & Marusic, I. 2010 Constant adverse pressure gradient turbulent boundary layers. In 17th Australasian Fluid Mechanics Conference, Auckland, New Zealand.
Harun, Z., Monty, J. P., Mathis, R. & Marusic, I. 2013 Pressure gradient effects on the large-scale structure of turbulent boundary layers. J. Fluid Mech. 715, 477498.
George, W. K., Stanislas, M. & Laval, J.-P. 2012 New insights into adverse pressure gradient boundary layers. In Progress in Turbulence and Wind Energy IV, Proceedings of the iTi Conference in Turbulence 2010, vol. 141. Springer.
Gibson, M. M., Verriopoulos, C. A. & Vlachos, N. S. 1984 Turbulent boundary layer on a mildly curved convex surface. Exp. Fluids 2, 1724.
Gutmark, E. & Ho, C. M. 1983 Preferred modes and the spreading rates of jets. Phys. Fluids 26 (10), 29322938.
Karlsson, S. K. F. 1959 An unsteady turbulent boundary layer. J. Fluid Mech. 5, 622636.
Klebanoff, P. S.1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA Tech. Rep. 1247.
Koromilas, C. A. & Telionis, D. P. 1980 Unsteady laminar separation: an experimental study. J. Fluid Mech. 97, 347384.
Kovasznay, L. S. G. 1970 The turbulent boundary layer. Annu. Rev. Fluid Mech. 2, 95112.
Krogstad, P. A. & Skåre, P. E. 1995 Influence of a strong adverse pressure gradient on the turbulent structure in a boundary layer. Phys. Fluids 7, 20142024.
Lee, J.-H. & Sung, H. J. 2009 Structures in turbulent boundary layers subjected to adverse pressure gradients. J. Fluid Mech. 639, 101131.
Leishman, J. G. 2000 Principles of helicopter aerodynamics. Cambridge University Press.
Lu, S. S. & Willmarth, W. W. 1973 Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60, 481581.
Marquillie, M., Ehrenstein, U. & Laval, J.-P. 2011 Instability of streaks in wall turbulence with adverse pressure gradient. J. Fluid Mech. 681, 205240.
Marusic, I. & Perry, A. E. 1995 A wall wake model for the turbulent structure of boundary layers. Part 2. Further experimental support. J. Fluid Mech. 298, 389407.
Monty, J. P., Harun, Z. & Marusic, I. 2011 A parametric study of adverse pressure gradient turbulent boundary layers. Intl J. Heat Fluid Flow 32, 575585.
Moreau, E. 2007 Airflow control by non-thermal plasma actuators. J. Phys. D: Appl. Phys. 40, 605636.
Muck, K. C., Hoffman, P. H. & Bradshaw, P. 1985 The effect of convex surface curvature on turbulent boundary layers. J. Fluid Mech. 161, 347396.
Nagano, Y., Tsuji, T. & Houra, T. 1998 Structure of turbulent boundary layer subjected to adverse pressure gradient. Intl J. Heat Fluid Flow 19, 563572.
Nagib, H. M. & Chauhan, K. A. 2008 Variation of the Karman coefficient in canonical flows. Phys. Fluids 20 (10), 15181528.
Narasimha, R., Kumar, S. R., Prabhu, A. & Kailas, S. V. 2010 Turbulent flux events in a nearly neutral atmospheric boundary layer. Phil. Trans. R. Soc. Lond. A 365, 841858.
Oster, D. & Wygnanski, I. 1982 The forced mixing layer between parallel streams. J. Fluid Mech. 123, 91130.
Parikh, P. G., Reynolds, W. C. & Jayaraman, R. 1982 Behavior of an unsteady turbulent boundary layer. AIAA J. 20, 769775.
Patel, M. P., Ng, T. T., Vasudevan, S., Corke, T. C., Post, M. L., Mclaughlin, T. E. & Suchomel, C. F. 2008 Scaling effects of an aerodynamic plasma actuator. AIAA J. 45, 223236.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601639.
Samuel, A. E. & Joubert, P. N. 1974 A boundary layer developing in an increasingly adverse pressure gradient. J. Fluid Mech. 66 (3), 481505.
Sears, W. R. & Telionis, D. P. 1975 Boundary layer separation in unsteady flow. SIAM J. Appl. Maths 28 (1), 215235.
Seifert, A., Bachar, T., Koss, D., Shepshelovich, D. & Wygnanski, I. 1993 Oscillatory blowing: a tool to delay boundary-layer separation. AIAA J. 31, 20522060.
Seifert, A., Darabi, A. & Wygnanski, I. 1996 Delay of airfoil stall by periodic excitation. AIAA J. 33, 691698.
Seifert, A. & Pack, L. G. 1999 Oscillatory control of separation at high Reynolds number. AIAA J. 37, 10631071.
Shah, S. I., Laval, J. P. & Stanislas, M.2009 A specific behaviour of adverse pressure gradient near wall flows. In Proceedings of WALLTURB International Workshop, 21–23 April 2009, Lille, France.
Simpson, R. L. 1996 Aspects of turbulent boundary-layer separation. Prog. Aerosp. Sci. 32, 457521.
Skåre, P. E. & Krogstad, P. A. 1994 A turbulent equilibrium boundary layer near separation. J. Fluid Mech. 272, 319348.
Song, S., Degraaff, D. B. & Eaton, J. K. 2000 Experimental study of a separating, reattaching, and redeveloping flow over a smoothly contoured ramp. Intl J. Heat Fluid Flow 21, 512519.
Song, S. & Eaton, J. K. 2004 Reynolds number effects on a turbulent boundary layer with separation, reattachment, and recovery. Exp. Fluids 36, 246258.
Sonnenberger, R., Graichen, K. & Erk, P. 2000 Fourier averaging: a phase-averaging method for periodic flow. Exp. Fluids 28, 217224.
Spalart, P. R. & Watmuff, J. H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradients. J. Fluid Mech. 249, 337371.
Thomas, F. O. 1991 Structure of mixing layers and jets. Appl. Mech. Rev. 44 (3), 119153.
Thomas, F. O., Corke, T. C., Iqbal, I., Kozlov, A. & Schatzmam, D. 2009 Optimization of dielectric barrier discharge plasma actuators for active aerodynamic flow control. AIAA J. 47 (9), 21692178.
Wallace, J. M., Eckelmann, H. & Brodkey, R. S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 54, 3948.
Willmarth, W. W. & Lu, S. S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 6592.
Wygnanski, I., Champagne, F. & Marasli, B. 1986 On the large-scale structures in two-dimensional, small-deficit, turbulent wakes. J. Fluid Mech. 168, 3171.
Zaragola, M. V. & Smits, A. J. 1998 Mean-flow scaling of turbulent pipe flow. J. Fluid Mech. 373, 3379.
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An experimental investigation of an unsteady adverse pressure gradient turbulent boundary layer: embedded shear layer scaling

  • D. M. Schatzman (a1) and F. O. Thomas (a2)


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