Skip to main content Accessibility help

Reattachment streaks in hypersonic compression ramp flow: an input–output analysis

  • Anubhav Dwivedi (a1), G. S. Sidharth (a1), Joseph W. Nichols (a1), Graham V. Candler (a1) and Mihailo R. Jovanović (a2)...


We employ global input–output analysis to quantify amplification of exogenous disturbances in compressible boundary layer flows. Using the spatial structure of the dominant response to time-periodic inputs, we explain the origin of steady reattachment streaks in a hypersonic flow over a compression ramp. Our analysis of the laminar shock–boundary layer interaction reveals that the streaks arise from a preferential amplification of upstream counter-rotating vortical perturbations with a specific spanwise wavelength. These streaks are associated with heat-flux striations at the wall near flow reattachment and they can trigger transition to turbulence. The streak wavelength predicted by our analysis compares favourably with observations from two different hypersonic compression ramp experiments. Furthermore, our analysis of inviscid transport equations demonstrates that base-flow deceleration contributes to the amplification of streamwise velocity and that the baroclinic effects are responsible for the production of streamwise vorticity. Finally, the appearance of the temperature streaks near reattachment is triggered by the growth of streamwise velocity and streamwise vorticity perturbations as well as by the amplification of upstream temperature perturbations by the reattachment shock.


Corresponding author

Email address for correspondence:


Hide All

Present address: X-Computational Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA



Hide All
Berlin, S., Lundbladh, A. & Henningson, D. S. 1994 Spatial simulations of oblique transition in a boundary layer. Phys. Fluids 6 (6), 19491951.
Bradshaw, P.1973 Effects of streamline curvature on turbulent flow. Tech. Rep. 169. AGARDograph.
Brandt, L., Sipp, D., Pralits, J. O. & Marquet, O. 2011 Effect of base-flow variation in noise amplifiers: the flat-plate boundary layer. J. Fluid Mech. 687, 503528.
Candler, G. V., Johnson, H. B., Nompelis, I., Gidzak, V. M., Subbareddy, P. K. & Barnhardt, M.2015 Development of the US3D code for advanced compressible and reacting flow simulations. In 53rd AIAA Aerospace Sciences Meeting, AIAA 2015-1893. AIAA.
Chang, C. L. & Malik, M. R. 1994 Oblique-mode breakdown and secondary instability in supersonic boundary layers. J. Fluid Mech. 273, 323360.
Chu, B.-T. 1965 On the energy transfer to small disturbances in fluid flow (part I). Acta Mech. 1 (3), 215234.
Chuvakhov, P. V., Borovoy, V. Y., Egorov, I. V., Radchenko, V. N., Olivier, H. & Roghelia, A. 2017 Effect of small bluntness on formation of Görtler vortices in a supersonic compression corner flow. J. Appl. Mech. Tech. Phys. 58 (6), 975989.
Dwivedi, A., Nichols, J. W., Jovanović, M. R. & Candler, G. V.2017 Optimal spatial growth of streaks in oblique shock/boundary layer interaction. In 8th AIAA Theoretical Fluid Mechanics Conference. AIAA 2017-4163. AIAA.
Dwivedi, A., Sidharth, G. S., Candler, G. V., Nichols, J. W. & Jovanović, M. R.2018 Input–output analysis of shock boundary layer interaction. In 2018 Fluid Dynamics Conference. AIAA 2018-3220. AIAA.
Ellingsen, T. & Palm, E. 1975 Stability of linear flow. Phys. Fluids 18 (4), 487488.
Fasel, H. F., Thumm, A. & Bestek, H. 1993 Direct numerical simulation of transition in supersonic boundary layers: oblique breakdown. In Fluids Engineering Conference, pp. 7792.
Fedorov, A. 2011 Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43, 7995.
Finnigan, J. J. 1983 A streamline coordinate system for distorted two-dimensional shear flows. J. Fluid Mech. 130, 241258.
Hall, P. 1983 The linear development of Görtler vortices in growing boundary layers. J. Fluid Mech. 130, 4158.
Hanifi, A., Schmid, P. J. & Henningson, D. S. 1996 Transient growth in compressible boundary layer flow. Phys. Fluids 8 (3), 826837.
Inger, G. R. 1977 Three-dimensional heat-and mass-transfer effects across high-speed reattaching flows. AIAA J. 15 (3), 383389.
Jeun, J., Nichols, J. W. & Jovanović, M. R. 2016 Input–output analysis of high-speed axisymmetric isothermal jet noise. Phys. Fluids 28 (4), 047101.
Jovanović, M. R.2004 Modeling, analysis, and control of spatially distributed systems. PhD thesis, University of California, Santa Barbara, CA.
Jovanović, M. R. & Bamieh, B. 2005 Componentwise energy amplification in channel flows. J. Fluid Mech. 534, 145183.
Kansa, E. J. 2002 Local, point-wise rotational transformations of the conservation equations into stream-wise coordinates. Comput. Maths Applics. 43 (3-5), 501511.
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98 (2), 243251.
Ma, Y. & Zhong, X. 2003 Receptivity of a supersonic boundary layer over a flat plate. Part 1: Wave structures and interactions. J. Fluid Mech. 488, 3178.
Maurizi, A., Di Sabatino, S., Trombetti, F. & Tampieri, F. 1997 A method of analysis for turbulent flows using the streamline coordinate system. Boundary-Layer Meteorol. 82 (3), 379397.
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336382.
Mustafa, M. A., Parziale, N. J., Smith, M. S. & Marineau, E. C. 2019 Amplification and structure of streamwise-velocity fluctuations in compression-corner shock-wave/turbulent boundary-layer interactions. J. Fluid Mech. 863, 10911122.
Navarro-Martinez, S. & Tutty, O. R. 2005 Numerical simulation of Görtler vortices in hypersonic compression ramps. Comput. Fluids 34 (2), 225247.
Nichols, J. W. 2018 Input/output analysis of f and s mode synchronization in hypersonic boundary layers. Phys. Rev. Fluids (submitted).
Fosas de Pando, M. & Schmid, P. J. 2017 Optimal frequency-response sensitivity of compressible flow over roughness elements. J. Turbul. 18 (4), 338351.
Patel, V. C. & Sotiropoulos, F. 1997 Longitudinal curvature effects in turbulent boundary layers. Prog. Aerosp. Sci. 33 (1–2), 170.
Ran, W., Zare, A., Hack, M. J. P. & Jovanović, M. R. 2019 Stochastic receptivity analysis of boundary layer flow. Phys. Rev. Fluids 4 (9), 093901.
Reshotko, E. 2001 Transient growth: a factor in bypass transition. Phys. Fluids 13 (5), 10671075.
Richmond, M. C., Chen, H. C. & Patel, V. C.1986 Equations of laminar and turbulent flows in general curvilinear coordinates. Tech. Rep. Iowa Institute of Hydraulic Research.
Roghelia, A., Chuvakhov, P., Olivier, H. & Egorov, I.2017a Experimental investigation of Görtler vortices in hypersonic ramp flows behind sharp and blunt leading edges. 47th AIAA Fluid Dynamics Conference. AIAA 2017-3463. AIAA.
Roghelia, A., Olivier, H., Egorov, I. & Chuvakhov, P. 2017b Experimental investigation of Görtler vortices in hypersonic ramp flows. Exp. Fluids 58 (10), 139.
Sandham, N. D., Adams, N. A. & Kleiser, L. 1995 Direct simulation of breakdown to turbulence following oblique instability waves in a supersonic boundary layer. Appl. Sci. Res. 54 (3), 223234.
Sandham, N. D., Schülein, E., Wagner, A., Willems, S. & Steelant, J. 2014 Transitional shock-wave/boundary-layer interactions in hypersonic flow. J. Fluid Mech. 752, 349382.
Schlichting, H. & Gersten, K. 2016 Boundary-layer Theory. Springer.
Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129162.
Schmid, P. J. & Henningson, D. S. 1992 A new mechanism for rapid transition involving a pair of oblique waves. Phys. Fluids 4 (9), 19861989.
Schmidt, O. T., Towne, A., Rigas, G., Colonius, T. & Brès, G. A. 2018 Spectral analysis of jet turbulence. J. Fluid Mech. 855, 953982.
Sidharth, G. S. & Candler, G. V. 2018 Subgrid-scale effects in compressible variable-density decaying turbulence. J. Fluid Mech. 846, 428459.
Sidharth, G. S., Candler, G. V. & Dimotakis, P.2014 Baroclinic torque and implications for subgrid-scale modeling. In 7th AIAA Theoretical Fluid Mechanics Conference. 2014-3214.
Sidharth, G. S., Dwivedi, A., Candler, G. V. & Nichols, J. W.2017 Global linear stability analysis of high speed flows on compression ramps. In 47th AIAA Fluid Dynamics Conference. AIAA 2017-3455. AIAA.
Sidharth, G. S., Dwivedi, A., Candler, G. V. & Nichols, J. W. 2018 Onset of three-dimensionality in supersonic flow over a slender double wedge. Phys. Rev. Fluids 3 (9), 093901.
Simeonides, G. & Haase, W. 1995 Experimental and computational investigations of hypersonic flow about compression ramps. J. Fluid Mech. 283, 1742.
Sipp, D. & Marquet, O. 2013 Characterization of noise amplifiers with global singular modes: the case of the leading-edge flat-plate boundary layer. Theor. Comput. Fluid Dyn. 27 (5), 617635.
Zapryagaev, V. I., Kavun, I. N. & Lipatov, II. 2013 Supersonic laminar separated flow structure at a ramp for a free-stream Mach number of 6. Prog. Flight Phys. 5, 349362.
Zhuang, Y., Tan, H., Liu, Y., Zhang, Y. & Ling, Y. 2017 High resolution visualization of Görtler-like vortices in supersonic compression ramp flow. J. Vis. 20 (3), 505508.
Zuccher, S., Tumin, A. & Reshotko, E.2005 Optimal disturbances in compressible boundary layers-complete energy norm analysis. In 4th AIAA Theoretical Fluid Mechanics Meeting. AIAA 2005-5314. AIAA.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Reattachment streaks in hypersonic compression ramp flow: an input–output analysis

  • Anubhav Dwivedi (a1), G. S. Sidharth (a1), Joseph W. Nichols (a1), Graham V. Candler (a1) and Mihailo R. Jovanović (a2)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed