Skip to main content
SpringerLink
Log in

Transition Control

  • Conference paper
Book cover Instability and Transition

Part of the book series: ICASE/NASA LaRC Series ((ICASE/NASA))

  • 357 Accesses

Abstract

The ability to actively or passively manipulate a boundary layer to delay or advance laminar-to-turbulent transition is of immense technological importance. The present article is an overview of available or contemplated techniques to control transition. The treatment is pedagogical, making the material accessible to newcomers to the field. Emphasis is placed on two-dimensional, incompressible flows, although more complex situations will be briefly mentioned.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ackeret, J., Ras, M., and Pfenninger, W. (1941), “Verhinderung des Turbulentwerdens einer Grenzschicht durch Absaugung,” Naturwissenschaften 29, pp. 622–623.

    Article  ADS  Google Scholar 

  2. Barker, S. J. and Gile, D. (1981), “Experiments on Heat- Stabilized Laminar Boundary Layers in Water,” J. Fluid Mech. 104, PP. 139–158.

    Article  ADS  Google Scholar 

  3. Batchelor, G. K. (1967), An Introduction to Fluid Dynamics, Cambridge University Press, London.

    MATH  Google Scholar 

  4. Benjamin, T. B. (1960), “Effects of a Flexible Boundary on Hydrodynamic Stability,” J. Fluid Mech. 9, pp. 513 – 532.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Biringen, S. (1984), “Active Control of Transition by Periodic Suction-Blowing,” Phys. Fluids 27, pp. 1345 – 1347.

    Article  ADS  Google Scholar 

  6. Braslow, A. L., Burrows, D. L., Tetervin, N., and Visconti, F. (1951), “Experimental and Theoretical Studies of Area Suction for the Control of Laminar Boundary Layer,” NACA Report No. 1025.

    Google Scholar 

  7. Bushnell, D. M. (1989), “Applications and Suggested Directions of Transition Research,” Fourth Symp. on Numerical and Phys¬ical Aspects of Aerodynamic Flows, Long Beach, CA, January 16 – 19.

    Google Scholar 

  8. Bushnell, D. M., Hefner, J. N., and Ash, R. L. (1977), “Effect of Compliant Wall Motion on Turbulent Boundary Layers,” Phys. Fluids 20, pp. S31 – S48.

    Article  ADS  Google Scholar 

  9. Bushnell, D. M. and Malik, M. R. (1988), “Compressibility In¬fluences on Boundary-Layer Transition,” Symp. on Physics of Compressible Turbulent Mixing, Princeton, NJ, October 25 – 27.

    Google Scholar 

  10. Bushnell, D. M., Malik, M. R., and Harvey, W. D. (1988), “Transition Prediction in External Flows via Linear Stability Theory,” Proc. IUTAM Symp. Transsonicum ///, Gottingen, Germany, May 24 – 27.

    Google Scholar 

  11. Bussmann, K. and Münz, H. (1942), “Die Stabilitat der 1am- inaren Reibungsschicht mit Absaugung,” Jharb. Dtsch. Luft-fahrtforschung 1, pp. 36 – 39.

    Google Scholar 

  12. Carpenter, P. W. and Garrad, A. D. (1985), “The Hydrodynamic Stability of Flow over Kramer-Type Compliant Surfaces. Part 1. Tollmien-Schlichting Instabilities,” J. Fluid Mecho. 155, pp. 465 – 510.

    Article  ADS  MATH  Google Scholar 

  13. Chen, C. P., Goland, Y., and Reshotko, E. (1979), “Generation Rate of Turbulent Patches in the Laminar Boundary Layer of a Submersible,” in Viscous Flow Drag Reduction, ed. G. R. Hough, AIAA Progress in Astronautics and Aeronautics 72, pp. 783 – 89.

    Google Scholar 

  14. DiPrima, R. C. and Swinney, H. L. (1985), “Instabilities and Transition in Flow between Concentric Rotating Cylinders,” in Hydrodynamic Instabilities and the Transition to Turbulence, eds. H. L. Swinney and J. P. Gollub, Second Edition, pp. 139 – 180, Springer-Verlag, Berlin.

    Google Scholar 

  15. Dougherty, N. S. and Fisher, D. F. (1980), “Boundary Layer Transition on a 10-Degree Cone,” AIAA Paper No. 80 – 0154.

    Google Scholar 

  16. Drazin, P. and Reid, W. (1981), Hydrodynamic Stability, Cam¬bridge University Press, London.

    MATH  Google Scholar 

  17. Frick, C. W. and McCullough, C. B. (1942), “Tests of a Heated Low Drag Airfoil,” NACA ARR, December.

    Google Scholar 

  18. Gad-el-Hak, M., Davis, S. H., McMurray, J. T., and Orszag, S. A. (1984), “On the Stability of the Decelerating Boundary Layer,” J. Fluid Mech. 138, pp. 297 – 323.

    Article  ADS  Google Scholar 

  19. Gad-el-Hak, M. and Ho, C.-M. (1985), “The Pitching Delta Wing,” AIAA J. 23, pp. 1660 - 1665.

    Article  ADS  Google Scholar 

  20. Gedney, C. J. (1983), “The Cancellation of a Sound-Excited Tollmien-Schlichting Wave with Plate Vibration,” Phys. Fluids 26, pp. 1158 1160.

    Article  ADS  Google Scholar 

  21. Goldstein, M. E. and Hultgren, L. S. (1989), “Boundary-Layer Receptivity to Long-Wave Free-Stream Disturbances,” Ann. Rev. Fluid Mech. 21, pp. 137 – 166.

    Article  MathSciNet  ADS  Google Scholar 

  22. Granville, P. S. (1979), “Drag of Underwater Bodies,” in Hydroballistics Design Handbook, Vol. 1, pp. 309–341, Naval Sea Systems Command, SEAHAC TR 79 – 1, Washington, D.C.

    Google Scholar 

  23. Hendricks, E. W. and Ladd, D. M. (1983), “Effect of Surface Roughness on the Delayed Transition on 9:1 Heated Ellipsoid,” AIAA J. 21 , pp. 1406 – 1409.

    Article  ADS  Google Scholar 

  24. Hinze, J. (1975), Turbulence , Second Edition, McGraw-Hill, New York.

    Google Scholar 

  25. Holmes, B. J. (1988), “NLF Technology is Ready to Go,” Aerospace America 26 , pp. 16 – 20.

    Google Scholar 

  26. Holstein, H. (1940), “Messungen zur Laminarhaltung der Grenzschicht an einem Flügel,” Lilienthal-Bericht S10, pp. 17 – 27.

    Google Scholar 

  27. Iglisch, R. (1944), “Exakte Berechnung der laminaren Reibungsschicht an der längsangeströmten ebenen Platte mit ho-mogener Absaugung,” Schr. Dtsh. Akad. Luftfahrtforschung 8B , pp. 1 – 51.

    Google Scholar 

  28. Itoh, N. (1987), “Another Route to the Three-Dimensional De¬velopment of Tollmien-Schlichting Waves with Finite Ampli¬tude,” J. Fluid Mech. 181, pp. 1 – 16.

    Article  ADS  MATH  Google Scholar 

  29. Jaffe, N. A., Okamura, T. T., and Smith, A. M. 0. (1970), “Determination of Spatial Amplification Factors and Their Ap¬plication to Predicting Transition,” AIAA J. 8 , pp. 301 – 308.

    Article  ADS  Google Scholar 

  30. Kachanov, Y. S., Koslov, V. V., and Levchenko, V. Ya. (1974), “Experimental Study of the Influence of Cooling on the Stability of Laminar Boundary Layers,” Izvestia Sibirskiogo Otdielenia Ak. Nauk SSSR, Seria Technicheskikh Nauk, Novosibirsk, No. 8–2, pp. 75 – 79.

    Google Scholar 

  31. Kaplan, R. E. (1964), “The Stability of Laminar Incompress¬ible Boundary Layers in the Presence of Compliant Bound¬aries,” Sc.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA.

    Google Scholar 

  32. Kays, W. M. and Crawford, M. E. (1980), Convective Heat and Mass Transfer , McGraw-Hill, New York.

    Google Scholar 

  33. Klebanoff, P. S., Schubauer, G. B., and Tidstrom, K. D. (1955), “Measurements of the Effect of Two-Dimensional and Three-Dimensional Roughness Elements on Boundary-Layer Transi¬tion,” J. Aero. Sci . 22, pp. 803 – 804.

    Google Scholar 

  34. Klebanoff, P. S., Tidstrom, K. D., and Sargent, L. M. (1962), “The Three-Dimensional Nature of Boundary Layer Instability,” J. Fluid Mech. 12, pp. 1 – 34.

    Article  ADS  MATH  Google Scholar 

  35. Kosecoff, M. A., Ko, D. R. S., and Merkle, C. L. (1976), “An Analytical Study of the Effect of Surface Roughness on the Sta¬bility of a Heated Water Boundary Layer,” Dynamics Technol¬ogy, Inc., Final Report PDT 76–131, Torrance, CA.

    Google Scholar 

  36. Krämer, M. 0. (1960), “Boundary Layer Stabilization by Dis¬tributing Damping,” J. Am. Soc. Naval Engrs. 72 , pp. 25 – 33.

    Article  Google Scholar 

  37. Ladd, D. M. and Hendricks, E. W. (1988), “Active Control of 2-D Instability Waves on an Axisymmetric Body,” Exp. Fluids 6 , pp. 69 – 70.

    Article  Google Scholar 

  38. Landahl, M. T. (1962), “On the Stability of a Laminar Incom¬pressible Boundary Layer Over a Flexible Surface,” J. Fluid Mech. 13 , pp. 609 – 632.

    Article  ADS  MATH  Google Scholar 

  39. Landau, L. D. and Lifshitz, E. M. (1963), Fluid Mechanics , translated from the Russian, Pergamon Press, Oxford.

    MATH  Google Scholar 

  40. Lauchle, G. C. and Gurney, G. B. (1984), “Laminar Boundary- Layer Transition on a Heated Underwater Body,” J. Fluid Mech. 144, PP. 79 – 101.

    Article  ADS  Google Scholar 

  41. Lees, L. (1947), “The Stability of the Laminar Boundary Layer in Compressible Fluid,” NACA Report No. 876.

    Google Scholar 

  42. Liepmann, H. W., Brown, G. L., and Nosenchuck, D. M. (1982), “Control of Laminar Instability Waves Using a New Technique,” J. Fluid Mech. 118, pp. 187 – 200.

    Article  ADS  Google Scholar 

  43. Liepmann, H. W. and Fila, G. H. (1947), “Investigations of Effects of Surface Temperature and Single Roughness Elements on Boundary Layer Transition,” NACA Report No. 890.

    Google Scholar 

  44. Liepmann, H. W. and Nosenchuck, D. M. (1982), “Active Con¬trol of Laminar-Turbulent Transition,” J. Fluid Mech. 118, pp. 201 – 204.

    Article  ADS  Google Scholar 

  45. Lighthill, M. J. (1963), “Introduction - Boundary Layer The¬ory,” in Laminar Boundary Layers, ed. L. Rosenhead, pp. 46 – 113, Clarendon Press, Oxford.

    Google Scholar 

  46. Lin, C. C. (1945), “On the Stability of Two-Dimensional Parallel Flows,” Parts I, II, and III, Q. Appl Maths. 13, pp. 117–142, 218–234, 277 – 301.

    Google Scholar 

  47. Linke, W. (1942), “Uber den Stromungswiderstand einer be- heizten ebenen Platte,” Luftfahrtforschung 19, pp. 157 – 160.

    Google Scholar 

  48. Lowell, R. L. and Reshotko, E. (1974), “Numerical Study of the Stability of a Heated Water Boundary Layer,” Case Western University, Report No. FTAS/TR-73–93, Cleveland, OH.

    Google Scholar 

  49. McMurray, J. T., Metcalfe, R. W., and Riley, J. J. (1983), “Di¬rect Numerical Simulations of Active Stabilization of Boundary Layer Flows,” Proc. Eighth Biennial Symp. on Turbulence, ed. J. L. Zakin and G. K. Patterson, Paper No. 36, University Mis¬souri, Rolla.

    Google Scholar 

  50. Milling, R. W. (1981), “Tollmien-Schlichting Wave Cancella¬tion,” Phys. Fluids 24, pp. 979 – 981.

    Article  ADS  Google Scholar 

  51. Milne-Thomson, L. M. (1968), Theoretical Hydrodynamics , Fifth Edition, Macmillan, London.

    MATH  Google Scholar 

  52. Morkovin, M. V. (1969), “Critical Evaluation of Transition from Laminar to Turbulent Shear Layers with Emphasis on Hypersonically Traveling Bodies,” Air Force Flight Dynamics Laboratory Report No. AFFDL-TR-68–149, Wright-Patterson AFB, OH.

    Google Scholar 

  53. Morkovin, M. V. (1984), “Bypass Transition to Turbulence and Research Desiderata,” in Transition in Turbines Symposium , NASA CP-2386.

    Google Scholar 

  54. Morkovin, M. V. (1988), “Recent Insights into Instability and Transition to Turbulence in Open-Flow Systems,” AIAA Paper No. 88 – 3675.

    Google Scholar 

  55. Orszag, S. A. (1971), “Accurate Solution of the Orr-Sommerfeld Stability Equation,” J. Fluid Mech. 50, pp. 689 – 703.

    Article  ADS  MATH  Google Scholar 

  56. Panton, R. L. (1984), Incompressible Flow , Wiley-Interscience, New York.

    Google Scholar 

  57. Pfenninger, W. (1946), “Untersuchungen über Reibungsverminderung an Tragflügeln, insbesondere mit Hilfe von Grenzschichtabsaugung,” Reports of the Inst, of Aerodynamics, ETH Zurich, No. 13.

    Google Scholar 

  58. Prandtl, L. (1904), “über Fliissigkeitsbewegung bei sehr kleiner Reibung,” Proc. Third Int. Math. Congrpp. 484–491, Heidel¬berg, Germany.

    Google Scholar 

  59. Pretsch, J. (1942), “Umschlagbeginn und Absaugung,” Jahrb. Dtsch. Luftfahrtforschung 1 , pp. 54 – 71.

    Google Scholar 

  60. Ragab, S. A. and Nayfeh, A. H. (1980), “A Comparison of the Second-Order Triple-Deck Theory and Interacting Bound¬ary Layers for Incompressible Flows Past a Hump,” AIAA Paper No. 80 – 0072.

    Google Scholar 

  61. Ras, M. and Ackeret, J. (1941), “über Verhinderung der Grenzachicht-Turbulenz durch Absaugung,” Helv. Phys. Acta 14 , p. 323.

    Google Scholar 

  62. Raspet, A. (1952), “Boundary-Layer Studies on a Sailplane,” Aeronaut. Eng. Rev . 11, pp. 52 – 60.

    Google Scholar 

  63. Rayleigh, F. (1880), “On the Stability, or Instability, of Certain Fluid Motions,” Proc. London Math. Soc . 11, pp. 57 – 70.

    Article  MATH  Google Scholar 

  64. Reed, H. L. and Nayfeh, A. H. (1986), “Numerical-Perturbation Technique for Stability of Flat-Plate Boundary Layers with Suc¬tion,” AIAA J. 24, pp. 208 – 214.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  65. Reed, H. L. and Saric, W. S. (1987), “Stability and Transition of Three-Dimensional Flows,” Proc. 10th U. S. National Cong. of App. Mech., ed. J. P. Lamb, pp. 457–468, ASME, New York.

    Google Scholar 

  66. Reed, H. L. and Saric, W. S. (1989), “Stability of Three- Dimensional Boundary Layers,” Ann. Rev. Fluid Mech. 21, pp. 235 – 284.

    Article  MathSciNet  ADS  Google Scholar 

  67. Reshotko, E. (1976), “Boundary-Layer Stability and Transi¬tion,” Ann. Rev. Fluid Mech. 8 , pp. 311 – 349.

    Article  ADS  Google Scholar 

  68. Reshotko, E. (1979), “Drag Reduction by Cooling in Hydrogen- Fueled Aircraft,” J. Aircraft 16 , pp. 584 – 590.

    Article  Google Scholar 

  69. Reshotko, E. (1985), “Control of Boundary Layer Transition,” AIAA Paper No. 85 – 0562.

    Google Scholar 

  70. Reshotko, E. (1987), “Stability and Transition, How Much Do We Know?” Proc. 10th U. S. National Cong. of App. Mech. , ed. J. P. Lamb, pp. 421–434, ASME, New York.

    Google Scholar 

  71. Reynolds, G. A. and Saric, W. S. (1986), “Experiments on the Stability of the Flat-Plate Boundary Layer with Suction,” AIAA J. 24 , pp. 202 – 207.

    Article  ADS  Google Scholar 

  72. Riley, J. J., Gad-el-Hak, M., and Metcalfe, R. W. (1988), “Com¬pliant Coatings,” Ann. Rev. Fluid Mech. 20 , pp. 393 – 420.

    Article  ADS  Google Scholar 

  73. Rosenhead, L. (1963), Laminar Boundary Layers , Clarendon Press, Oxford.

    MATH  Google Scholar 

  74. Runyan, L. J. and Steers, L. L. (1980), “Boundary Layer Sta¬bility Analysis of a Natural Laminar Flow Glove on the F-lll TACT Airplane,” in Viscous Flow Drag Reduction, ed. G. R. Hough, AIAA Progress in Astronautics and Aeronautics 72, pp. 17 – 32.

    Google Scholar 

  75. Saric, W. S. and Reed, H. L. (1986), “Effect of Suction and Weak Mass Injection on Boundary-Layer Transition,” AIAA J. 24 , pp. 383 – 389.

    Article  ADS  Google Scholar 

  76. Schilz, W. (1965/66), “Experimented Untersuchungen zur Akustischen Beeinflussung der Strömungsgrenzachicht in Luft,” Acustica 16, pp. 208–223.

    Google Scholar 

  77. Schlichting, H. (1979), Boundary-Layer Theory, Seventh Edi¬tion, McGraw-Hill, New York.

    Google Scholar 

  78. Schlichting, H. and Ulrich, A. (1940), “Zur Berechnung des Um- schlages Laminar-Turbulent,” Jahrb. Dtsch. Luftfahrtforschung 1, pp. 8 – 35.

    Google Scholar 

  79. Scott, M. R. and Watts, H. A. (1977), “Computational Solution of Linear Two-Point Boundary Value Problems via Orthonormalization,” J. Numerical Analysis 14, pp. 40 – 70.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  80. Smith, A. M.(1957), “Transition, Pressure Gradient, and Stability Theory,” Actes IX Congrès International de Mécanique Appliquée, Vol. 4, pp. 234–244, Universite de Bruxelles, Belgique.

    Google Scholar 

  81. Smith, A. M. O. and Gamberoni, N. (1956), “Transition, Pres¬sure Gradient and Stability Theory,” Rep. ES-26388, Douglas Aircraft Company, El Segundo, CA.

    Google Scholar 

  82. Squire, H. B. (1933), “On the Stability for Three-Dimensional Disturbances of Viscous Fluid Flow between Parallel Walls,” Proc. R. Soc. Lond. A 142, pp. 621 – 628.

    Article  ADS  MATH  Google Scholar 

  83. Strazisar, A. J., Reshotko, E., and Prahl, J. M. (1977), “Ex¬perimental Study of the Stability of Heated Laminar Boundary Layers in Water,” J. Fluid Mech. 83, pp. 225 – 247.

    Article  ADS  Google Scholar 

  84. Stuart, J. T. (1963), “Hydrodynamic Stability,” in Laminar Boundary Layer Theory, ed. L. Rosehead, pp. 492 – 579, Claren¬don Press, Oxford.

    Google Scholar 

  85. Tani, I. (1969), “Boundary-Layer Transition,” Ann. Rev. Fluid Mech. 1, pp. 169 – 196.

    Article  ADS  Google Scholar 

  86. Thomas, A. S. W. (1983), “The Control of Boundary-Layer Transition using a Wave Superposition Principle,” J. Fluid Mech. 137, pp. 233 – 250.

    Article  ADS  Google Scholar 

  87. Tollmien, W. (1935), “Ein allgemeines Kriterium der Insta¬bility laminarer Geschwindigkeitsverteilungen,” Nachr. Wiss. Fachgruppe, Gottingen, Math. Phys. K1 1, pp. 79 – 114.

    Google Scholar 

  88. Ulrich, A. (1944), “Theoretische Untersuchungen fiber die Widerstandsersparnis durch Laminarhaltung mit Absaugung,” Schriften Dtsch. Akad. Luftfahrtforschung 8B, p. 53.

    Google Scholar 

  89. Van Ingen, J. L. (1956), “A Suggested Semiempirical Method for the Calculation of the Boundary-Layer Transition Region,” Rep. V.T.H. 74, Department of Aero, and Eng., Institute of Technology, Delft, Holland.

    Google Scholar 

  90. Wagner, R. D. and Fischer, M. C. (1984), “Fresh Attack on Laminar Flow,” Aerospace America 22, pp. 72 – 76.

    Google Scholar 

  91. Wagner, R. D., Maddalon, D. V., and Fischer, M. C. (1984), “Technology Development for Laminar Boundary Control on Subsonic Transport Aircraft,” AGARD CP-365, Paper No. 16.

    Google Scholar 

  92. Wazzan, A. R., Okamura, T. T., and Smith, A. M. O. (1968), “Stability of Water Flow over Heated and Cooled Flat Plates,” J. Heat Transfer 90, pp. 109 – 114.

    Google Scholar 

  93. Wazzan, A. R., Okamura, T. T., and Smith, A. M. (1970), “The Stability and Transition of Heated and Cooled Incompress¬ible Boundary Layers,” Proc. 4th Int. Heat Transfer Conf, Vol. 2, ed. U. Grigull and E. Hahne, FC 1.4, Elsevier, New York.

    Google Scholar 

  94. Whites, R. C., Sudderth, R. W., and Wheldon, W. G. (1966), “Laminar Flow Control on the X-21”, Astro, and Aero 4, pp. 38 – 43.

    Google Scholar 

  95. Willis, G. J. K. (1986), “Hydrodynamic Stability of Boundary Layers over Compliant Surfaces,” Ph.D. Thesis, University of Exeter, United Kingdom.

    Google Scholar 

  96. Wuest, W. (1961), “Survey of Calculation Methods of Lami¬nar Boundary Layers with Suction in Incompressible Flow,” in Boundary Layer and Flow Control, Vol. 2, ed. G. V. Lachmann, pp. 771–800, Pergamon Press, New York.

    Google Scholar 

  97. Yeo, K. S. and Dowling, A. P. (1987), “The Stability of Inviscid Flows over Passive Compliant Walls,” J. Fluid Mech. 183, pp. 265 – 292.

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Mohamed Gad-el-Hak

Authors
  1. Mohamed Gad-el-Hak
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Instiute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, 23665, Hampton, VA, USA

    M. Y. Hussaini  & R. G. Voigt  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag New York Inc.

About this paper

Cite this paper

Gad-el-Hak, M. (1990). Transition Control. In: Hussaini, M.Y., Voigt, R.G. (eds) Instability and Transition. ICASE/NASA LaRC Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3430-2_38

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-3430-2_38

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8008-8

  • Online ISBN: 978-1-4612-3430-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation