Skip to main content

Wave Propagation in Non-Viscous Fluids

  • Chapter
For Dirk Struik

Part of the book series: Boston Studies in the Philosophy of Science ((BSPS,volume 15))

  • 188 Accesses

Abstract

In this paper, we will discuss the development in the theory of wave propagation. This will consist of two topics: the linear theory as developed by C. Huygens and many other mathematicians and physicists of eighteenth and nineteenth centuries; the non-linear theory which has been developed since that time. The first topic has its origins in the theory of optics. However, the second topic has its roots in the theory of supersonic flow of compressible fluids. We will outline the main contributions to the non-linear theory.

This work was done under Grant No. GP 19009 of the National Science Foundation administered by the Office of Research Administration of the University of Michigan.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 299.99
Price excludes VAT (USA)
  • Durable hardcover 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.

Bibliography

  • Bazer, J. and Fleishman, O.: ‘Propagation of Weak Hydromagnetic Discontinuities’, Phys. Fluids 2 (1959) 366–373.

    Article  Google Scholar 

  • Coburn, N. and Sommerfield, M.: ‘The Propagation of Discontinuities along Characteristic Surfaces in Non-Equilibrium Fluids’, to appear J. Math. Anal. Appl. (1973a), in press.

    Google Scholar 

  • Coburn, N. and Sommerfield, M, N. and Sommerfield, M.: ‘The Propagation of Discontinuities along Characteristic Surfaces in Non-Equilibrium Magnetic Fluids’ (1973b) in preparation.

    Google Scholar 

  • Cohen, H. and Suh, S. L., Wave Propagation in Elastic Surfaces, J. Math. Mech. 19 (1970).

    Google Scholar 

  • Courant, R. and Friedrichs, K. O.: Supersonic Flow and Shock Waves, Interscience Publishers, Inc., New York, 1948.

    Google Scholar 

  • Courant, R. and Hilbert, D.: Methods of Mathematics Physics, Interscience Publishers, Inc., New York, 1962.

    Google Scholar 

  • Gopalakrishna, A. V.: Propagation of Weak Discontinuities in Collisionless Plasma’, J. Math. Anal. Appl. (1973), in press.

    Google Scholar 

  • Jeffrey, A. and Taniuti, T.: Non-Linear Wave Propagation, Academic Press, New York, 1964.

    Google Scholar 

  • Juneja, B. L.: ‘Growth of Weak Discontinuities in Quasi-Linear Hyperbolic Systems’.

    Google Scholar 

  • Kato, Y.: ‘Interaction of Hydromagnetic Waves’, Prog. Theoret. Phys. (Kyoto) 21 (1959) 409–420.

    Article  Google Scholar 

  • Kaul, C. N.: ‘Weak Discontinuities in Shallow-Liquid Magnetohydrodynamics’, J. Math. Anal. Appl. 11 (1956) 1–10.

    Google Scholar 

  • Nariboli, G. A. and Rangarao, M. P.: ‘Anisotropic Wave Propagation in Magneto- gasdynamics’, J. Math. Phys. Sci. 1 (1967) 4.

    Google Scholar 

  • Stoker, J. J.: Water Waves, Interscience Publishers, Inc., New York, 1957.

    Google Scholar 

  • Struik, D. J.: ‘Détermination rigoureuse des ondes irrotationnelles périodiques dans un canal à profondeur finii’, Mathematische Annalen 95 (1926) 595–634.

    Article  Google Scholar 

  • Thomas, Tracy Y.: Plastic Flow and Fracture In Solids, Academic Press, New York, 1961.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1974 D. Reidel Publishing Company, Dordrecht-Holland

About this chapter

Cite this chapter

Coburn, N. (1974). Wave Propagation in Non-Viscous Fluids. In: Cohen, R.S., Stachel, J.J., Wartofsky, M.W. (eds) For Dirk Struik. Boston Studies in the Philosophy of Science, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2115-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-2115-9_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-277-0379-8

  • Online ISBN: 978-94-010-2115-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics