Internal waves in fluids with rapidly varying density

R. E. L. Turner

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1981)

  • Volume: 8, Issue: 4, page 513-573
  • ISSN: 0391-173X

How to cite

top

Turner, R. E. L.. "Internal waves in fluids with rapidly varying density." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 8.4 (1981): 513-573. <http://eudml.org/doc/83868>.

@article{Turner1981,
author = {Turner, R. E. L.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {incompressible; inviscid; region between two horizontal planes; rapidly varying density; travelling waves of permanent form; two-dimensional steady; Euler equations; Long-Yih equation; variational formulation singular; regularized problem; symmetry properties},
language = {eng},
number = {4},
pages = {513-573},
publisher = {Scuola normale superiore},
title = {Internal waves in fluids with rapidly varying density},
url = {http://eudml.org/doc/83868},
volume = {8},
year = {1981},
}

TY - JOUR
AU - Turner, R. E. L.
TI - Internal waves in fluids with rapidly varying density
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1981
PB - Scuola normale superiore
VL - 8
IS - 4
SP - 513
EP - 573
LA - eng
KW - incompressible; inviscid; region between two horizontal planes; rapidly varying density; travelling waves of permanent form; two-dimensional steady; Euler equations; Long-Yih equation; variational formulation singular; regularized problem; symmetry properties
UR - http://eudml.org/doc/83868
ER -

References

top
  1. [1] T.B. Benjamin, Internal waves of finite amplitude and permanent form, J. Fluid Mech., 25 (1966), pp. 241-270. Zbl0145.23602
  2. [2] G.H. Keulegan, Characteristics of internal solitary waves, J. Res. Nat. Bur. Standards, 51 (1953), pp. 133-140. Zbl0052.21601
  3. [3] R.R. Long, Solitary waves in one- and two-fluid systems, Tellus, 8 (1956), pp. 460-471. 
  4. [4] A.S. Peters - J.J. Stoker, Solitary waves in liquids having non-constant density, Comm. Pure Appl. Math., 13 (1960), pp. 115-164. Zbl0090.43301MR112445
  5. [5] R.R. Long, Some aspects of the flow of stratified fluids. Part I : A theoretical investigation, Tellus, 5 (1953), pp. 42-57. MR57094
  6. [6] M.L. Dubreil-Jacotin, Sur les théorèmes d'existence relatifs aux ondes permanentes periodiques à deux dimensions dans les liquides hétérogènes, J. Math. Pures Appl. (9), 19 (1937), pp. 43-67. Zbl0016.05905JFM63.0771.03
  7. [7] C.-S. Yih, Exact solutions for steady two-dimensional flow of a stratified fluid, J. Fluid Mech., 9 (1960), pp. 161-174. Zbl0094.21204MR115460
  8. [8] A.M. Ter-Krikorov, Théorie exacte des ondes longues stationnaires dans un liquide hétérogène, J. Mécanique, 2 (1963), pp. 351-376. MR160400
  9. [9] K.O. Friedrichs - D.H. Hyers, The existence of solitary waves, Comm. Pure Appl. Math., 7 (1954), pp. 517-550. Zbl0057.42204MR65317
  10. [10] J. Bona - D. Bose - R.E.L. Turner, A global theory of steady waves in continuously stratified fluids, Math. Res. Center Tech. Rep., University of Wisconsin, to appear. 
  11. [11] T.B. Benjamin, A unified theory of conjugate flows, Philos. Trans. Roy. Soc. London, A269 (1971), pp. 587-643. Zbl0226.76037MR446075
  12. [12] E. Zfidlfr, Bifurcation theory and permanent waves, in Applications of Bifurcation Theory, P. Rabinowitz ed., Academic Press, New York, 1977. MR459200
  13. [13] J.J. Stoker, Water Waves, Interscience Publishers, Inc., New York, 1957. Zbl0078.40805MR103672
  14. [14] J.B. McLeod - R.E.L. Turner, Bifurcation for non-differentiable operators with an application to elasticity, Arch. Rational Mech. Anal., 63 (1976), pp. 1-45. Zbl0356.47030MR473953
  15. [15] D. Gilbarg - N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Grundlehren der mathematische Wissenschaften224, Springer-Verlag, Berlin, Heidelberg, New York, 1977. Zbl0361.35003MR473443
  16. [16] A. Ambrosetti - P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Functional Analysis, 14 (1973), pp. 349-381. Zbl0273.49063MR370183
  17. [17] O.A. Ladyzhenskaya - N.N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. Zbl0164.13002MR244627
  18. [18] R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975. Zbl0314.46030MR450957
  19. [19] G. Polya - G. Szego, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematical Studies27, Princeton University Press, Princeton, 1950. Zbl0044.38301MR43486
  20. [20] S. Agmon - A. Douglis - L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math., 12 (1959), pp. 623-727. Zbl0093.10401MR125307
  21. [21] R. Courant - D. Hilbert, Methods of Mathematical Physics, vol. II, Interscience Publishers, New York, 1962. Zbl0099.29504MR65391
  22. [22] C.J. Amick - J.F. Toland, On Solitary Water-Waves of Finite Amplitude, Arch. Rat. Mech. Anal., 76 (1981), pp. 9-95. Zbl0468.76025MR629699
  23. [23] G. Keady - J. Norbury, On the existence theory for irrotational water waves, Math. Proc. Cambridge Philos. Soc., 83 (1978), pp. 137-157. Zbl0393.76015MR502787
  24. [24] L.R. Walker, Interfacial solitary waves in a two-fluid medium, The Physics of Fluids, 16 (1973), pp. 1796-1804. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.