David J. Benney: Nonlinear Wave and Instability Processes in Fluid Flows

Literature Cited

1. Ablowitz MJ, Akylas TR, Lin CC 2002. Research contributions of David J. Benney. Stud. Appl. Math. 108:1–6
   [Google Scholar]
2. Ablowitz MJ, Baldwin DE 2012. Nonlinear shallow ocean-wave soliton interactions on flat beaches. Phys. Rev. E 86:036305
   [Google Scholar]
3. Akylas TR 1994. Three-dimensional long water-wave phenomena. Annu. Rev. Fluid Mech. 26:191–210
   [Google Scholar]
4. Antar BN, Collins FG 1975. Numerical calculation of finite amplitude effects in unstable boundary layers. Phys. Fluids 18:289–97
   [Google Scholar]
5. Beal RC, Deleonibus PS, Katz I 1981. Spaceborne Synthetic Aperture Radar for Oceanography Baltimore: Johns Hopkins Univ. Press
6. Benjamin TB 1957. Wave formation in laminar flow down an inclined plane. J. Fluid Mech. 2:544–47
   [Google Scholar]
7. Benjamin TB 1962. The solitary wave on a stream with an arbitrary distribution of vorticity. J. Fluid Mech. 12:97–116
   [Google Scholar]
8. Benjamin TB 1967. Instability of periodic wavetrains in nonlinear dispersive systems. Proc. R. Soc. Lond. A 299:59–75
   [Google Scholar]
9. Benjamin TB, Feir JE 1967. The disintegration of wavetrains on deep water. Part 1. Theory. J. Fluid Mech. 27:417–30
   [Google Scholar]
10. Benney DJ 1961. A non-linear theory for oscillations in a parallel flow. J. Fluid Mech. 10:209–36
    [Google Scholar]
11. Benney DJ 1962. Non-linear gravity wave interactions. J. Fluid Mech. 14:577–84
    [Google Scholar]
12. Benney DJ 1964. Finite-amplitude effects in an unstable laminar boundary layer. Phys. Fluids 7:319–26
    [Google Scholar]
13. Benney DJ 1966a. Long non-linear waves in fluid flows. J. Math. Phys. 45:52–63
    [Google Scholar]
14. Benney DJ 1966b. Long waves on liquid films. J. Math. Phys. 45:150–55
    [Google Scholar]
15. Benney DJ 1973. Some properties of long nonlinear waves. Stud. Appl. Math. 52:45–50
    [Google Scholar]
16. Benney DJ 1976. Significant interactions between small and large scale surface waves. Stud. Appl. Math. 55:93–106
    [Google Scholar]
17. Benney DJ 1977. General theory for interactions between short and long waves. Stud. Appl. Math. 56:81–94
    [Google Scholar]
18. Benney DJ 1983. Nonlinear wavepackets in flows with critical layers. Stud. Appl. Math. 69:177–200
    [Google Scholar]
19. Benney DJ 1984. The evolution of disturbances in shear flows at high Reynolds numbers. Stud. Appl. Math. 70:1–19
    [Google Scholar]
20. Benney DJ, Bergeron RF 1969. A new class of nonlinear waves in parallel flows. Stud. Appl. Math. 48:181–204
    [Google Scholar]
21. Benney DJ, Chow KW 1985. An alternative approach to nonlinear instabilities in hydrodynamics. Stud. Appl. Math. 73:261–67
    [Google Scholar]
22. Benney DJ, Chow KW 1989. A mean flow 1st harmonic theory for hydrodynamic instabilities. Stud. Appl. Math. 80:37–73
    [Google Scholar]
23. Benney DJ, Lin CC 1960. On the secondary motion induced by oscillations in a shear flow. Phys. Fluids 3:656–57
    [Google Scholar]
24. Benney DJ, Luke JC 1964. On the interaction of permanent waves of finite amplitude. J. Math. Phys. 43:309–13
    [Google Scholar]
25. Benney DJ, Newell AC 1967a. Sequential time closures for interacting random waves. J. Math. Phys. 46:363–93
    [Google Scholar]
26. Benney DJ, Newell AC 1967b. The propagation of nonlinear wave envelopes. J. Math. Phys. 46:133–39
    [Google Scholar]
27. Benney DJ, Roskes GJ 1969. Wave instabilities. Stud. Appl. Math. 48:377–85
    [Google Scholar]
28. Benney DJ, Saffman PG 1966. Nonlinear interactions of random waves in a dispersive medium. Proc. R. Soc. Lond. A 289:301–20
    [Google Scholar]
29. Berger KM, Milewski PA 2000. The generation and evolution of lump solitary waves in surface-tension-dominated flows. SIAM J. Appl. Math. 61:731–50
    [Google Scholar]
30. Bogoliubov NN, Mitropolsky YA 1961. Asymptotic Methods in the Theory of Non-Linear Oscillations New Delhi: Hindustan
31. Boussinesq J 1871. Théorie de l'intumescence liquide appelée onde solitaire ou de translation se propageant dans un canal rectangulaire. C.R. 72:755–59
    [Google Scholar]
32. Bryant PJ 1990. Professor David Benney. N.Z. Math. Soc. Newsl. 50:1–2
    [Google Scholar]
33. Caillol P, Grimshaw RH 2007. Rossby solitary waves in the presence of a critical layer. Stud. Appl. Math. 118:313–64
    [Google Scholar]
34. Chang H 1994. Wave evolution on a falling film. Annu. Rev. Fluid Mech. 26:103–36
    [Google Scholar]
35. Chu VC, Mei CC 1970. On slowly varying Stokes waves. J. Fluid Mech. 41:873–87
    [Google Scholar]
36. Davey A, Stewartson K 1974. On three-dimensional packets of surface waves. Proc. R. Soc. Lond. A 338:101–10
    [Google Scholar]
37. Drazin PG, Reid WH 1982. Hydrodynamic Stability Cambridge, UK: Cambridge Univ. Press
38. Feir JE 1967. Discussion: some results from wave pulse experiments. Proc. R. Soc. Lond. A 299:54–58
    [Google Scholar]
39. Funakoshi M 1980. Reflection of obliquely incident solitary waves. J. Phys. Soc. Jpn. 49:2371–79
    [Google Scholar]
40. Haberman R 1972. Critical layers in parallel flows. Stud. Appl. Math. 51:139–61
    [Google Scholar]
41. Hamilton J, Kim J, Waleffe F 1995. Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287:317–48
    [Google Scholar]
42. Hasimoto H, Ono H 1972. Nonlinear modulation of gravity waves. J. Phys. Soc. Jpn. 33:805–11
    [Google Scholar]
43. Hasselmann K 1962. On the nonlinear energy transfer in a gravity wave spectrum. Part 1: general theory. J. Fluid Mech. 12:481–500
    [Google Scholar]
44. Kadomtsev BB, Petviashvili VI 1970. On the stability of solitary waves in weakly dispersive media. Sov. Phys. Dokl. 15:539–41
    [Google Scholar]
45. Klebanoff PS, Tidstrom KD, Sargent LM 1962. The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12:1–34
    [Google Scholar]
46. Korteweg DJ, deVries G 1895. On the change of form of long waves advancing in a rectangular channel, and on a new type of long stationary waves. Lond. Edinb. Dublin Philos. Mag. J. Sci. 39:422–43
    [Google Scholar]
47. Lin CC, Benney DJ 1964. On the instability of shear flows and their transition to turbulence. Applied Mechanics: Proceedings of the Eleventh International Congress of Applied Mechanics H Görtler797–802 Berlin: Springer
    [Google Scholar]
48. Long RR 1956. Solitary waves in the one-fluid and two-fluid systems. Tellus 8:460–71
    [Google Scholar]
49. Longuet-Higgins MS 1962. Resonant interactions between two trains of gravity waves. J. Fluid Mech. 12:321–32
    [Google Scholar]
50. Maslowe SA 1981. Shear flow instabilities and transition. Hydrodynamic Instabilities and the Transition to Turbulence HL Swinney, JP Gollub181–228 Berlin: Springer
    [Google Scholar]
51. Maslowe SA 1986. Critical layers in shear flows. Annu. Rev. Fluid Mech. 18:405–32
    [Google Scholar]
52. Maslowe SA 2014. Evolution equations for finite amplitude waves in parallel shear flows. Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations ON Kirillov, DE Pelinovsky223–46 Hoboken, NJ: Wiley
    [Google Scholar]
53. Maslowe SA, Benney DJ, Mahoney DJ 1994. Wave packet critical layers in shear flows. Stud. Appl. Math. 91:1–16
    [Google Scholar]
54. Maslowe SA, Clarke SR 2002. Subcritical Rossby waves in zonal shear flows with nonlinear critical layers. Stud. Appl. Math. 108:89–103
    [Google Scholar]
55. Miles JW 1977a. Obliquely interacting solitary waves. J. Fluid Mech. 79:157–69
    [Google Scholar]
56. Miles JW 1977b. Resonantly interacting solitary waves. J. Fluid Mech. 79:171–79
    [Google Scholar]
57. MIT Math. Dep 2015. David Benney, emeritus professor of mathematics, dies at 85. MIT News http://news.mit.edu/2015/david-benney-mit-applied-mathematician-dies-1016
    [Google Scholar]
58. Newell AC, Nazarenko S, Biven L 2001. Wave turbulence and intermittency. Physica D 152:520–50
    [Google Scholar]
59. Oron A, Davis SH, Bankoff GS 1997. Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69:931–80
    [Google Scholar]
60. Orszag SA, Patera AT 1983. Secondary instability of wall-bounded shear flows. J. Fluid Mech. 128:347–85
    [Google Scholar]
61. Peters AS, Stoker JJ 1960. Solitary waves in liquids having non-constant density. Commun. Pure Appl. Math. 8:115–64
    [Google Scholar]
62. Phillips OM 1960. On the dynamics of unsteady gravity waves of finite amplitude. Part 1. The elementary interactions. J. Fluid Mech. 9:193–217
    [Google Scholar]
63. Phillips OM 1981. Wave interactions—the evolution of an idea. J. Fluid Mech. 106:215–27
    [Google Scholar]
64. Rayleigh L 1876. On waves. Lond. Edinb. Dublin Philos. Mag. J. Sci. 1:5257–79
    [Google Scholar]
65. Redekopp LG 1977. On the theory of solitary Rossby waves. J. Fluid Mech. 82:725–45
    [Google Scholar]
66. Russell JS 1844. Report on waves. Report of the Fourteenth Meeting of the British Association for the Advancement of Science311–90 London: John Murray
    [Google Scholar]
67. Skopovi I, Akylas TR 2004. Transient nonlinear disturbances and shelves in a stratified fluid layer. Stud. Appl. Math. 113:139–61
    [Google Scholar]
68. Stokes GG 1847. On the theory of oscillatory waves. Trans. Camb. Philos. Soc. 8:441–73
    [Google Scholar]
69. Stuart JT 1962. Nonlinear effects in hydrodynamic stability. Proceedings of the 10th International Congress of Applied Mechanics F Rolla, WT Koiter63–97 Amsterdam: Elsevier
    [Google Scholar]
70. Tabaei A, Akylas TR 2007. Resonant long-short wave interactions in an unbounded rotating stratified fluid. Stud. Appl. Math. 119:271–96
    [Google Scholar]
71. Waleffe F 1995a. Hydrodynamic stability and turbulence: beyond transients to a self-sustaining process. Stud. Appl. Math. 95:319–43
    [Google Scholar]
72. Waleffe F 1995b. Transition in shear flows. Nonlinear normality versus non-normal linearity. Phys. Fluids 7:3060–66
    [Google Scholar]
73. Waleffe F 1997. On a self-sustaining process in shear flows. Phys. Fluids 9:883–900
    [Google Scholar]
74. Waleffe F 1998. Three-dimensional coherent states in plane shear flows. Phys. Rev. Lett. 81:4140–48
    [Google Scholar]
75. Waleffe F, Wang J 2005. Transition threshold and the self-sustaining process. IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions T Mullin, RR Kerswell85–106 Dordrecht, Neth.: Springer
    [Google Scholar]
76. Whitham GB 1967. Nonlinear dispersion of water waves. J. Fluid Mech. 27:399–412
    [Google Scholar]
77. Whitham GB 1974. Linear and Nonlinear Waves New York: Wiley
78. Wilhelm J, Akylas TR, Boloni G, Wei J, Ribstein B et al. 2018. Interactions between mesoscale and submesoscale gravity waves and their efficient representation in mesoscale-resolving models. J. Atmos. Sci. 75:2257–80
    [Google Scholar]
79. Yih CS 1963. Stability of liquid flow down an inclined plane. Phys. Fluids 6:321–34
    [Google Scholar]
80. Zakharov VE 1968. Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 2:190–94
    [Google Scholar]