The role of surface-wave breaking in air-sea interaction

Annual Review of Fluid Mechanics

Volumn 28, Issue , 1996, Pages 279-321

  Melville, W K ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Air sea fluxes; Geophysical turbulence; Mixed layers; Ocean waves

Indexed keywords

EID: 0000246604     PISSN: 00664189     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev.fl.28.010196.001431     Document Type: Article

References (153)

1. Agrawal YC, Terray EA, Donelan MA, Hwang PA, Williams AJ III, et al. 1992. Enhanced dissipation of kinetic energy beneath breaking waves. Nature 359:219-20
2. Anis A, Mourn JN. 1992. The superadiabatic surface layer of the ocean during convection. J. Phys. Oceanogr. 22:1221-27
3. Baggeroer A, Munk W. 1992. The Heard Island Feasibility Test. Phys. Today 45:22-30
4. Banner ML. 1990a. The influence of wave breaking on the surface pressure distribution in wind wave interactions, J. Fluid Mech. 211:463-95
5. Banner ML. 1990b. Equilibrium spectra of wind waves. J. Phys. Oceanogr. 20:966-84
6. Banner ML, Cato DH. 1988. Physical mechanisms of noise generation by breaking waves - a laboratory study. See Kerman 1988, pp. 429-36
7. Banner ML, Fooks EH. 1985. On the microwave reflectivity of small-scale breaking water waves. Proc. R. Soc. London Ser. A 399:93-109
8. Banner ML, Jones ISF, Trinder JC. 1989. Wavenumber spectra of short gravity waves. J. Fluid Mech. 198:321-44
9. Banner ML, Melville WK. 1976. On the separation of air flow over water waves. J. Fluid Mech. 77:825-42
10. Banner ML, Peregrine DH. 1993. Wave breaking in deep water. Annu. Rev. Fluid Mech. 25:373-97
11. Banner ML, Phillips OM. 1974. On the incipient breaking of small scale waves, J. Fluid Mech. 65:647-56
12. Batchelor GK. 1959. Small-scale variation of convected quantities like temperature in turbulent fluid, Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5:113-33
13. Benjamin TB, Feir JE. 1967. The disintegration of wave trains in deep water. Part 1, Theory. J. Fluid Mech. 27:417-30
14. Bonmarin PJ. 1989. Geometric properties of deep-water breaking waves. J. Fluid Mech. 209:405-33
15. Broecker HC, Siems W. 1984. The role of bubbles for gas transfer from water to air at higher windspeeds. In Gas Transfer at Water Surfaces, ed. W Brutsaert, GH Jirka, pp. 229-36, Dordrecht: Reidel. 639 pp.
16. Carey WM, Browning DG. 1988. Low frequency ocean ambient noise: measurements and theory. See Kerman 1988, pp. 361-76
17. Cointe R, Tulin MP. 1994. A theory of steady breakers. J. Fluid Mech. 276:1-20
18. Craig PD, Banner ML. 1994. Modeling wave-enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr. 24:2546-59
19. Crowther PA, Hansla A. 1993. The lifetimes, velocities and probable origin of sonic and ultrasonic noise sources on the sea surface. In Natural Physical Sources of Underwater Sound, ed. BR Kerman, pp. 379-92, Dordrecht: Kluwer. 750 pp.
20. d' Agostino L, Brennan CE. 1983. On the acoustical dynamics of bubble clouds. In Cavitation and Multiphase Flow Forum - 1983, ed. JW Hoyt, pp. 72-75. New York: ASME. 96 pp.
21. Dickey TD, Hartman B, Hammond D, Hurst E. 1984. A laboratory technique for investigating the relationship between gas transfer and fluid turbulence. In Gas Tranfer at Water Surfaces, ed. W Brutsaert, GH Jirka, pp. 93-100. Dordrecht: Reidel. 639 pp.
22. Ding L, Farmer DM. 1994a. Observations of breaking surface wave statistics. J. Phys. Oceanogr. 24:1368-87
23. Ding L, Farmer DM. 1994b. On the dipole acoustic source level of breaking waves. J. Acous. Soc. Am. 96:3036-44
24. Dold JW, Peregrine DH. 1986. Water-wave modulation. Proc. 20th Conf. Coastal Eng., Taipei, 1:163-75. Minneapolis: ASCE
25. Dommermuth DG, Yue DKP, Rapp RJ, Chan E-S, Melville WK. 1987. Deep-water breaking waves: a comparison between potential theory and experiments. J. Fluid Mech. 89:432-42
26. Donelan M, Longuet-Higgins MS, Turner JS. 1972. Periodicity in whitecaps. Nature 239:449-51
27. Donelan MA, Hamilton J, Hui WH. 1985. Directional spectra of wind-generated waves. Phil. Trans. R. Soc. London Ser. A 315:509-62
28. Drennan WM, Kahma KK, Terray EA, Donelan MA, Kitaigorodskii SA. 1992. Observations of the enhancement of kinetic energy dissipation beneath breaking wind waves. In Breaking Waves: IUTAM Symposium Sydney, Australia 1991, ed. ML Banner, RHJ Grimshaw, pp. 95-102. Berlin/Heidelberg: Springer-Verlag. 387 pp.
29. Duncan JH. 1981. An experimental investigation of breaking waves produced by a towed hydrofoil. Proc. A. Soc. London Ser. A 377:331-48
30. Duncan JH. 1983. The breaking and non-breaking wave resistance of a two-dimensional hydrofoil. J. Fluid Mech. 126:507-20
31. Duncan JH, Philomin V, Behres M, Kimmel J. 1994a. The formation of spilling breaking water waves. Phys. Fluids. 6:2558-60
32. Duncan JH, Philomin V, Qiao H, Kimmel J. 1994b. The formation of a spilling breaker. Phys. Fluids 6:S2
33. Farmer DM, Gemmrich JR. 1995. Measurements of temperature fluctuations in breaking surface waves. J. Phys Oceanogr In press
34. Farmer DM, McNeil CL, Johnson BD. 1993. Evidence for the importance of bubbles in increasing air-sea gas flux. Nature 361:620-23
35. Farmer DM, Vagle S. 1988. On the determination of breaking wave distributions using ambient sound. J. Geophys. Res. 93:3591-600
36. Felizardo FC, Melville WK. 1995. Correlations between ambient noise and the ocean surface wave field. J. Phys. Oceanogr. 25:513-32
37. Forristall GZ. 1981. Measurement of a saturation range in ocean wave spectra. J. Geophys. Res 86:8075-84
38. Frasier SJ, Liu Y, Moller D, McIntosh RE, Mead JB. 1995. Directional ocean wave measurements in a coastal setting using a focused array imaging radar. IEEE Trans. Geosci. Rem. Sens. 33:428-40
39. Gargett AE. 1989. Ocean turbulence. Annu. Rev. Fluid Mech. 21:419-51
40. Gill AE. 1982. Atmosphere-Ocean Dynamics. London: Academic. 662 pp.
41. Hasselmann K. 1962. On the nonlinear energy transfer in a gravity-wave spectrum. Part 1 : General theory. J. Fluid Mech. 12:481-500
42. Hasselmann K. 1974. On the spectral dissipation of ocean waves due to white capping. Boundary-Layer Meteorol. 6:107-27
43. Hollet R. 1989. Underwater sound from white caps at sea. J. Acous. Soc. Am. 85(S1): S145
44. Holthuijsen LH, Herbers THC. 1986. Statistics of breaking waves observed as whitecaps in the open sea. J. Phys. Oceanogr. 16:290-97
45. Hopfinger EJ, Toly J-A. 1976. Spatially decaying turbulence and its relation to mixing across density interfaces. J. Fluid Mech. 78:155-75
46. Hornung HG, Willert C, Turner S. 1995. The flow field downstream of a hydraulic jump. J. Fluid Mech. 287:299-316
47. Hsu CT, Hsu EY, Street RL. 1981. On the structure of turbulent flow over a progessive water wave: theory and experiment in a transformed, wave following co-ordinate system. J. Fluid Mech. 105:87-117
48. Hsu CT, Wu HW, Hsu EY, Street RL. 1982. Momentum and energy transfer in wind generation of waves. J. Phys. Oceanogr. 12:929-51
49. Jähne B. 1990. New experimental results on the parameters influencing air-sea gas exchange. In Proc. Air-Water Mass Transfer: Second Int. Symp, ed. SC Wilhelms, JS Gulliver, pp. 582-92. Minneapolis: ASCE
50. Jessup AT. 1995. The infrared signature of breaking waves. In Proc. Symp. on Air-Sea Interaction, Marseille, France 1993, ed. MA Donelan, WJ Plant, WH Hui. Toronto: Univ. Toronto Press
51. Jessup AT, Keller WC, Melville WK. 1990. Measurements of sea spikes in microwave backscatter at moderate incidence. J. Geophys. Res. 95:9679-88
52. Jessup AT, Melville WK, Keller WC. 1991a. Breaking waves affecting microwave backscatter. 1. Detection and verification. J. Geophys. Res. 96:20,547-59
53. Jessup AT, Melville WK, Keller WC. 1991b. Breaking waves affecting microwave backscatter. 2. Dependence on wind and wave conditions. J. Geophys. Res. 96:20,561-69
54. -4 -spectral form for growing wind waves. J. Oceanogr. Soc. Jpn. 33:137-50
55. Keeling RF. 1993. On the role of large bubbles in air-sea gas exchange and supersaturation in the ocean. J. Mar. Res. 51:237-71
56. Keller WC, Plant WJ, Valenzuela GR. 1986. Observations of breaking ocean waves with coherent microwave radar. In Wave Dynamics and Radio Probing of the Sea Surface, ed. OM Phillips, K Hasselmann, pp. 285-93. New York: Plenum
57. Kennedy RM. 1992. Sea surface dipole sound source dependence on wave-breaking variables. J. Acous. Soc. Am. 91:1974-82
58. Kennedy RM. 1993. Acoustic radiation due to surface wave breaking. J. Acous. Soc. Am. 94:2443-45
59. Kerman BR, ed. 1988. Sea Surface Sound-Natural Mechanisms of Surface Generated Noise in the Ocean. Dordrecht: Kluwer. 639 PP.
60. Khoo BC, Sonin AA. 1992. Augmented gas exchange across wind-sheared and shear-free air-water interfaces. J. Geophys. Res. 97:14,413-16
61. Kitaigorodskii SA. 1983. On the theory of the equilibrium range in the spectrum of wind-generated gravity waves. J. Phys. Oceanogr. 13:816-27
62. Kitaigorodskii SA. 1984. On the fluid dynamical theory of turbulent gas transfer across an air-sea interface in the presence of breaking wind-waves. J. Phys. Oceanogr. 14:960-72
63. Kitaigorodskii SA, Donelan MA, Lumley JL, Terray EA. 1983. Wave-turbulence interactions in the upper ocean. Part II. J. Phys. Oceanogr. 13:1988-99
64. Komen GJ, Cavaleri L, Donelan M, Hasselmann K, Hasselmann S, Janssen PAEM. 1994. Dynamics and Modelling of Ocean Waves. Cambridge: Cambridge Univ. Press. 532 pp.
65. Komen GJ, Hasselmann S, Hasselmann K. 1984. On the existence of a fully developed wind-sea spectrum. J. Phys. Oceanogr. 14:1271-85
66. Lamarre E. 1993. An experimental study of air entrainment by breaking waves. PhD Thesis. MIT/WHOI Joint Program, Cambridge/Woods Hole, MA. 327 pp.
67. Lamarre E, Melville WK. 1991. Air entrainment and dissipation in breaking waves. Nature 351:469-72
68. Lamarre E, Melville WK. 1992. Instrumentation for the measurement of void fraction in breaking waves: laboratory and field results. IEEE J. Ocean. Eng. 17:204-15
69. Lamarre E, Melville WK. 1994. Void-fraction measurements and sound speed fields in bubble plumes generated by breaking waves. J. Acous. Soc. Am. 95:1317-28
70. Lamont JC, Scott DS. 1970. An eddy cell model of mass transfer into the surface of a turbulent liquid. AIChE J. 16:513-19
71. Leighton TG. 1994. The Acoustic Bubble. New York: Academic. 613 pp.
72. Lighthill MJ. 1965. Contributions to the theory of waves in nonlinear dispersive systems. J. Inst. Math Appl. 1:269-306
73. Lin JC, Rockwell D, 1994. Instantaneous structure of a breaking wave. Phys. Fluids 6:2877-79
74. Lin JC, Rockwell D. 1995. Evolution of a quasisteady breaking wave. J. Fluid Mech. In press
75. Liss PS. 1988. Tracers of air-sea gas exchange. Phil. Trans. R. Soc. London Ser. A 325:93-103
76. Liss PS, Merlivat L. 1986. Air-sea gas exchange: introduction and synthesis. In The Role of Air-Sea Exchange in Geochemical Cycling, ed. P Buat-Menard, pp. 113-27. Dordrecht: Reidel. 549 pp.
77. Loewen MR, Melville WK. 1991a. Microwave backscatter and acoustic radiation from breaking waves. J. Fluid Mech. 224:601-23
78. Loewen MR, Melville WK. 1991b. A model of the sound generated by breaking waves. J. Acous Soc. Am. 90:2075-80
79. Loewen MR, Melville WK. 1994. An experimental investigation of collective oscillations of bubble plumes entrained by breaking waves. J. Acous. Soc. Am. 95:1329-43
80. Longuet-Higgins MS. 1974. Breaking waves in deep or shallow water. In Proc. 10th Conf. on Naval Hydrodynamics. MIT, pp. 597-605. Washinton DC: US Govt. Print. Office. 792 PP.
81. Longuet-Higgins MS. 1987. The propagation of short surface waves on longer gravity waves. J. Fluid Mech. 177:293-306
82. Longuet-Higgins MS. 1988. Mechanisms of wave breaking in deep water. See Kerman 1988, pp. 1-30
83. Longuet-Higgins MS. 1992. Capillary rollers and bores. J. Fluid Mech. 240:659-79
84. Longuet-Higgins MS. 1994. Shear instability in spilling breakers. Proc. R. Soc. London Ser. A 446:399-409
85. Longuet-Higgins MS. 1995. Parasitic capillary waves: a direct calculation. J. Fluid Mech. Submitted
86. Longuet-Higgins MS, Cleaver RP. 1994. Crest instabilities of gravity waves. 1. The almost highest wave. J. Fluid Mech. 258:115-29
87. Longuet-Higgins MS, Cleaver RP, Fox MJH. 1994. Crest instabilities of gravity waves. 2. Matching and asymptotic analysis. J. Fluid Mech. 259:333-44
88. Longuet-Higgins MS, Cokelet ED. 1978. The deformation of steep surface waves on water II. Growth of normal mode instabilities. Proc. R. Soc. London Ser. A 364:1-28
89. Longuet-Higgins MS, Smith ND. 1983. Measurements of breaking waves by a surface jump meter. J. Geophys. Res. 88:9823-31
90. Longuet-Higgins MS, Stewart RW. 1960. Changes in the form of short gravity waves on long waves and tidal currents. J. Fluid Mech. 8:565-83
91. Longuet-Higgins MS, Stewart RW. 1964. Radiation stress in water waves: a physical discussion with applications. Deep-Sea Res. 11:529-62
92. Longuet-Higgins MS, Ursell F. 1948. Seawaves and microseisms. Nature 162:700
93. McLean JW, Ma YC, Martin DU, Saffman PG, Yuen HC. 1981. Three-dimensional instability of finite-amplitude water waves. Phys. Rev. Lett. 46:817-20
94. Medwin H, Beaky MM. 1989. Bubble sources of the Knudsen Sea noise spectrum. J. Acous. Soc. Am. 86:1124-30
95. Medwin H, Daniel AC. 1990. Acoustical measurement of bubble production by spilling breakers. J. Acous. Soc. Am. 88:40,812
96. Melville WK. 1982. The instability and breaking of deep-water waves. J. Fluid Mech. 115:163-85
97. Melville WK. 1983. Wave modulation and breakdown. J. Fluid Mech. 128:489-506
98. Melville WK. 1993. The role of wave breaking in air-sea interaction. In Theoretical and Applied Mechanics, 1992: Proc. 15th Int. Congr. Theoret. Appl. Math., Haifa, Israel, ed SR Bodner, J Singer, A Solan, Z Hashin, pp. 99-117. Amstredam/New York: Elsevier
99. Melville WK. 1994. Energy dissipation by breaking waves. J. Phys. Oceanogr. 24:2041-49
100. Melville WK, Loewen MR, Felizardo FC, Jessup AT, Buckingham MJ. 1988. Acoustic and microwave signatures of breaking waves. Nature 336:54-59
101. Melville WK, Rapp RJ. 1985. Momentum flux in breaking waves. Nature 317:514-16; see also cover photograph
102. Melville WK, Rapp RJ. 1988. The surface velocity field in steep and breaking waves. J. Fluid Mech. 189:1-22
103. Merlivat L, Memery L. 1983. Gas exchange across an air-water interface: experimental results and modeling of bubble contribution to transfer. J. Geophys. Res. 88:707-24
104. Miche A. 1944. Mouvements ondulatoires de la mer en profondeur constante ou decroissante. Ann. Ponts Chaussees, pp. 25-78, 131-64, 270-92, 369-406
105. Miles JW. 1957. On the generation of surface waves by shear flows, Part I. J. Fluid Mech. 3:185-204
106. Miles J. 1993. Surface-wave generation revisited. J. Fluid Mech. 256:427-41
107. Miller RL. 1976. Role of vortices in surf zone prediction: sedimentation and wave forces. In Beach and Nearshore Sedimentation, ed. RA Davis, RL Ethington, pp. 92-114. Tulsa: Soc. Econ. Paleontol. Mineral. 187 pp.
108. Miller SJ, Shemdin OH, Longuet-Higgins MS. 1991. Laboratory measurements of short-wave slopes on long surface waves. J. Fluid Mech. 233:389-404
109. Minnaert M. 1933. On musical air bubbles and the sounds of running water. Phil. Mag. 16:235-48
110. Mitsuyasu H. 1985. A note on the momentum transfer from wind to waves. J. Geophys. Res. 90:3343-45
111. Monahan EC, McNiocaill G, eds. 1986. Ocean Whitecaps and Their Role in Air-Sea Exchange Processes. Dordrecht: Reidel. 294 pp.
112. Oakey NS, Elliot JA. 1982. Dissipation within the surface mixed layer. J. Phys. Ocean. 12:171-85
113. Oguz HN. 1994. A theoretical study of low-frequency oceanic ambient noise. J. Acous. Soc. Am. 95:1895-912
114. Osborne AR, Burch TL. 1980. Internal solitons in the Andaman Sea. Science 208:451-59; see also cover photograph
115. Phillips OM. 1958. The equilibrium range in the spectrum of wind-generated ocean waves. J. Fluid Mech. 4:426-34
116. Phillips OM. 1960. On the dynamics of unsteady gravity waves of finite amplitude. Part 1. J. Fluid Mech. 9:193-217
117. Phillips OM. 1977. The Dynamics of the Upper Ocean. Cambridge: Cambridge Univ. Press. 336 pp. 2nd ed.
118. Phillips OM. 1981. The dispersion of short wavelets in the presence of a dominant long wave. J. Fluid Mech. 107:465-85
119. Phillips OM. 1985. Spectral and statistical properties of the equilibrium range in wind-generated gravity waves. J. Fluid Mech. 156:505-31
120. Phillips OM. 1988. Radar returns from the sea surface - Bragg scattering and breaking waves. J. Phys. Oceanogr. 18:1065-74
121. Pierson WJ, Moskowitz L. 1964. A proposed spectral form for fully-developed wind seas based on the similarity theory of SA Kitaigorodskii. J. Geophys. Res. 69:5191-203
122. Pinkel R, Smith JA. 1987, Open ocean surface wave measurement using Doppler sonar. J. Geophys Res 92:12,967-73
123. Plant WJ. 1982. A relationship between wind stress and wave slope. J. Geophys. Res. 87:1961-67
124. Prosperetti A. 1988. Bubble dynamics in oceanic ambient noise. See Kerman 1988, pp. 151-71
125. Rapp RJ, Melville WK. 1990. Laboratory measurements of deep-water breaking waves. Phil. Trans. R. Soc. London Ser. A 331:735-800
126. Smith MJ, Poulter EM, McGregor JA. 1995. Doppler radar measurements of wave groups and breaking waves. J. Geophys. Res. Submitted
127. Snyder RL, Dobson FW, Elliott JA, Long RB. 1981. Array measurements of atmospheric pressure fluctuations above surface gravity waves. J. Fluid Mech. 102:1-59
128. Spitzer WS, Jenkins WJ. 1989. Rates of vertical mixing, gas exchange and new production: estimates from seasonal gas cycles in the upper ocean. J. Mar. Res. 47:169-96
129. Stokes GG. 1847. On the theory of oscillatory waves. Trans. Cambridge. Phil. Soc. 8:441-55
130. Su M-Y, Bergin M, Marlev P, Myrick RJ. 1982. Experiments on nonlinear instabilities and evolution of steep gravity-wave trains. J. Fluid Mech. 124:4572
131. Terray AM, Agrawal YC, Drennan WM, Kahma KK, Williams AJ III, et al. 1995. Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr. In press
132. Thorpe SA. 1982. On the clouds of bubbles formed by breaking wind waves in deep water, and their role in air-sea gas transfer. Phil. Trans R. Soc. London Ser. A 304:155-210
133. Thorpe SA. 1984. The role of bubbles produced by breaking waves in supersaturating the near-surface ocean mixing layer with oxygen. Ann. Geophys 2:53-56
134. Thorpe SA. 1985. Small-scale processes in the upper ocean boundary layer. Nature 318:519-22
135. Thorpe SA. 1992. Bubble clouds and the dynamics of the upper ocean. Q J. R. Meteorol. Soc. 118:1-22
136. Thorpe SA. 1993. Energy loss by breaking waves. J. Phys. Oceanogr. 23:2498-502
137. Thorpe SA, 1995. Dynamical processes of transfer at the sea surface. Prog. Oceanogr 35(4): In press
138. Thorpe SA, Hall AJ. 1983. The characteristics of breaking waves, bubble clouds and near-surface currents observed using side-scan sonar. Cont. Shelf Res. 1:353-84
139. Thorpe SA, Humphries PN. 1980. Bubbles and breaking waves. Nature 283:463-65
140. Toba Y. 1973. Local balance in the air-sea boundary processes. III. On the spectrum of wind waves. J. Oceanogr. Soc. Jpn. 29:209-20
141. Trulsen K, Dysthe KB. 1992. Action of wind-stress and breaking on the evolution of a wavetrain. In Breaking Waves: IUTAM Symp. Sydney, Australia 1991, ed. ML Banner, RHJ Grimshaw, pp. 243-49. Berlin/Heidelberg: Springer-Verlag. 387 pp.
142. Vagle S, Farmer DM. 1992. The measurement of bubble-size distributions by acoustical backscatter. J. Atmos. Ocean. Tech. 9.630-44
143. Vagle S, Large WG, Farmer DM. 1990. An evaluation of the WOTAN technique for inferring oceanic winds from underwater ambient sound. J. Atmos. Ocean. Tech. 7:576-95
144. Wallace DWR, Wirick CD. 1992. Large air-sea fluxes associated with breaking waves. Nature 356:694-96
145. Watson AJ, Upstill-Goddard RC, Liss PS. 1991. Air-sea gas exchange in rough and stormy seas measured by a dual-tracer technique. Nature 349:145-47
146. Weissman MA, Katsaros KB, Atakturk SS. 1984. Detection of breaking events in a wind-generated wave field. J. Phys. Oceanogr. 14:1608-19
147. Wenz GM. 1962. Acoustic ambient noise in the ocean: spectra and sources. J. Acous. Soc. Am. 34:1936-56
148. Woolf DK. 1993. Bubbles and the air-sea transfer velocity of gases. Atmos. Ocean 31:517-40
149. Woolf DK, Thorpe, SA. 1991. Bubbles and the air-sea exchange of gases in near-saturation conditions. J. Mar. Res. 49:435-66
150. Wu JZ. 1995. A theory of three-dimensional interfacial vorticity dynamics. Univ. Tenn. Space Inst, Rep. 95-01, Tullahoma, TN
151. Yuen HC, Lake BM. 1980. Instabilities of waves on deep water. Annu. Rev. Fluid Mech. 12:303-34
152. Zhang J, Melville WK. 1990. Evolution of weakly nonlinear short waves riding on long gravity waves. J. Fluid Mech. 214:321-46
153. Zhang J, Melville WK. 1992. On the stability of weakly nonlinear short waves on finite-amplitude long gravity waves. J. Fluid Mech. 243:51-72