Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-13T09:23:50.422Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  07 September 2010

Jean-Marc Vanden-Broeck
Affiliation:
University College London
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Acheson, D. J. 1990, Elementary Fluid DynamicsOxford University Press.Google Scholar
[2] Ackerberg, R. C. 1975, The effects of capillarity on free-streamline separation. J. Fluid Mech. 70, 333–352.CrossRefGoogle Scholar
[3] Akylas, T. R. 1993, Envelope solitons with stationary crests. Phys. Fluids A 5, 789–791.CrossRefGoogle Scholar
[4] Akylas, T. R. & Grimshaw, R. 1992, Solitary internal waves with oscillatory tails. J. Fluid Mech. 242, 279–298.CrossRefGoogle Scholar
[5] Amick, C. J., Fraenkel, L. E. & Toland, J. F. 1982, On the Stokes conjecture and the wave of extreme form. Acta Math. 148, 193–214.CrossRefGoogle Scholar
[6] Anderson, C. D. & Vanden-Broeck, J.-M. 1996, Bow flows with surface tension. Proc. Roy. Soc. Lond. A 452, 1985–1997.CrossRefGoogle Scholar
[7] Asavanant, J. & Vanden-Broeck, J.-M. 1994, Free-surface flows past a surface-piercing object of finite length. J. Fluid. Mech. 273, 109–124.CrossRefGoogle Scholar
[8] Batchelor, G. K.Fluid Dynamics. Cambridge University Press, 615 pp.
[9] Baker, G., Meiron, D. & Orszag, S. 1982, Generalised vortex methods for free surface flow problemsJ. Fluid Mech. 123, 477–501.CrossRefGoogle Scholar
[10] Beale, T. J. 1991, Solitary water waves with capillary ripples at infinity. Comm. Pure Appl. Maths 64, 211–257.CrossRefGoogle Scholar
[11] Benjamin, B. 1956, On the flow in channels when rigid obstacles are placed in the stream. J. Fluid Mech. 1, 227–248.CrossRefGoogle Scholar
[12] Benjamin, B. 1962, The solitary wave on a stream with arbitrary distribution of vorticity. J. Fluid Mech. 12, 97–116.CrossRefGoogle Scholar
[13] Billingham, J. & King, A. C. 2000, Wave Motion. Cambridge University Press.Google Scholar
[14] Binder, B. J., Dias, F. & Vanden-Broeck, J.-M. 2005, Forced solitary waves and fronts past submerged obstacles. Chaos 15, 037106.CrossRefGoogle ScholarPubMed
[15] Binder, B. J. & Vanden-Broeck, J.-M. 2005, Free surface flows past surfboards and sluice gates. Euro. J. Appl. Math. 16, 601–619.CrossRefGoogle Scholar
[16] Binder, B. J. & Vanden-Broeck, J.-M. 2007, The effect of disturbances on the flows under a sluice gate and past an inclined plate. J. Fluid Mech. 576, 475–490.CrossRefGoogle Scholar
[17] Binnie, A. M. 1952, The flow of water under a sluice gate. Q. J. Mech. Appl. Math. 5, 395–407.CrossRefGoogle Scholar
[18] Birkhoff, G. & Carter, D. 1957, Rising plane bubbles. J. Math. Phys. 6 769–779.Google Scholar
[19] Birkhoff, G. & Zarantonello, E. 1957, Jets, Wakes and CavitiesAcademic Press, 353 pp.Google Scholar
[20] Blyth, M. G. & Vanden-Broeck, J.-M. 2004, New solutions for capillary waves on fluid sheets. J. Fluid Mech. 507, 255–264.CrossRefGoogle Scholar
[21] Blyth, M. G. & Vanden-Broeck, J.-M. 2005, New solutions for capillary waves on curved sheets of fluids. IMA J. Appl. Math. 70, 588–601.CrossRefGoogle Scholar
[22] Brillouin, M. 1911, Les surfaces de glissement de Helmoltz at la résistance des fluides. Ann. de Chim. Phys. 23, 145–230.Google Scholar
[23] Brodetsky, S. 1923, Discontinuous fluid motion past circular and elliptic cylinders. Proc. Roy. Soc. London A 102, 1–14.CrossRefGoogle Scholar
[24] Budden, P. & Norbury, J. 1982, Uniqueness of free boundary flows under gravity. Arch. Rat. Mech. Anal. 78, 361–380.CrossRefGoogle Scholar
[25] Byatt-Smith, J. G. B. & Longuet-Higgins, M. S. 1976, On the speed and profile of steep solitary waves. Proc. Roy. Soc. London. A 350, 175–189.CrossRefGoogle Scholar
[26] Champneys, A. R., Vanden-Broeck, J.-M. & Lord, G. J. 2002, Do true elevation gravity–capillary solitary waves exist? A numerical investigation. J. Fluid Mech. 454, 403–417.CrossRefGoogle Scholar
[27] Chen, B. & Saffman, P. G. 1979, Steady gravity–capillary waves on deep water, Part I: Weakly nonlinear waves. Stud. Appl. Math. 60, 183–210.CrossRefGoogle Scholar
[28] Chen, B. & Saffman, P. G. 1980a, Numerical evidence for the existence of new types of gravity waves on deep water. Stud. Appl. Math. 62, 1–21.CrossRefGoogle Scholar
[29] Chen, B. & Saffman, P. G. 1980b, Steady gravity–capillary waves on deep water, Part II: Numerical results for finite amplitude. Stud. Appl. Math. 62, 95–111.CrossRefGoogle Scholar
[30] Chung, Y. K. 1972, Solution of flow under a sluice gates. ASCE J. Eng. Mech. Div. 98, 121–140.Google Scholar
[31] Cokelet, E. D. 1977, Steep gravity waves in water of arbitrary uniform depth, Phil. Trans. Roy. Soc. London A 286, 183–230.CrossRefGoogle Scholar
[32] Collins, R. 1965, A simple model of a plane gas bubble in a finite liquid. J. Fluid Mech. 22, 763–771.CrossRefGoogle Scholar
[33] Concus, P. 1962, Standing capillary–gravity waves of finite amplitude. J. Fluid Mech. 14, 568–576.CrossRefGoogle Scholar
[34] Concus, P. 1964, Standing capillary–gravity waves of finite amplitude: Corrigendum. J. Fluid Mech. 19, 264–266.CrossRefGoogle Scholar
[35] Cooker, M. J., Weidman, P. D. & Bale, D. S. 1997, Reflection of a high-amplitude solitary wave at a vertical wall. J. Fluid Mech. 342, 141–158.CrossRefGoogle Scholar
[36] Couët, B. & Strumolo, G. S. 1987, The effects of surface tension and tube inclination on a two-dimensional rising bubble. J. Fluid Mech. 213, 1–14.CrossRefGoogle Scholar
[37] Crapper, G. D. 1957, An exact solution for progressive capillary waves of arbitrary amplitude. J. Fluid Mech. 2, 572–540.CrossRefGoogle Scholar
[38] Crowdy, D. G. 1999, Exact solutions for steady capillary waves on a fluid annulus. J. Nonlinear Sci. 9, 615–640.CrossRefGoogle Scholar
[39] Cumberbatch, E. & Norbury, J. 1979, Capillarity modification of the singularity at a free-streamline separation point. Q. J. Mech. Appl. Math. 32, 303–312.CrossRefGoogle Scholar
[40] Dagan, G. & Tulin, M. P. 1972, Two-dimensional free surface gravity flows past blunt bodies. J. Fluid Mech. 51, 529–543.CrossRefGoogle Scholar
[41] Davies, T. V. 1951, Theory of symmetrical gravity waves of finite amplitude. Proc. Roy. Soc. London A 208, 475–486.CrossRefGoogle Scholar
[42] Dias, F. & Iooss, G. 1993, Capillary–gravity solitary waves with damped oscillations. Physica D 65, 399–423.CrossRefGoogle Scholar
[43] Dias, F. & Kharif, C. 1999, Nonlinear gravity and capillary–gravity waves. Ann. Rev. Fluid Mech. 31, 301–346.CrossRefGoogle Scholar
[44] Dias, F., Menasce, D. & Vanden-Broeck, J.-M. 1996, Numerical study of capillary–gravity solitary waves. Eur. J. Mech. B – Fluids 15, 17–36.Google Scholar
[45] Dias, F. & Vanden-Broeck, J.-M. 1989, Open channel flows with submerged obstructions. J. Fluid Mech. 206, 155–170.CrossRefGoogle Scholar
[46] Dias, F. & Vanden-Broeck, J.-M. 1992, Solitary waves in water of infinite depth and related free surface flows. J. Fluid Mech. 240, 549–557.Google Scholar
[47] Dias, F. & Vanden-Broeck, J.-M. 1993, Nonlinear bow flows with splashes. J. Fluid Mech. 255, 91–102.CrossRefGoogle Scholar
[48] Dias, F. & Vanden-Broeck, J.-M. 2002, Generalized critical free-surface flows. J. Eng. Math. 42, 291–301.CrossRefGoogle Scholar
[49] Dias, F. & Vanden-Broeck, J.-M. 2004a, Trapped waves between submerged obstacles. J. Fluid Mech. 509, 93–102.CrossRefGoogle Scholar
[50] Dias, F. & Vanden-Broeck, J.-M. 2004b, Two-layer hydraulic falls over an obstacle. Eur. J. Mech. B – Fluids 23, 879–898.CrossRefGoogle Scholar
[51] Dingle, R. B. 1973, Asymptotic Expansions: Their Derivation and Interpretation. Academic Press.Google Scholar
[52] Eggers, J. 1995, Theory of drop formation. Phys. Fluids 7, 941–953.CrossRefGoogle Scholar
[53] Evans, W. A. B. & Ford, M. J. 1996, An exact integral equation for solitary waves (with new numerical results for some ‘internal’ properties). Proc. Roy. Soc. London A 452, 373–390.CrossRefGoogle Scholar
[54] Fangmeier, D. D. & Strelkoff, T. S. 1968, Solution for gravity flow under a sluice gate. ASCE J. Eng. Mech. Div. 94, 153–176.Google Scholar
[55] Forbes, L.-K. 1981, On the resistance of a submerged semi-elliptical body. J. Eng. Math. 15, 287–298.CrossRefGoogle Scholar
[56] Forbes, L.-K. 1983, Free surface flow over a semicircular obstruction including the influence of gravity and surface tension. J. Fluid Mech. 127, 283–297.CrossRefGoogle Scholar
[57] Forbes, L.-K. 1988, Critical free-surface flow over a semi-circular obstruction. J. Eng. Math. 22, 3–13.CrossRefGoogle Scholar
[58] Forbes, L. K 1989, An algorithm for 3-dimensional free-surface problems in hydrodynamics. J. Comput. Phys. 82, 330–347.CrossRefGoogle Scholar
[59] Forbes, L. K. & Schwartz, L. W. 1982, Free-surface flow over a semicircular obstruction. J. Fluid Mech. 114, 299–314.CrossRefGoogle Scholar
[60] Forbes, L. K. & Hocking, G. C. 1990, Flow caused by a point sink in a fluid having a free surface. J. Austral. Math. Soc. Ser. B 32, 231–249.CrossRefGoogle Scholar
[61] Friedrics, K. O. & Hyers, D. H. 1954, The existence of solitary waves. Comm. Pure Appl. Math. 7, 517–550.CrossRefGoogle Scholar
[62] Garabedian, P. R. 1957, On steady state bubbles generated by Taylor instability. Proc. Roy. Soc. London A 241, 423–431.CrossRefGoogle Scholar
[63] Garabedian, P. R. 1985, A remark about pointed bubbles. Comm. Pure Appl. Math. 38, 609–612.CrossRefGoogle Scholar
[64] Gleeson, H., Papageorgiou, D. T. & Vanden-Broeck, J.-M. 2007, A new application of the Korteweg–de-Vries Benjamin–Ono equation in interfacial electrohydrodynamics. Phys. Fluids 19, 031703.CrossRefGoogle Scholar
[65] Grandison, S. & Vanden-Broeck, J.-M. 2006, Truncation methods for gravity capillary free surface flows. J. Eng. Math. 54, 89–97.CrossRefGoogle Scholar
[66] Grilli, S. T., Guyenne, P. & Dias, F. 2001, A fully non-linear model for three-dimensional overturning waves over an arbitrary bottom. Int. J. Numer. Meth. Fluids 35, 829–867.3.0.CO;2-2>CrossRefGoogle Scholar
[67] Grimshaw, R. H. J. & Smyth, N. 1986, Resonant flow of a stratified fluid over topography. J. Fluid Mech. 169, 429–464.CrossRefGoogle Scholar
[68] Groves, M. D. & Sun, M. S. 2008, Fully localised solitary-wave solutions of the three-dimensional gravity–capillary water-wave problem. Arch. Rat. Mech. Anal. 188. 1–91.CrossRefGoogle Scholar
[69] Gurevich, M. 1965, Theory of Jets and Ideal Fluids. Academic Press, 585 pp.Google Scholar
[70] Havelock, T. H. 1919, Periodic irrotational waves of finite amplitude. Proc. Roy. Soc. London Ser. A 95, 38–51.CrossRefGoogle Scholar
[71] Helmholtz, H. 1868, Über discontinuierliche Flüssigkeitsbewegungen. Monatsber, Berlin Akad., 215–228, reprinted in Phil. Mag.36, 337–346.Google Scholar
[72] Hocking, G. C. & Vanden-Broeck, J.-M. 1997, Draining of a fluid of finite depth into a vertical slot. Applied Math. Modelling 21, 643–649.CrossRefGoogle Scholar
[73] Hocking, G. C., Vanden-Broeck, J.-M. & Forbes, L. K. 2002, A note on withdrawal from a fluid of finite depth through a point sink. ANZIAM J. 44, 181–191.CrossRefGoogle Scholar
[74] Hogan, S. J. 1980, Some effects of surface tension on steep water waves. Part 2. J. Fluid Mech. 96, 417–445.CrossRefGoogle Scholar
[75] Hunter, J. K. & Scherule, J. 1988, Existence of perturbed solitary wave solutions to a model equation for water waves. Physica D 32, 253–268.CrossRefGoogle Scholar
[76] Hunter, J. K. & Vanden-Broeck, J.-M. 1983a, Solitary and periodic gravity–capillary waves of finite amplitude. J. Fluid Mech. 134, 205–219.CrossRefGoogle Scholar
[77] Hunter, J. K. & Vanden-Broeck, J.-M. 1983b, Accurate computations for steep solitary waves. J. Fluid Mech. 136, 63–71.CrossRefGoogle Scholar
[78] Iooss, G. & Kirrmann, P. 1996, Capillary gravity waves on the free surface of an inviscid fluid of infinite depth – existence of solitary waves. Arch. Rat. Mech. Anal. 136, 1–19.CrossRefGoogle Scholar
[79] Iooss, G. & Kirchgassner, K. 1990, Bifurcation d'ondes solitaires en présences d'une faible tension superficielle. C.R. Acad. Sci. Paris 311 I, 265–268.Google Scholar
[80] Iooss, G. & Kirchgassner, K. 1992, Water waves for small surface tension: an approach via normal form. Proc. Roy. Soc. Edinburgh 122A, 267–299.CrossRefGoogle Scholar
[81] Iooss, G., Plotnikov, P. & Toland, J. F. 2005, Standing waves on an infinitely deep perfect fluid under gravity. Arch. Rat. Mech. Anal. 177, 367–478.CrossRefGoogle Scholar
[82] Kang, Y. & Vanden-Broeck, J.-M. 2002, Stern waves with vorticityANZIAM J. 43, 321–332.Google Scholar
[83] Kawahara, T. 1972, Oscillatory solitary waves in dispersive media. J. Phys. Soc. Japan 33, 260–264.CrossRefGoogle Scholar
[84] Keller, H. B. 1977, Applications of Bifurcation Theory. Academic Press.Google Scholar
[85] Keller, J. B. & Miksis, M. J. 1983, Surface tension driven flows. SIAM J. Appl. Math. 43, 268–277.CrossRefGoogle Scholar
[86] Keller, J. B., Milewski, P. & Vanden-Broeck, J.-M. 2000, Wetting and merging driven by surface tension. Euro. J. Mech. B – Fluids 19, 491–502.CrossRefGoogle Scholar
[87] Kim, B. & Akylas, T. R. 2005, On gravity–capillary lumps. J. Fluid Mech. 540, 337–351.CrossRefGoogle Scholar
[88] Kim, B. & Akylas, T. R. 2006, On gravity–capillary lumps, Part 2. Two dimensional Benjamin equation. J. Fluid Mech. 557, 237–256.CrossRefGoogle Scholar
[89] Kinnersley, W. 1976, Exact large amplitude capillary waves on sheets of fluid. J. Fluid Mech. 77, 229–241.CrossRefGoogle Scholar
[90] Kirchhoff, G. 1869, Zur Theorie freier Flüssigkeitsstrahlen. J. Reine Angew. Math. 70, 289–298.CrossRefGoogle Scholar
[91] Korteweg, D. J. & G., de Vries 1895, On the change of form of long waves advancing in a rectangular channel and on a new type of long stationary waves. Phil. Mag. 39, 422–443.CrossRefGoogle Scholar
[92] Lamb, H. 1945, Hydrodynamics, 6th edn, Cambridge University Press.Google Scholar
[93] Larock, B. E. 1969, Gravity-affected flow from planar sluice gate. ASCE J. Engng Mech. Div. 96, 1211–1226.Google Scholar
[94] Lee, J. W. & Vanden-Broeck, J.-M. 1993, Two-dimensional jets falling from funnels and nozzles. Phys. Fluids A5, 2454–2460.CrossRefGoogle Scholar
[95] Lee, J. W. & Vanden-Broeck, J.-M. 1998, Bubbles rising in an inclined two-dimensional tube and jets falling from along a wall. J. Austral. Math. Soc. B 39, 332–349.CrossRefGoogle Scholar
[96] Lenau, C. W. 1966, The solitary wave of maximum amplitude. J. Fluid Mech. 26, 309–320.CrossRefGoogle Scholar
[97] Lombardi, E. 2000, Oscillatory Integrals on Phenomena Beyond All Orders: with Applications to Homoclinic Orbits in reversible systems. Lecture Notes in Mathematics 1741, Springer.CrossRefGoogle Scholar
[98] Lighthill, M. J. 1946, A note on cusped cavities. Aero. Res. Councial Rep. and Mem. 2328.Google Scholar
[99] Lighthill, M. J. 1953, On boundary layers and upstream influence, I. A comparison between subsonic and supersonic flows. Proc. Roy. Soc. London A 217, 344–357.CrossRefGoogle Scholar
[100] Lighthill, M. J. 1978, Waves in Fluids, Cambridge University Press, 504 pp.Google Scholar
[101] Longuet–Higgins, M. S. 1975, Integral properties of periodic gravity waves of finite amplitude. Proc. Roy. London A 342, 157–174.CrossRefGoogle Scholar
[102] Longuet-Higgins, M. S. 1989, Capillary-gravity waves of solitary type on deep water. J. Fluid Mech. 200, 451–478.CrossRefGoogle Scholar
[103] Longuet-Higgins, M. S. 1993, Capillary–gravity waves of solitary type and envelope solitons on deep water. J. Fluid Mech. 252, 703–711.CrossRefGoogle Scholar
[104] Longuet-Higgins, M. S. & Cokelet, E. 1976, The deformation of steep surface waves on water, I. A numerical method of computation. Proc. Roy. Soc. London A 350, 1–26.CrossRefGoogle Scholar
[105] Longuet-Higgins, M. S. & Fenton, J. D. 1974, On the mass, momentum, energy and circulation of a solitary wave, II. Proc. R. Soc. Lond. A 340, 471–493.CrossRefGoogle Scholar
[106] Longuet-Higgins, M. S. & Fox, M. J. H. 1978, Theory of the almost highest wave, Part 2. Matching and analytical extension. J. Fluid Mech. 85, 769–786.CrossRefGoogle Scholar
[107] Maneri, C. C. 1970, The motion of plane bubbles in inclined ducts. Ph.D. thesis, Polytechnic Institute of Brooklyn, New York.
[108] McCue, S. W. & Forbes, L. K. 2002, Free surface flows emerging from beneath a semi-infinite plate with constant vorticity. J. Fluid Mech. 461, 387–407.CrossRefGoogle Scholar
[109] McLean, J. W. & Saffman, P. G. 1981, The effect of surface tension on the shape of fingers in a Hele Shaw cell. J. Fluid Mech. 102, 455–469.CrossRefGoogle Scholar
[110] Mekias, H. & Vanden-Broeck, J.-M. 1991, Subcritical flow with a stagnation point due to a source beneath a free surface. Phys. Fluids A 3, 2652–2658.CrossRefGoogle Scholar
[111] Michallet, H. & Dias, F. 1999, Numerical study of generalized interfacial solitary waves. Phys. Fluids 11, 1502–1511.CrossRefGoogle Scholar
[112] Michell, J. H. 1883, The highest wave in water. Phil. Mag. 36, 430–437.CrossRefGoogle Scholar
[113] Miksis, M., Vanden-Broeck, J.-M. & Keller, J. B. 1981, Axisymmetric bubble or drop in a uniform flow. J. Fluid Mech. 108, 89–101.CrossRefGoogle Scholar
[114] Miksis, M., Vanden-Broeck, J.-M. & Keller, J. B. 1982, Rising bubbles. J. Fluid Mech. 123, 31–41.CrossRefGoogle Scholar
[115] Milewski, P. A. 2005, Three-dimensional localized solitary gravity–capillary waves. Comm. Math. Sc. 3, 89–99.CrossRefGoogle Scholar
[116] Nayfeh, A. H. 1970, Triple and quintuple-dimpled wave profiles in deep water. J. Fluid Mech. 13, 545–550.Google Scholar
[117] Ockendon, H. & Ockendon, J. R. 2004, Viscous Flow. Cambridge Texts in Applied Mathematics.Google Scholar
[118] Olfe, D. B. & Rottman, J. W. 1980, Some new highest-wave solutions for deep-water waves of permanent form. J. Fluid Mech. 100, 801–810.CrossRefGoogle Scholar
[119] Osher, S. & Fedkiw, R. 2003, Level Set Methods and Dynamic Implicit Surfaces. Applied Mathematical Sciences 153, Springer.CrossRefGoogle Scholar
[120] Papageorgiou, D. T. & Vanden-Broeck, J.-M. 2003, Large amplitude capillary waves in electrified fluid sheets. J. Fluid Mech. 508, 71–88.CrossRefGoogle Scholar
[121] Papageorgiou, D. T. & Vanden-Broeck, J.-M. 2004, Antisymmetric capillary waves in electrified fluid sheets. Eur. J. Appl. Math. 15, 609–623.CrossRefGoogle Scholar
[122] Parau, E. & Vanden-Broeck, J.-M. 2002, Nonlinear two- and three-dimensional free surface flows due to moving disturbances. Eur. J. Mech. B – Fluids 21, 643–656.CrossRefGoogle Scholar
[123] Parau, E., Vanden-Broeck, J.-M. & Cooker, M. 2005a, Nonlinear three dimensional gravity capillary solitary waves. J. Fluid Mech. 536, 99–105.CrossRefGoogle Scholar
[124] Parau, E., Vanden-Broeck, J.-M. & Cooker, M. 2005b, Three-dimensional gravity–capillary solitary waves in water of finite depth and related problems. Phys. Fluids 17, 122 101.CrossRefGoogle Scholar
[125] Parau, E., Vanden-Broeck, J.-M. & Cooker, M. 2007a, Three-dimensional capillary–gravity waves generated by a moving disturbance. Phys. Fluids 19, 082 102.CrossRefGoogle Scholar
[126] Parau, E., Vanden-Broeck, J.-M. & Cooker, M. 2007b, Nonlinear three dimensional interfacial flows with a free surface. J. Fluid Mech. 591, 481–494.CrossRefGoogle Scholar
[127] Pullin, D. I. & Grimshaw, R. H. J. 1988, Finite amplitude solitary waves at the interface between two homogeneous fluids. Phys. Fluids 31, 3550–3559.CrossRefGoogle Scholar
[128] Rayleigh, Lord 1883, The form of standing waves on the surface of running water. Proc. Lond. Math. Soc. 15, 69–78.CrossRefGoogle Scholar
[129] Romero, L. 1982, Ph.D. thesis, California Institute of Technology.
[130] Saffman, P. G. 1980, Long wavelength bifurcation of gravity waves on deep water. J. Fluid Mech. 101, 567–581.CrossRefGoogle Scholar
[131] Saffman, P. G. 1986, Viscous fingering in Hele Shaw cells. J. Fluid Mech. 173, 73–94.CrossRefGoogle Scholar
[132] Saffman, P. G. & Taylor, G. I. 1958, The penetration of a fluid into a porous medium or Hele Shaw cell containing a more viscous fluid. Proc. Roy. Soc. London A 245, 312–329.CrossRefGoogle Scholar
[133] Schwartz, L. W. 1974, Computer extension and analytic continuation of Stokes' expansion for gravity waves. J. Fluid Mech. 62, 553–578.CrossRefGoogle Scholar
[134] Schwartz, L. W. & Fenton, J. 1982, Strongly nonlinear waves. Ann. Rev. Fluid Mech. 14, 39–60.CrossRefGoogle Scholar
[135] Schwartz, L. W. & Vanden-Broeck, J.-M. 1979, Numerical solution of the exact equations for capillary–gravity waves. J. Fluid Mech. 95, 119–139.CrossRefGoogle Scholar
[136] Schultz, W. W., Vanden-Broeck, J.-M., Jiang, L. & Perlin, M. 1998, Highly nonlinear water waves with small capillary effect. J. Fluid Mech. 369, 253–272.Google Scholar
[137] Sethian, J. A.Level Set Methods. Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press.
[138] Sha, H. & Vanden-Broeck, J.-M. 1993, Two-layer flows past a semicircular obstaclePhys. Fluids A 5, 2661–2668.CrossRefGoogle Scholar
[139] Sha, H. & Vanden-Broeck, J.-M. 1997, Internal solitary waves with stratification in density. J. Austral. Math. Soc. B 38, 563–580.CrossRefGoogle Scholar
[140] Shen, S.-P. 1995, On the accuracy of the stationary forced Korteweg-de-Vries equation as a model equation for flows over a bump. Quart. J. Appl. Math. 53, 701–719.CrossRefGoogle Scholar
[141] Simmen, J. A. & Saffman, P. G. 1985, Steady deep water waves on a linear shear current. Stud. Appl. Maths 75, 35–57.CrossRefGoogle Scholar
[142] Southwell, R. V. & Vaisey, G. 1946, Fluid motions characterised by ‘free’ streamlines. Phil. Trans. Roy. Soc. A 240, 117–161.CrossRefGoogle Scholar
[143] Stokes, G. G. 1847, On the theory of oscillatory waves. Camb. Trans. Phil. Soc. 8, 441–473.Google Scholar
[144] Stokes, G. G. 1880, in Mathematical and Physical Papers, Vol. 1, p. 314, Cambridge University Press.Google Scholar
[145] Sun, S. M. 1991, Existence of generalized solitary wave solution for water with positive Bond number less than ⅓. J. Math. Anal. Appl. 156, 471–504.CrossRefGoogle Scholar
[146] Sun, S. M. 1999, Nonexistence of truly solitary waves in water with small surface tensionProc. Roy. Soc. London A 455, 2191–2228.CrossRefGoogle Scholar
[147] Sun, S. M. & Shen, M. C. 1993, Exponentially small estimate for the amplitude of capillary ripples of generalised solitary waves. J. Math. Anal. Appl. 172, 533–566.CrossRefGoogle Scholar
[148] Tadjbakhsh, I. & Keller, J. B. 1960, Standing surface waves of finite amplitude. J. Fluid Mech. 8, 442–451.CrossRefGoogle Scholar
[149] Tanaka, M., Dold, J. W., Lewy, M. & Peregrine, D. H. 1987, Instability and breaking of a solitary wave. J. Fluid Mech. 185, 235–248.CrossRefGoogle Scholar
[150] Teles da Silva, A. F. & Peregrine, D. H. 1988, Steep solitary waves in water of finite depth with constant vorticity. J. Fluid Mech. 195, 281–305.CrossRefGoogle Scholar
[151] Tooley, S. & Vanden-Broeck, J.-M. 2002, Waves and singularities in nonlinear capillary free-surface flows. J. Eng. Math. 43, 89–99.CrossRefGoogle Scholar
[152] Tsai, W. T. & Yue, D. K. 1996, Computation of nonlinear free surface flows. Ann. Rev. Fluid Mech. 28, 249–278.CrossRefGoogle Scholar
[153] Tseluiko, D., Blyth, M. & Papageorgiou, D. T. 2008a, Electrified viscous thin film over topography. J. Fluid Mech. 597, 449–475.CrossRefGoogle Scholar
[154] Tseluiko, D., Blyth, M. & Papageorgiou, D. T. 2008b, Effect of an electric field on film flow down a corrugated wall at zero Reynolds number. Phys. Fluids 20, 042 103CrossRefGoogle Scholar
[155] Turner, R. E. L. & Vanden-Broeck, J.-M. 1986, The limiting configuration of interfacial gravity waves. Phys. Fluids 29, 372–375.CrossRefGoogle Scholar
[156] Turner, R. E. L. & Vanden-Broeck, J.-M. 1988, Broadening on interfacial solitary waves. Phys. Fluids 31, 2486–2490.CrossRefGoogle Scholar
[157] Turner, R. E. L. & Vanden-Broeck, J.-M. 1992, Long internal waves. Phys. Fluids A 4, 1929–1935.Google Scholar
[158] Vanden-Broeck, J.-M. 1980, Nonlinear stern waves. J. Fluid Mech. 96, 601–610.CrossRefGoogle Scholar
[159] Vanden-Broeck, J.-M. 1981, The influence of capillarity on cavitating flow past a flat plate. Quart. J. Mech. Appl. Math. 34, 465–473.CrossRefGoogle Scholar
[160] Vanden-Broeck, J.-M. 1983a, The influence of surface tension on cavitating flow past a curved obstacle. J. Fluid Mech. 133, 255–264.CrossRefGoogle Scholar
[161] Vanden-Broeck, J.-M. 1983b, Fingers in a Hele-Shaw cell with surface tension. Phys. Fluids 26, 2033–2034.CrossRefGoogle Scholar
[162] Vanden-Broeck, J.-M. 1983c, Some new gravity waves in water of finite depth. Phys. Fluids 26, 2385–2387.CrossRefGoogle Scholar
[163] Vanden-Broeck, J.-M. 1984a, The effect of surface tension on the shape of the Kirchhoff jet. Phys. Fluids 27, 1933–1936.CrossRefGoogle Scholar
[164] Vanden-Broeck, J.-M. 1984b, Numerical solutions for cavitating flow of a fluid with surface tension past a curved obstacle. Phys. Fluids 27, 2601–2603.CrossRefGoogle Scholar
[165] Vanden-Broeck, J.-M. 1984c, Bubbles rising in a tube and jets falling from a nozzle. Phys. Fluids 27, 1090–1093.CrossRefGoogle Scholar
[166] Vanden-Broeck, J.-M. 1984d, Rising bubbles in a two-dimensional tube with surface tension. Phys. Fluids 27, 2604–2607 and 1992, Rising bubbles in a two-dimensional tube: asymptotic behavior for small values of the surface tension, Phys. Fluids A4, 2332–2334.CrossRefGoogle Scholar
[167] Vanden-Broeck, J.-M. 1984e, Nonlinear gravity–capillary standing waves in water of arbitrary uniform depth. J. Fluid Mech. 139, 97–104.CrossRefGoogle Scholar
[168] Vanden-Broeck, J.-M. 1985, Nonlinear free-surface flows past two-dimensional bodies. In Advances in Nonlinear Waves, Vol. II, L., Debnath, ed., Boston, Pitman.Google Scholar
[169] Vanden-Broeck, J.-M. 1986a, Pointed bubbles rising in a two dimensional tube. Phys. Fluids 29, 1343–1344.CrossRefGoogle Scholar
[170] Vanden-Broeck, J.-M. 1986b, A free streamline model for a rising bubble. Phys. Fluids 29, 2798–2801.CrossRefGoogle Scholar
[171] Vanden-Broeck, J.-M. 1986c, Flow under a gate. Phys. Fluids 29, 3148–3151.CrossRefGoogle Scholar
[172] Vanden-Broeck, J.-M. 1986d, Steep gravity waves: Havelock's method revisited. Phys. Fluids 29, 3084–3085.CrossRefGoogle Scholar
[173] Vanden-Broeck, J.-M. 1987, Free-surface flow over an obstruction in a channel. Phys. Fluids 30, 2315–2317.CrossRefGoogle Scholar
[174] Vanden-Broeck, J.-M. 1988, Joukovskii's model for a rising bubble. Phys. Fluids 31, 974–977.CrossRefGoogle Scholar
[175] Vanden-Broeck, J.-M. 1989, Bow flows in water of finite depth. Phys. Fluids A1, 1328–1330.CrossRefGoogle Scholar
[176] Vanden-Broeck, J.-M. 1991a, Cavitating flow of a fluid with surface tension past a circular cylinder. Phys. Fluids A 3, 263–266.CrossRefGoogle Scholar
[177] Vanden-Broeck, J.-M. 1991b, Elevation solitary waves with surface tensionPhys. Fluids A 3, 2659–2663.CrossRefGoogle Scholar
[178] Vanden-Broeck, J.-M. 1994, Steep solitary waves in water of finite depth with constant vorticity. J. Fluid Mech. 274, 339–348.CrossRefGoogle Scholar
[179] Vanden-Broeck, J.-M. 1995, New families of steep solitary waves in water of finite depth with constant vorticity. Eur. J. Mech. B – fluids 14, 761–774.Google Scholar
[180] Vanden-Broeck, J.-M. 1996a, Periodic waves with constant vorticity in water of infinite depth. IMA J. Appl. Math. 56, 207–217.CrossRefGoogle Scholar
[181] Vanden-Broeck, J.-M. 1996b, Numerical calculations of the free-surface flow under a sluice gate. J. Fluid Mech. 330, 339–347.CrossRefGoogle Scholar
[182] Vanden-Broeck, J.-M. 2002, Wilton ripples generated by a moving pressure distribution. J. Fluid Mech. 451, 193–201.CrossRefGoogle Scholar
[183] Vanden-Broeck, J.-M. 2004, Nonlinear capillary free-surface flows. J. Eng. Math. 50, 415–426.CrossRefGoogle Scholar
[184] Vanden-Broeck, J.-M. & Dias, F. 1992, Gravity–capillary solitary waves in water of infinite depth and related free-surface flows. J. Fluid Mech. 240, 549–557.CrossRefGoogle Scholar
[185] Vanden-Broeck, J.-M. & Keller, J. B. 1980, A new family of capillary waves. J. Fluid Mech. 98, 161–169.CrossRefGoogle Scholar
[186] Vanden-Broeck, J.-M. & Keller, J. B. 1989, Surfing on solitary waves. J. Fluid Mech. 198, 115–125.CrossRefGoogle Scholar
[187] Vanden-Broeck, J.-M. & Keller, J. B. 1997, An axisymmetric free surface with a 120 degree angle along a circle. J. Fluid Mech. 342, 403–409.CrossRefGoogle Scholar
[188] Vanden-Broeck, J.-M. & Miloh, T. 1995, Computations of steep gravity waves by a refinement of the Davies–Tulin approximation. Siam J. Appl. Math. 55, 892–903.CrossRefGoogle Scholar
[189] Vanden-Broeck, J.-M. & Schwartz, L. W. 1979, Numerical computation of steep gravity waves in shallow water. Phys. Fluids 22, 1868–1871.CrossRefGoogle Scholar
[190] Vanden-Broeck, J.-M., Schwartz, L. W. & Tuck, E. O. 1978, Divergent low-Froude-number series expansion in nonlinear free-surface flow problems. Proc. Roy. Soc. London A 361, 207–224.CrossRefGoogle Scholar
[191] Vanden-Broeck, J.-M. & Shen, M. C. 1983, A note on solitary and periodic waves with surface tension. Z. Angew. Math. Phys. 34, 112–117.CrossRefGoogle Scholar
[192] Vanden-Broeck, J.-M. & Tuck, E. O. 1977. Computation of near-bow or stern flows, using series expansion in the Froude number. In Proc. 2nd Int. Conf. on Num. Ship Hydrodynamics, Berkeley, California, 371–381.Google Scholar
[193] Vanden-Broeck, J.-M. & Tuck, E. O. 1994, Steady inviscid rotational flows with free surfacesJ. Fluid Mech. 258, 105–113.CrossRefGoogle Scholar
[194] Villat, H. 1914, Sur la validité des solutions de certains problèmes d'hydrodynamique. J. de Math. 10, 231–290.Google Scholar
[195] Whitham, G. B. 1974, Linear and nonlinear waves. Wiley Interscience, John Wiley & Sons.Google Scholar
[196] Wehausen, J. V. & Laitone, E. V. 1960, Surface waves. In Handbuch der Physik, C., Truesdell, ed., Vol. IX, pp. 446–778, Springer.Google Scholar
[197] Williams, J. M. 1981, Limiting gravity waves in water of finite depth. Phil. Trans. R. Soc. Lond. A 302, 139–188.CrossRefGoogle Scholar
[198] Wilton, J. R., 1915, On ripples. Phil. Mag. 29, 688–700.CrossRefGoogle Scholar
[199] Zufuria, J. A. 1987, Symmetry breaking in periodic and solitary gravity–capillary waves on water of finite depth. J. Fluid Mech. 184, 183–206.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Jean-Marc Vanden-Broeck, University College London
  • Book: Gravity–Capillary Free-Surface Flows
  • Online publication: 07 September 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511730276.013
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Jean-Marc Vanden-Broeck, University College London
  • Book: Gravity–Capillary Free-Surface Flows
  • Online publication: 07 September 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511730276.013
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Jean-Marc Vanden-Broeck, University College London
  • Book: Gravity–Capillary Free-Surface Flows
  • Online publication: 07 September 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511730276.013
Available formats
×