water waves

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1: Sidebar 21.SB1: Periodic Surface Waves

… ►Two-dimensional periodic waves in a shallow water wave tank. Taken from Joe Hammack, Daryl McCallister, Norman Scheffner and Harvey Segur, “Two-dimensional periodic waves in shallow water. …The caption reads “Mosaic of two overhead photographs, showing surface patterns of waves in shallow water”. …

2: Sidebar 21.SB2: A two-phase solution of the Kadomtsev–Petviashvili equation (21.9.3)

… ►The agreement of these solutions with two-dimensional surface water waves in shallow water was considered in Hammack et al. (1989, 1995).

3: 11.12 Physical Applications

§11.12 Physical Applications

►Applications of Struve functions occur in water-wave and surface-wave problems (Hirata (1975) and Ahmadi and Widnall (1985)), unsteady aerodynamics (Shaw (1985) and Wehausen and Laitone (1960)), distribution of fluid pressure over a vibrating disk (McLachlan (1934)), resistive MHD instability theory (Paris and Sy (1983)), and optical diffraction (Levine and Schwinger (1948)). …

4: 21.9 Integrable Equations

… ►Particularly important for the use of Riemann theta functions is the Kadomtsev–Petviashvili (KP) equation, which describes the propagation of two-dimensional, long-wave length surface waves in shallow water (Ablowitz and Segur (1981, Chapter 4)): … ►

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Figure 21.9.1: Two-dimensional periodic waves in a shallow water wave tank, taken from Hammack et al. (1995, p. 97) by permission of Cambridge University Press. The original caption reads “Mosaic of two overhead photographs, showing surface patterns of waves in shallow water. … Magnify

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Figure 21.9.2: Contour plot of a two-phase solution of Equation (21.9.3). … Magnify

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5: 36.13 Kelvin’s Ship-Wave Pattern

§36.13 Kelvin’s Ship-Wave Pattern

►A ship moving with constant speed $V$ on deep water generates a surface gravity wave. … ►For further information see Lord Kelvin (1891, 1905) and Ursell (1960, 1994).

6: 13.28 Physical Applications

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§13.28(i) Exact Solutions of the Wave Equation

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7: Bibliography U

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Ship Hydrodynamics, Water Waves and Asymptotics. Collected works of F. Ursell, 1946-1992, Vol. 2, World Scientific, Singapore.

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8: 9.16 Physical Applications

… ►These first appeared in connection with the equation governing the evolution of long shallow water waves of permanent form, generally called solitons, and are predicted by the Korteweg–de Vries (KdV) equation (a third-order nonlinear partial differential equation). …

9: 22.19 Physical Applications

… ►Such solutions include standing or stationary waves, periodic cnoidal waves, and single and multi-solitons occurring in diverse physical situations such as water waves, optical pulses, quantum fluids, and electrical impulses (Hasegawa (1989), Carr et al. (2000), Kivshar and Luther-Davies (1998), and Boyd (1998, Appendix D2.2)). …

10: Bibliography S

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Perturbational results for diffraction of water-waves by nearly-vertical barriers. IMA J. Appl. Math. 34 (1), pp. 99–117.

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§11.12.

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