Space–time surface gravity wave caustics: structurally stable extreme wave events

Wave Motion - Tập 33 - Trang 117-143 - 2001
Michael G. Brown1
1Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Cswy, Miami, FL, 33149, USA

Tài liệu tham khảo

V.I. Arnol’d, Catastrophe Theory, 3rd Edition, Springer, Berlin, 1992.

R.C. Beal (Ed.), Directional Ocean Wave Spectra, Johns Hopkins University Press, Baltimore, MD, 1991, pp. 202–203.

Berry, 1979, The elliptic umbilic diffraction catastrophe, Philos. Trans. R. Soc. London A, 291, 453, 10.1098/rsta.1979.0039

Boccotti, 1981, On the highest waves in a stationary Gaussian process, Atti Acc. Ligure, 38, 271

Boccotti, 1989, On mechanics of irregular gravity waves, Atti Acc. Naz. Lincei Mem., 19, 109

Boccotti, 1997, A general theory of three-dimensional wave groups. Part 1. The formal derivation, Ocean Eng., 24, 265, 10.1016/S0029-8018(96)00013-3

Boccotti, 1993, A field experiment on the mechanics of irregular gravity waves, J. Fluid Mech., 252, 173, 10.1017/S0022112093003714

Brown, 1986, The transient wavefields in the vicinity of the cuspoid caustics, J. Acoust. Soc. Am., 79, 1367, 10.1121/1.393665

Brown, 1986, The transient wavefields in the vicinity of the elliptic, hyperbolic and parabolic umbilic caustics, J. Acoust. Soc. Am., 79, 1385, 10.1121/1.393666

Brown, 1987, Catastrophe theory, caustics and travel time diagrams in seismology, Geophys. J. R. Astr. Soc., 88, 217, 10.1111/j.1365-246X.1987.tb01376.x

Chester, 1957, An extension of the method of steepest descents, Proc. Camb. Philos. Soc., 53, 599, 10.1017/S0305004100032655

Donato, 1999, The focusing of surface waves by internal waves, J. Fluid Mech., 384, 27, 10.1017/S0022112098003917

Gerber, 1993, The interaction of deep-water gravity waves and an annular current: linear theory, J. Fluid Mech., 248, 153, 10.1017/S0022112093000722

J. Lighthill, Waves in Fluids, Cambridge University Press, Cambridge, 1978.

Marston, 1987, Transverse cusp diffraction catastrophes: some pertinent wave fronts and a Pearcy approximation to the wavefield, J. Acoust. Soc. Am., 81, 226, 10.1121/1.394941

Marston, 1984, Hyperbolic umbilic diffraction catastrophe and rainbow scattering from spheroidal drops, Nature, 312, 529, 10.1038/312529a0

Nye, 1984, Rainbow scattering from spheroidal drops — an explanation of the hyperbolic umbilic foci, Nature, 312, 531, 10.1038/312531a0

Nye, 1992, Rainbows from ellipsoidal water drops, Proc. R. Soc. London A, 438, 397, 10.1098/rspa.1992.0115

J.F. Nye, Natural Focusing and the Fine Structure of Light: Caustics and Wave Dislocations, Institute of Physics Publishing, Bristol, 1999.

Pearcy, 1946, The structure of an electromagnetic field in the neighborhood of a cusp of a caustic, Philos. Mag., 37, 311, 10.1080/14786444608561335

Peregrine, 1976, Interactions of water waves and currents, Adv. Appl. Mech., 16, 9, 10.1016/S0065-2156(08)70087-5

Peregrine, 1981, Refraction of finite amplitude water waves: deep water waves approaching circular caustics, J. Fluid Mech., 109, 63, 10.1017/S0022112081000931

Peregrine, 1983, Wave jumps and caustics in the propagation of finite-amplitude water waves, J. Fluid Mech., 136, 435, 10.1017/S0022112083002220

Peregrine, 1979, Nonlinear effects upon waves near caustics, Philos. Trans. R. Soc. London A, 292, 341, 10.1098/rsta.1979.0065

Phillips, 1993, Expected structure of extreme waves in a Gaussian sea. Part I. Theory and SWADE buoy measurements, J. Phys. Ocean., 23, 992, 10.1175/1520-0485(1993)023<0992:ESOEWI>2.0.CO;2

Phillips, 1993, On the expected structure of extreme waves in a Gaussian sea. Part II. SWADE scanning radar altimeter measurements, J. Phys. Ocean., 23, 2297, 10.1175/1520-0485(1993)023<2297:OTESOE>2.0.CO;2

T. Poston, I. Stewart, Catastrophe Theory and its Applications, Pitman, Boston, MA, 1978.

W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes, Cambridge University Press, Cambridge, 1986.

Rapp, 1990, Laboratory measurements of deep water breaking waves, Philos. Trans. R. Soc. London A, 331, 735, 10.1098/rsta.1990.0098

Smith, 1975, The reflection of short gravity waves on a nonuniform current, Math. Proc. Camb. Philos. Soc., 78, 517, 10.1017/S0305004100052002

Smith, 1976, Giant waves, J. Fluid Mech., 77, 417, 10.1017/S002211207600219X

R. Thom, Structurally Stability and Morphogenesis, Benjamin, Reading, MA, 1974.

Trinkaus, 1977, On the analysis of diffraction catastrophes, J. Phys. A, 10, 11, 10.1088/0305-4470/10/1/003

White, 1998, On the chance of freak waves at sea, J. Fluid Mech., 355, 113, 10.1017/S0022112097007751