Mean length of runs of ocean waves

Chakrabarti, S.; Snider, Robert H.; Feldhausen, Peter H.

doi:10.1029/jc079i036p05665

Cited by 12 publications

(6 citation statements)

References 6 publications

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“…Previous observations of ocean group statistics have been limited to a narrow range of spectral conditions [Chakrabarti et al, 1974;Goda, 1983], have not given the relevant spectral parameters [Wilson and Baird, 1970;Rye, 1974], or have used such short time series that the statistical stability of the observations is doubtful [Andrew and Borgman, 1981;Goda, 1983]. In spite of these limitations, these studies show rough, qualitative agreement between linear theory and observations.…”

Section: Introductionmentioning

confidence: 99%

Groups of waves in shallow water

Elgar¹,

Guza²,

Seymour³

1984

J. Geophys. Res.

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Wave group statistics predicted by linear theories are compared to numerical simulations, thus determining ranges of spectral shapes for which the theories are valid. It is found that these theories are not generally valid for ocean data because of many assumptions and simplifications beyond linearity and random phase or because their range of applicability does not include the vast majority of ocean conditions. The simulations also provide quantitative information about the variability of linear wave group statistics which is useful when examining ocean field data. The simulation technique is used to show that important ocean gravity wave group statistics are not inconsistent with an underlying wave field composed of linearly superposed random waves. The majority of the field data examined were collected in 10 m depth; significant wave heights varied from about 20 to 200 cm, and the spectral shapes ranged from fairly narrow to broad (1 < Q•, < 6). For the 10-m depth data, the observed mean run length, variance of run length, and probabilities of runs of a given number of waves were statistically consistent with the simulations. In contrast to the apparently linear groups observed in 10 m depth, waves in 2-3 m depth showed marked departures from the linear simulations.

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Section: Introductionmentioning

confidence: 99%

Groups of waves in shallow water

Elgar¹,

Guza²,

Seymour³

1984

J. Geophys. Res.

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“…In other words, A of Equation (11) presents the envelope surface created by wavenumber-based nearly monochromatic waves. We derive the governing equation for A using Equations (8), (9), (10), and (11). First, the dispersion relation for A is led by substituting Equation (11) into Equation (8) w2 = k4 .…”

Section: Wavenumber-based Nearly Monochromatic Wavesmentioning

confidence: 99%

“…Similarly, we eliminate the terms that produce secular terms in the equation obtained from Equations (10) and (11) and recall that wl = 0, then we obtain the solvability condition as follows: 2z (6k2 cos t 00 + 2k 2 sine 00) a + 4ik3 cos 00 DA + 4k 2 sin 20o a A áX 1 áX2 áX 1 aY1…”

Section: Wavenumber-based Nearly Monochromatic Wavesmentioning

confidence: 99%

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Governing equations of envelope surface created by nearly bichromatic waves propagating on an elastic plate and their stability

Nohara

2005

Japan J. Indust. Appl. Math.

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Plates are common structural elements of most engineering structures, including aerospace, automotive, and civil engineering structures. The study of plates from theoretical perspective as well as experimental viewpoint is fundamental to understanding of the behavior of such structures. The dynamic characteristics of plates, such as natural vibrations, transient responses for the external forces and so on, are especially of importance in actual environments. In this paper, we consider natural vibrations of an elastic plate and the propagation of a wavepacket on it. We derive the two-dimensional equations that govern the spatial and temporal evolution of the amplitude of a wavepacket and discuss its features. We especially consider wavenumber-based nearly bichromatic waves and direction-based nearly bichromatic waves on an elastic plate. The former waves are defined by the waves that almost concentrate the energy in two wavenumbers, which are very closely approached each other. The latter waves are defined by the waves that almost concentrate the energy in two propagation directions and two propagation directions are very close each other. The fact that the solution of the governing equation for wavenumber-based nearly bichromatic waves is stable is also shown. NomenclatureA = slowly varying amplitude in space and/or time of a wavepacket CI = the function space consisting of functions f (x) which is lth differentiable at any point of x and the lth derivative of f is continuous D = plate flexural rigidity E = elastic modulus G = direction-based spectrum of a wavepacket or Green's function H = value used in boundary conditions L = linear operator defined by Equations (A.19) and (A.20) or value used in boundary conditions Al = positive integer N = positive integer O = function of order Q = function defined by Equation (A.18) or Fourier coefficient R = real space S = function used by the method of separation of variables in Equation (A.3) 88 B.T. NOHARA U = function used by the method of separation of variables in Equation (A.3) a = cos Bo b = sin Bo c = Fourier coefficient cc = complex conjugate f = function of initial condition h = plate thickness i = imaginary unit or unit vector along x axis j = unit vector along y axis k = wave number m = integer n = integer t = time u = function v = function v = velocity of envelope surface w = plane traveling waves x, y = rectangular coordinate system W = function used by the method of separation of variables in Equation (A.9) 0 = function used by the method of separation of variables in Equation (A.9) a = coefficient in Equation (A.34) ß = coefficient in Equation (A.34) -y = coefficient in Equations (A.10) and (A.11) S = Delta function e = order of time and spacial scales 0 = propagation direction A = separation constant p = separation constant v = Poisson's ratio p = mass density w = angular frequency ÖD = boundary of rectangle V4 = biharmonic operator Subscript 0 = dominant value 1, 2 = number of function or value m = number of coefficient n = number of function or coefficie...

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“…In the course of studying the physical characteristics of group waves (wave packets) [1][2][3][4][5][6][7][8][9] for water waves, the Schrödinger equation has played an important role in the mathematical and physical analysis. The envelope, which is created by group waves, has been considered to model them.…”

Section: Introductionmentioning

confidence: 99%

Governing equations of envelopes created by nearly bichromatic waves on deep water

Nohara

2006

Nonlinear Dyn

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In this paper, the author derives the modified Schrödinger equation that governs the envelope created by nearly bichromatic waves, which are defined by the waves whose energy is almost concentrated in two closely approached wavenumbers. The stability of the solution of the modified Schrödinger equation for nearly bichromatic waves on deep water is discussed and the fact that the Benjamin-Feir instability occurs in a condition is shown. Moreover, the solutions of the modified Schrödinger equation for nearly bichromatic waves on deep water are obtained and, in a special case, the solution becomes the standing wave solution is shown. NomenclatureA slowly varying amplitude in space and/or time of nearly monochromatic waves and nearly bichromatic waves K real wavenumber

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Mean length of runs of ocean waves

Cited by 12 publications

References 6 publications

Groups of waves in shallow water

Groups of waves in shallow water

Governing equations of envelope surface created by nearly bichromatic waves propagating on an elastic plate and their stability

Governing equations of envelopes created by nearly bichromatic waves on deep water

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