Directional seas should be ergodic

Jefferys, E.R.

doi:10.1016/0141-1187(87)90001-0

Cited by 47 publications

(30 citation statements)

References 3 publications

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“…As pointed out by Jeffreys (1987), this is because the phase difference between wave components with identical frequencies but propagating in different directions is no longer random but locked. An extreme example of this phenomenon is the standing wave pattern that is produced when incident waves are fully reflected by a vertical wall.…”

Section: Chapter 3 Numerical Solutionmentioning

confidence: 97%

BOUSS-2D: A Boussinesq Wave Model for Coastal Regions and Harbors

Nwogu¹,

Demirbilek²

2001

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Section: Chapter 3 Numerical Solutionmentioning

confidence: 97%

BOUSS-2D: A Boussinesq Wave Model for Coastal Regions and Harbors

Nwogu¹,

Demirbilek²

2001

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“…A number of methods exist to simulate deterministically ergodic directional sea states (see, e.g., Jefferys 1987;Miles & Funke 1989). Most methods are based on multiple frequency wave spectra, for which a realization of the random sea state is generated by a double sum over the directional and frequency range of plane waves with random characteristics.…”

Section: Random Sea Statesmentioning

confidence: 99%

Attenuation and directional spreading of ocean wave spectra in the marginal ice zone

2016

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A theoretical model is used to study wave energy attenuation and directional spreading of ocean wave spectra in the marginal ice zone (MIZ). The MIZ is constructed as an array of tens of thousands of compliant circular ice floes, with randomly selected positions and radii determined by an empirical floe size distribution. Linear potential flow and thin elastic plate theories model the coupled water-ice system. A new method is proposed to solve the time-harmonic multiple scattering problem under a multi-directional incident wave forcing with random phases. It provides a natural framework for tracking the evolution of the directional properties of a wave field through the MIZ. The attenuation and directional spreading are extracted from ensembles of the wave field with respect to realizations of the MIZ and incident forcing randomly generated from prescribed distributions. The averaging procedure is shown to converge rapidly so that only a small number of simulations need to be performed. Far field approximations are investigated, allowing efficiency improvements with negligible loss of accuracy. A case study is conducted for a particular MIZ configuration. Observed exponential attenuation of wave energy through the MIZ is reproduced by the model, while the directional spread is found to grow linearly with distance. Directional spreading is shown to weaken when the wavelength becomes larger than the maximum floe size.

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“…To achieve the latter, the amplitudes of the generated wave components were calculated based upon a weighted Rayleigh distribution following the discussion outlined by Tucker et al [46]. In the case of directionally spread seas, it is also important that the sea state remains ergodic [47]. This is achieved by ensuring that each frequency component is generated in a single direction.…”

Section: (C) Calibration and Wave Generationmentioning

confidence: 99%

A laboratory study of wave crest statistics and the role of directional spreading

Latheef

Swan

2013

Proc. R. Soc. A.

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This paper concerns the crest height statistics arising in sea states that are broad banded in both frequency and direction. A new set of laboratory observations are presented and the results compared with the commonly applied statistical distributions. Taken as a whole, the data confirm that the crest-height distributions are critically dependent upon the directionality of the sea state. Although nonlinear effects arising at third order and above are most pronounced in uni-directional seas, the present data show that they are also important in directionally spread seas, provided the seas are sufficiently steep and not too short crested. The data also highlight the limiting effects of wave breaking. With individual breaking events dependent upon the local wave steepness, the directionality of the sea state again plays a significant role. Indeed, the present observations confirm that the two competing processes of nonlinear amplification and wave breaking can have a profound influence on the crest-height distributions leading to significant departures from established theory. In such cases, the key parameters are the sea state steepness and directional spread; the latter acting to counter the former in terms of nonlinear changes in the crestheight distributions.

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Directional seas should be ergodic

Cited by 47 publications

References 3 publications

BOUSS-2D: A Boussinesq Wave Model for Coastal Regions and Harbors

BOUSS-2D: A Boussinesq Wave Model for Coastal Regions and Harbors

Attenuation and directional spreading of ocean wave spectra in the marginal ice zone

A laboratory study of wave crest statistics and the role of directional spreading

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