Nonlinear Space–Time Evolution of Wave Groups With a High Crest

The theory of quasi-determinism, for the mechanics of linear random wave groups was obtained by Boccotti in the eighties. The first formulation of the theory deals with the largest crest amplitude; the second formulation deals with the largest wave height. In this paper the first formulation of Boccotti’s theory, particularized for long-crested waves, is extended to the second-order. The analytical expressions of the nonlinear free surface displacement and velocity potential are obtained. The space–time evolution of the nonlinear wave group, when a very large crest occurs at a fixed time and location, is then shown. Finally the second-order probability of exceedance of the crest amplitude is obtained and validated by Monte Carlo simulation.

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Non-Linear Space-Time Evolution of Wave Groups With a High Crest

Volume 2: Safety and Reliability; Pipeline Technology ◽

10.1115/omae2003-37161 ◽

2003 ◽

Author(s):

Felice Arena ◽

Francesco Fedele

Keyword(s):

Time Evolution ◽

Field Experiments ◽

Surface Displacement ◽

Fixed Time ◽

Space Time ◽

Second Order ◽

Small Scale ◽

Free Surface Displacement ◽

Non Linear ◽

Space Time Evolution

The theory of quasi-determinism, for the mechanics of linear three-dimensional waves, was obtained by Boccotti in the eighties. The first formulation of the theory deals with the largest crest amplitude; the second formulation deals with the largest wave height. The theory was verified in the nineties with some small-scale field experiments. In this paper the first formulation of Boccotti’s theory, valid for the space-time domain, is extended to the second order. The analytical expressions of the non-linear free surface displacement and velocity potential are obtained. Therefore the space-time evolution of a wave group, to the second-order in a Stokes expansion, when a very large crest occurs at a fixed time and location, is investigated. Finally the second-order probability of exceedance of the crest amplitude is obtained, as a function of two deterministic parameters.

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Space-time evolution of random wave groups with high waves based on the quasi-determinism theory

Ocean Engineering ◽

10.1016/j.oceaneng.2011.07.021 ◽

2011 ◽

Vol 38 (14-15) ◽

pp. 1640-1648 ◽

Cited By ~ 12

Author(s):

Petya G. Petrova ◽

Felice Arena ◽

C. Guedes Soares

Keyword(s):

Time Evolution ◽

Space Time ◽

Random Wave ◽

Wave Groups ◽

Space Time Evolution

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Non-Linear Random Wave Groups With a Superimposed Current

Volume 3: Safety and Reliability; Materials Technology; Douglas Faulkner Symposium on Reliability and Ultimate Strength of Marine Structures ◽

10.1115/omae2006-92477 ◽

2006 ◽

Author(s):

Vincenzo Nava ◽

Felice Arena ◽

Alessandra Romolo

Keyword(s):

Velocity Potential ◽

Surface Displacement ◽

Second Order ◽

Random Wave ◽

Wave Groups ◽

Wave Kinematics ◽

Free Surface Displacement ◽

Non Linear ◽

Uniform Current ◽

Current Interaction

In this paper a new solution for non-linear random wave groups in the presence of a uniform current is obtained, by extending to the second-order the Boccotti’s ‘Quasi-Determinism’ (QD) theory. The second formulation of the QD theory gives the mechanics of linear random wave groups when a large crest-to-trough wave height occurs. Here the linear QD theory is firstly applied to the wave-current interaction. Therefore the nonlinear expressions both of free surface displacement and velocity potential are obtained, to the second-order in a Stokes’ expansion. Finally some numerical applications are presented in order to analyze both the wave profile and the wave kinematics.

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Analysis of Experimental Results on the Space-Time Evolution of Wave Groups in Crossing Seas

Volume 2B: Structures, Safety and Reliability ◽

10.1115/omae2013-11533 ◽

2013 ◽

Cited By ~ 1

Author(s):

Anita Santoro ◽

C. Guedes Soares ◽

Felice Arena

Keyword(s):

Time Evolution ◽

Laboratory Data ◽

Low Frequency ◽

Frequency Component ◽

Space Time ◽

The Other ◽

Specific Point ◽

Wave Groups ◽

Related Group ◽

Space Time Evolution

The space-time evolution of high wave groups in crossing seas is studied. Profiles are calculated by applying Quasideterminism theory of Boccotti to laboratory data, given that a high crest takes place in a fixed point in the basin. It is observed that the high waves group is given by the superposition of two wave groups, associated one to the low-frequency component of the frequency spectrum and the other to the high-frequency one. It is shown how in crossing seas, the change in direction of one system affects the evolution of the related group, without any influence on the evolution of the other one. Different locations of high crest occurrence have been considered in order to study the effect of the change in spectrum on the deterministic profiles. It is shown that in crossing seas the profile at each location reflects the spectrum related to that specific point.

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