Non-Linear Random Wave Groups With a Superimposed Current

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.

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

2005 ◽  
Vol 127 (1) ◽  
pp. 46-51 ◽  
Author(s):  
Felice Arena ◽  
Francesco Fedele
Keyword(s):  
Time Evolution ◽  
Surface Displacement ◽  
Fixed Time ◽  
Space Time ◽  
Second Order ◽  
Random Wave ◽  
Wave Groups ◽  
Free Surface Displacement ◽  
Nonlinear Free Surface ◽  
Space Time Evolution

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.

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

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.

Some Effects of Non-Linearity for High Wave Groups in Front of a Vertical Wall

2007 ◽  
Author(s):  
Alessandra Romolo ◽  
Felice Arena
Keyword(s):  
Velocity Potential ◽  
Vertical Wall ◽  
Surface Displacement ◽  
Wave Crest ◽  
Sea Waves ◽  
Wave Groups ◽  
Large Wave ◽  
High Wave ◽  
Free Surface Displacement ◽  
Sea Wave

The upright fully reflective wall-types breakwaters have been widely adopted for development of harbours. The design of these structures depends on the characteristic wave field resulting from the interaction of the sea waves with the reflective structure, which is strongly irregular and nonlinear. This paper deals with the mechanics of long-crested wave groups in front of a vertical wall. For this purpose the ‘Quasi Determinism’ theory, particularized for the reflection of sea wave groups, is extended up to the second-order. The nonlinear processes free surface displacement and velocity potential, when a large wave crest occurs on the vertical wall or in front of it, are obtained. In the application some properties of nonlinear wave groups in reflection, when a high wave crest occurs on the wall or in front of it, are investigated.

Conditional Short-Crested Second Order Waves in Shallow Water and With Superimposed Current

2004 ◽  
Author(s):  
Jo̸rgen Juncher Jensen
Keyword(s):  
Shallow Water ◽  
Wave Spectrum ◽  
Ocean Waves ◽  
Offshore Structures ◽  
Second Order ◽  
Stokes Wave ◽  
Wave Crest ◽  
Wave Kinematics ◽  
Wave Approach ◽  
Non Linear

For bottom-supported offshore structures like oil drilling rigs and oil production platforms, a deterministic design wave approach is often applied using a regular non-linear Stokes’ wave. Thereby, the procedure accounts for non-linear effects in the wave loading but the randomness of the ocean waves is poorly represented, as the shape of the wave spectrum does not enter the wave kinematics. To overcome this problem and still keep the simplicity of a deterministic approach, Tromans, Anaturk and Hagemeijer (1991) suggested the use of a deterministic wave, defined as the expected linear Airy wave, given the value of the wave crest at a specific point in time or space. In the present paper a derivation of the expected second order short-crested wave riding on a uniform current is given. The analysis is based on the second order Sharma and Dean shallow water wave theory and the direction of the main wind direction can make any direction with the current. Numerical results showing the importance of the water depth, the directional spreading and the current on the conditional mean wave profile and the associated wave kinematics are presented. A discussion of the use of the conditional wave approach as design waves is given.

scholarly journals NONLINEAR WAVE PRESSURES GIVEN BY EXTREME WAVES ON AN UPRIGHT BREAKWATER: THEORY AND EXPERIMENTAL VALIDATION

2012 ◽  
Vol 1 (33) ◽  
pp. 33
Author(s):  
Alessandra Romolo ◽  
Felice Arena
Keyword(s):  
Nonlinear Wave ◽  
Three Dimensional ◽  
Surface Displacement ◽  
Nonlinear Effects ◽  
Breaking Waves ◽  
Small Scale ◽  
Ocean Engineering ◽  
Wave Groups ◽  
Free Surface Displacement ◽  
Experimental Comparisons

An analytical nonlinear theory is presented for the interaction between three-dimensional sea wave groups and a seawall during the occurrence of an exceptionally high crest or deep trough of the water elevation. The solution to the second order of the free surface displacement and of the velocity potential is derived by considering an irrotational, inviscid, incompressible flow bounded by a horizontal seabed and a vertical impermeable seawall. The analytical expression of the nonlinear wave pressure is derived. The resulting theory is able to fully describe the mechanics at the seawall and in front of it, which represents a strongly nonhomogeneous wave field, then demonstrating that it is influenced by characteristic parameters and wave conditions. The theoretical results are in good agreement with measurements carried out during a small-scale field experiment at the Natural Ocean Engineering Laboratory in Reggio Calabria (Italy). The theoretical and experimental comparisons show that some distinctive phenomena regarding wave pressures of very high standing wave groups at a seawall, in the absence of either overturning or breaking waves, may be associated with nonlinear effects.

Aspects of Nonlinear Random Wave Kinematics

2002 ◽  
Author(s):  
Dag Myrhaug ◽  
Carl Trygve Stansberg ◽  
Hanne Therese Wist
Keyword(s):  
Free Surface ◽  
Second Order ◽  
Difference Frequency ◽  
Stokes Wave ◽  
Frequency Effect ◽  
Random Wave ◽  
Sum Frequency ◽  
Wave Kinematics ◽  
Nonlinear Random Wave ◽  
Nonlinear Free Surface

Statistics of the nonlinear free surface elevation as well as the nonlinear random wave kinematics in terms of the horizontal velocity component in arbitrary water depth are addressed. Two different methods are considered: a simplified analytical approach based on second-order Stokes wave theory including the sum-frequency effect only, and a second-order random wave model including both sum-frequency and difference-frequency effects. The paper compares results for the statistics of the nonlinear free surface, and the consequences of neglecting the difference-frequency effect in the first method are discussed.

Second-Order Random Wave Kinematics and Resulting Loads on a Bottom-Fixed Slender Monopile

2013 ◽  
Author(s):  
Carl Trygve Stansberg ◽  
Andreas Amundsen ◽  
Sebastien Fouques ◽  
Ole David Økland
Keyword(s):  
Second Order ◽  
Offshore Wind ◽  
Random Wave ◽  
Wave Loads ◽  
Random Waves ◽  
Shear Forces ◽  
Traditional Use ◽  
Wave Kinematics ◽  
Drag Forces ◽  
Particle Velocities

The importance of including second-order nonlinear random wave kinematics in the numerical prediction of drag-induced shear forces and moments, at various levels on a bottom-fixed slender monopile in 40m water depth, is investigated. A vertical circular cylinder of diameter 0.5m is considered, representing typical dimensions of members in jacket type foundations of offshore wind turbines. The focus is here on the wave loads only, and wind and a propeller are therefore not included in this study. In particular, the main focus is on the effects from second-order random wave kinematics on the structural quasi-static time-varying loads due to drag forces in heavy storm wave conditions. Comparisons are made to the traditional use of Airy waves with various ways of stretching. An in-house numerical FEM code developed for structural analysis, NIRWANA, is used for this study. Thus one purpose of the present work is also to verify the implementation of the second-order random waves in the code. The results show significant effects, especially in the wave zone. Extreme crests are around 15%–20% increased, free-surface extreme particle velocities increase by around 30%–40%, while the velocities at levels below MWL are, on the other hand, somewhat reduced. The resulting peak shear forces, and in particular the moments, are thereby increased by typically 50%–100% in the upper parts of the column. At the base the peak shear forces are comparable to the traditional methods, while moments are still somewhat higher. Another effect is the generation of more high-frequency load contributions, which may be important to address further with respect to natural frequencies of such towers.

NON-LINEAR RANDOM WAVE GROUPS IN FINITE WATER DEPTH

2007 ◽  
Author(s):  
Felice Arena ◽  
Vincenzo Nava ◽  
Diego Pavone ◽  
Alessandra Romolo
Keyword(s):  
Water Depth ◽  
Random Wave ◽  
Wave Groups ◽  
Non Linear ◽  
Finite Water Depth

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

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