First Order Stochastic Lagrange Model for Asymmetric Ocean Waves

The stochastic Lagrange wave model is a realistic alternative to the Gaussian linear wave model, which has been successfully used in ocean engineering for more than half a century. In this paper we present the slope distributions and other characteristic distributions at level crossings for asymmetric Lagrange time waves, i.e. what can be observed at a fixed measuring station, thereby extending results previously given for space waves. The distributions are given as expectations in a multivariate normal distribution, and they have to be evaluated by simulation or numerical integration. Interesting characteristic variables are the slope in time, the slope in space, and the vertical particle velocity when the waves are observed close to instances when the water level crosses a predetermined level. The theory has been made possible by recent generalizations of Rice's formula for the expected number of marked crossings in random fields.

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Slope distribution in front-back asymmetric stochastic Lagrange time waves

Advances in Applied Probability ◽

10.1239/aap/1275055239 ◽

2010 ◽

Vol 42 (2) ◽

pp. 489-508 ◽

Cited By ~ 7

Author(s):

G. Lindgren

Keyword(s):

Particle Velocity ◽

Random Fields ◽

Wave Model ◽

Linear Wave ◽

Multivariate Normal ◽

Ocean Engineering ◽

Expected Number ◽

Measuring Station ◽

Predetermined Level ◽

The Waves

The stochastic Lagrange wave model is a realistic alternative to the Gaussian linear wave model, which has been successfully used in ocean engineering for more than half a century. In this paper we present the slope distributions and other characteristic distributions at level crossings for asymmetric Lagrange time waves, i.e. what can be observed at a fixed measuring station, thereby extending results previously given for space waves. The distributions are given as expectations in a multivariate normal distribution, and they have to be evaluated by simulation or numerical integration. Interesting characteristic variables are the slope in time, the slope in space, and the vertical particle velocity when the waves are observed close to instances when the water level crosses a predetermined level. The theory has been made possible by recent generalizations of Rice's formula for the expected number of marked crossings in random fields.

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CFD Modeling of Regular and Irregular Waves Generated by Flap Type Wave Maker

Journal of Advanced Research in Fluid Mechanics and Thermal Sciences ◽

10.37934/arfmts.85.2.128144 ◽

2021 ◽

Vol 85 (2) ◽

pp. 128-144

Author(s):

Ali Shehab Shams Eldeen ◽

Ahmed M. R. El-Baz ◽

Abdalla Mostafa Elmarhomy

Keyword(s):

Numerical Simulation ◽

Simulation Method ◽

Irregular Waves ◽

Cfd Modeling ◽

Linear Wave ◽

Ocean Engineering ◽

Navier Stokes Equation ◽

Type Wave ◽

Wave Maker ◽

Numerical Beach

The improvement of wave generation in numerical tanks represents the key factor in ocean engineering development to save time and effort in research concerned with wave energy conversion. For this purpose, this paper introduces a numerical simulation method to generate both regular and irregular waves using Flap-Type wave maker. A 2D numerical wave tank model is constructed with a numerical beach technique, the independence of the numerical beach slope is tested to reduce the wave reflections. The different governing parameters of the Flap type wave maker were studied such as periodic time dependency and length of the flap stroke. The linear wave generated was validated against the wave maker theory WMT, the numerical results agreed with WMT. The Pierson-Moskowitz model is used to generate irregular waves with different frequencies and amplitudes. The numerical model succeeded to generate irregular waves which was validated against published experimental data and with Pierson-Moskowitz spectrum model using Fourier expansion theory in the frequency domain. Useful results are presented in this paper based on the numerical simulation to understand the characteristics of the waves. This paper produces a full guide to generate both regular and irregular waves numerically using ANSYS-CFX approach to solve the 2D Unsteady Reynolds Averaged Navier-Stokes Equation (URANS).

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Ocean Surface Modeling in Vary Wind Field

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.480-481.1452 ◽

2011 ◽

Vol 480-481 ◽

pp. 1452-1456

Author(s):

Li Bo ◽

Zhong Yi Li ◽

Yue Jin Zhang

Keyword(s):

Wind Field ◽

Wave Spectrum ◽

Wave Model ◽

Ocean Surface ◽

Ocean Waves ◽

Surface Modeling ◽

Ocean Wave ◽

Statistical Characteristics ◽

Linear Wave ◽

Wave Models

In ocean surface modeling a popular method of wave modeling is making use of ocean wave spectrum, which is a physical wave model and based on linear wave theories. The ocean waves produced in this way can reflect the statistical characteristics of the real ocean well. However, few investigations of ocean simulation have been focused on turbulent fluid under vary wind field in this way, while all ocean wave models are built with the same wind parameters. In order to resolve the problem of traditional method, we proposed a new method of dividing the ocean surface into regular grids and generating wave models with different parameters of wind in different location of view scope. The method not only preserves the fidelity of statistical characteristics, but also can be accelerated with the processing of GPU and widely used in VR applications.

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Phase-Resolved Reconstruction Algorithm and Deterministic Prediction of Nonlinear Ocean Waves From Spatio-Temporal Optical Measurements

Volume 7B: Ocean Engineering ◽

10.1115/omae2018-78367 ◽

2018 ◽

Author(s):

Nicolas Desmars ◽

Yves Pérignon ◽

Guillaume Ducrozet ◽

Charles-Antoine Guérin ◽

Stephan T. Grilli ◽

...

Keyword(s):

Free Surface ◽

Wave Model ◽

Reconstruction Algorithm ◽

Wave Theory ◽

Ocean Waves ◽

Optical Measurements ◽

Linear Wave ◽

Offshore Structure ◽

Highly Nonlinear ◽

Spatio Temporal

We investigate a nonlinear phase-resolved reconstruction algorithm and models for the deterministic prediction of ocean waves based on a large number of spatio-temporal optical measurements of surface elevations. We consider a single sensor (e.g., LIDAR, stereo-video, etc.) mounted on a fixed offshore structure and remotely measuring fields of free surface elevations. Assuming a uniform distribution of measurement points over the sensor aperture angles, the density of free surface observation points geometrically decreases with the distance from the sensor. Additionally, wave shadowing effects occur, which become more important at small viewing angles (i.e., grazing incidence on the surface). These effects result in observations of surface elevation that are sparsely distributed. Here, based on earlier work by [1], we present and discuss the characteristics of an algorithm, aimed at assimilating such sparse data and able to deterministically reconstruct and propagate ocean surface elevations for their prediction in time and space. This algorithm could assist in the automatic steering and control of a variety of surface vehicles. Specifically, we compare prediction results using linear wave theory and the weakly nonlinear Choppy Wave Model [2, 3], extended here to an “improved” second order formulation. The latter model is based on an efficient Lagrangian formulation of the free surface and was shown to be able to model wave properties that are important to the proper representation of nonlinear free surfaces, namely wave shape and celerity. Synthetic datasets from highly nonlinear High Order Spectral simulations are used as reference oceanic surfaces. Predicted results are analyzed over an area that evolves in time, using the theoretical amount of information assimilated during the reconstruction of the wave field. For typical horizons of prediction, we discuss the capabilities of our assimilation process for each wave model considered.

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A CFD Study of Focused Extreme Wave Impact on Decks of Offshore Structures

Volume 2: CFD and VIV ◽

10.1115/omae2014-23804 ◽

2014 ◽

Cited By ~ 2

Author(s):

Xin Lu ◽

Pankaj Kumar ◽

Anand Bahuguni ◽

Yanling Wu

Keyword(s):

Real World ◽

Offshore Structures ◽

Air Gap ◽

Irregular Waves ◽

Linear Wave ◽

Extreme Wave ◽

Wave Impact ◽

Loading Test ◽

Wide Range ◽

Wave Maker

The design of offshore structures for extreme/abnormal waves assumes that there is sufficient air gap such that waves will not hit the platform deck. Due to inaccuracies in the predictions of extreme wave crests in addition to settlement or sea-level increases, the required air gap between the crest of the extreme wave and the deck is often inadequate in existing platforms and therefore wave-in-deck loads need to be considered when assessing the integrity of such platforms. The problem of wave-in-deck loading involves very complex physics and demands intensive study. In the Computational Fluid Mechanics (CFD) approach, two critical issues must be addressed, namely the efficient, realistic numerical wave maker and the accurate free surface capturing methodology. Most reported CFD research on wave-in-deck loads consider regular waves only, for instance the Stokes fifth-order waves. They are, however, recognized by designers as approximate approaches since “real world” sea states consist of random irregular waves. In our work, we report a recently developed focused extreme wave maker based on the NewWave theory. This model can better approximate the “real world” conditions, and is more efficient than conventional random wave makers. It is able to efficiently generate targeted waves at a prescribed time and location. The work is implemented and integrated with OpenFOAM, an open source platform that receives more and more attention in a wide range of industrial applications. We will describe the developed numerical method of predicting highly non-linear wave-in-deck loads in the time domain. The model’s capability is firstly demonstrated against 3D model testing experiments on a fixed block with various deck orientations under random waves. A detailed loading analysis is conducted and compared with available numerical and measurement data. It is then applied to an extreme wave loading test on a selected bridge with multiple under-deck girders. The waves are focused extreme irregular waves derived from NewWave theory and JONSWAP spectra.

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A Second Order Lagrangian Model for Irregular Ocean Waves

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.2199563 ◽

2005 ◽

Vol 128 (3) ◽

pp. 177-183 ◽

Cited By ~ 14

Author(s):

Sébastien Fouques ◽

Harald E. Krogstad ◽

Dag Myrhaug

Keyword(s):

Specular Reflection ◽

Fluid Velocity ◽

Equations Of Motion ◽

Wave Theory ◽

Ocean Waves ◽

Second Order ◽

Lagrangian Model ◽

Lagrangian Description ◽

Linear Wave ◽

Irregular Solution

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

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The Road to Modern Logic—An Interpretation

Bulletin of Symbolic Logic ◽

10.2307/2687794 ◽

2001 ◽

Vol 7 (4) ◽

pp. 441-484 ◽

Cited By ~ 30

Author(s):

José Ferreirós

Keyword(s):

Order Logic ◽

Point Of View ◽

First Order Logic ◽

Theoretical Point ◽

Primary Role ◽

Philosophical Discussion ◽

Modern Logic ◽

Core System ◽

First Order ◽

The Road

AbstractThis paper aims to outline an analysis and interpretation of the process that led to First-Order Logic and its consolidation as a core system of modern logic. We begin with an historical overview of landmarks along the road to modern logic, and proceed to a philosophical discussion casting doubt on the possibility of a purely rational justification of the actual delimitation of First-Order Logic. On this basis, we advance the thesis that a certain historical tradition was essential to the emergence of modern logic; this traditional context is analyzed as consisting in some guiding principles and, particularly, a set of exemplars (i.e., paradigmatic instances). Then, we proceed to interpret the historical course of development reviewed in section 1, which can broadly be described as a two-phased movement of expansion and then restriction of the scope of logical theory. We shall try to pinpoint ambivalencies in the process, and the main motives for subsequent changes. Among the latter, one may emphasize the spirit of modern axiomatics, the situation of foundational insecurity in the 1920s, the resulting desire to find systems well-behaved from a proof-theoretical point of view, and the metatheoretical results of the 1930s. Not surprisingly, the mathematical and, more specifically, the foundational context in which First-Order Logic matured will be seen to have played a primary role in its shaping.Mathematical logic is what logic, through twenty-five centuries and a few transformations, has become today. (Jean van Heijenoort)

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Note on Interference Effects in Two-Step Reaction Processes

Canadian Journal of Physics ◽

10.1139/p75-315 ◽

1975 ◽

Vol 53 (23) ◽

pp. 2590-2592

Author(s):

J. Cejpek ◽

J. Dobeš

Keyword(s):

Perturbation Theory ◽

Point Of View ◽

Order Perturbation ◽

Interference Effects ◽

Qualitative Explanation ◽

First Order ◽

One Step ◽

Step Transition ◽

Reaction Processes ◽

First Order Perturbation

The reaction processes in which a one-step transition is forbidden are analyzed from the point of view of the first order perturbation theory. The interference between two competing two-step reaction paths is found to be always constructive. A qualitative explanation of the experimentally observed reaction intensities is presented.

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