scholarly journals VALIDATION OF A DOUBLE-LAYER BOUSSINESQ-TYPE MODEL FOR HIGHLY NONLINEAR AND DISPERSIVE WAVES

2011 ◽  
Vol 1 (32) ◽  
pp. 14
Author(s):  
Florent Chazel ◽  
Michel Benoit ◽  
Alexandre Ern
Keyword(s):  
Laboratory Experiments ◽  
Irregular Waves ◽  
Type Model ◽  
Breaking Wave ◽  
Test Cases ◽  
Regular Waves ◽  
Dispersive Waves ◽  
One Dimensional ◽  
Highly Nonlinear ◽  
Nonlinearity Dispersion

A two-layer Boussinesq-type mathematical model has been recently introduced by the authors with the goal of modeling highly nonlinear and dispersive waves (Chazel et al. 2009). The analysis of this model has previously shown that it possesses excellent linear properties, up to kh = 10 at least, for dispersion, shoaling coefficient and vertical profile of orbital velocities. In the present work a numerical one-dimensional (1DH) version of model is developed based on a finite difference technique for meshing the spatial domain. It is then applied and verified against a set of three one-dimensional (1DH) test-cases for which either numerical or experimental reference results are available: i. nonlinear and dispersive regular waves of permanent form; ii. propagation of regular waves on a trapezoidal bar (laboratory experiments by Dingemans (1994)); iii. shoaling and propagation of irregular waves on a barred beach profile (laboratory experiments by Becq-Girard et al. (1999)). The test-cases considered in this study confirm the very good capabilities of the model to reproduce either exact solutions, high-precision numerical simulations and experimental measurements in a variety of non-breaking wave conditions and types of bottom profiles. Nonlinearity, dispersion and bathymetric effects are well accounted for by the model, which appears to possess a rather wide domain of validity while maintaining a reasonable level of complexity.

scholarly journals A double-layer Boussinesq-type model for highly nonlinear and dispersive waves

2009 ◽  
Vol 465 (2108) ◽  
pp. 2319-2346 ◽  
Author(s):  
F. Chazel ◽  
M. Benoit ◽  
A. Ern ◽  
S. Piperno
Keyword(s):  
Double Layer ◽  
Deep Water ◽  
Type Model ◽  
Nonlinear Behaviour ◽  
Approximate Inverse ◽  
Dispersive Waves ◽  
Final Model ◽  
Water Value ◽  
Highly Nonlinear ◽  
Model Derivation

We derive and analyse, in the framework of the mild-slope approximation, a new double-layer Boussinesq-type model that is linearly and nonlinearly accurate up to deep water. Assuming the flow to be irrotational, we formulate the problem in terms of the velocity potential, thereby lowering the number of unknowns. The model derivation combines two approaches, namely the method proposed by Agnon et al. ( Agnon et al. 1999 J. Fluid Mech. 399 , 319–333) and enhanced by Madsen et al. ( Madsen et al. 2003 Proc. R. Soc. Lond. A 459 , 1075–1104), which consists of constructing infinite-series Taylor solutions to the Laplace equation, to truncate them at a finite order and to use Padé approximants, and the double-layer approach of Lynett & Liu ( Lynett & Liu 2004 a Proc. R. Soc. Lond. A 460 , 2637–2669), which allows lowering the order of derivatives. We formulate the model in terms of a static Dirichlet–Neumann operator translated from the free surface to the still-water level, and we derive an approximate inverse of this operator that can be built once and for all. The final model consists of only four equations both in one and two horizontal dimensions, and includes only second-order derivatives, which is a major improvement in comparison with so-called high-order Boussinesq models. A linear analysis of the model is performed, and its properties are optimized using a free parameter determining the position of the interface between the two layers. Excellent dispersion and shoaling properties are obtained, allowing the model to be applied up to the deep-water value k h =10. Finally, numerical simulations are performed to quantify the nonlinear behaviour of the model, and the results exhibit a nonlinear range of validity reaching at least k h =3π.

scholarly journals OPPORTUNITIES FOR INTERACTIVE, PHYSICS-DRIVEN WAVE SIMULATION USING THE BOUSSINESQ-TYPE MODEL, CELERIS

2017 ◽  
pp. 11
Author(s):  
Sasan Tavakkol ◽  
Patrick Lynett
Keyword(s):  
Boundary Conditions ◽  
Wave Model ◽  
Simulation Software ◽  
Irregular Waves ◽  
Type Model ◽  
Model Parameters ◽  
Breaking Wave ◽  
Wave Simulation ◽  
Recent Developments ◽  
Language Environment

In this paper, we discuss the recent developments of our GPU-based Boussinesq-type wave simulation software, Celeris. This software is meant to serve the primary purpose of being interactive – i.e. allowing the user to modify the boundary conditions and model parameters as the model is running, and to see the effect of these changes immediately. To accomplish this, the model is coded in a shader language environment, and our physical variables (e.g. ocean surface elevation, water velocity) are represented in the model as graphical textures, which can therefore be rapidly rendered and visualized via a GPU. The model may run faster than real-time for problems with practical setups. Following a description of the numerical development of the wave model, we elaborate on the recent features that are added to the software such as irregular waves and uniform time series boundary conditions. Since the model is previously validated for breaking and non-breaking wave, in this paper, we compare the numerical results of the model with experimental results of a current benchmark and show its good agreement.

scholarly journals Applicability of Nonlinear Wavemaker Theory

2019 ◽  
Vol 7 (1) ◽  
pp. 14 ◽  
Author(s):  
Mads Røge Eldrup ◽  
Thomas Lykke Andersen
Keyword(s):  
Ad Hoc ◽  
Wave Theory ◽  
Wave Generation ◽  
Second Order ◽  
Irregular Waves ◽  
Test Results ◽  
Regular Waves ◽  
Simple Modification ◽  
Wave Kinematics ◽  
Highly Nonlinear

Generation of high-quality waves is essential when making numerical or physically model tests. When using a wavemaker theory outside the validity area, spurious waves are generated. In order to investigate the validity of different wave generation methods, new model test results are presented where linear and nonlinear wave generation theories are tested on regular and irregular waves. A simple modification to the second-order wavemaker theory is presented, which significantly reduces the generation of spurious waves when used outside its range of applicability. For highly nonlinear regular waves, only the ad-hoc unified wave generation based on stream function wave theory was found acceptable. For irregular waves, similar conclusions are drawn, but the modified second-order wavemaker method is more relevant. This is because the ad-hoc unified generation method for irregular waves requires the wave kinematics to be calculated by a numerical model, which might be quite time-consuming. Finally, a table is presented with the range of applicability for each wavemaker method for regular and irregular waves.

QUASI-ONE-DIMENSIONAL SEPARATION TYPE MODEL OF PSEUDO-SHOCK IN A DUCT

2013 ◽  
Vol 44 (5) ◽  
pp. 639-664 ◽  
Author(s):  
Evgeniy Aleksandrovich Meshcheryakov ◽  
Violetta Vasilievna Yashina
Keyword(s):  
Type Model ◽  
One Dimensional

scholarly journals Time Scale for Scour Beneath Pipelines Due to Long-Crested and Short-Crested Nonlinear Random Waves Plus Current

2021 ◽  
Vol 9 (2) ◽  
pp. 114
Author(s):  
Dag Myrhaug ◽  
Muk Chen Ong
Keyword(s):  
Time Scale ◽  
Current Flow ◽  
Irregular Waves ◽  
Wave Crest ◽  
Random Wave ◽  
Random Waves ◽  
Flow Conditions ◽  
Regular Waves ◽  
Nonlinear Random Waves ◽  
2D And 3D

This article derives the time scale of pipeline scour caused by 2D (long-crested) and 3D (short-crested) nonlinear irregular waves and current for wave-dominant flow. The motivation is to provide a simple engineering tool suitable to use when assessing the time scale of equilibrium pipeline scour for these flow conditions. The method assumes the random wave process to be stationary and narrow banded adopting a distribution of the wave crest height representing 2D and 3D nonlinear irregular waves and a time scale formula for regular waves plus current. The presented results cover a range of random waves plus current flow conditions for which the method is valid. Results for typical field conditions are also presented. A possible application of the outcome of this study is that, e.g., consulting engineers can use it as part of assessing the on-bottom stability of seabed pipelines.

Channeling Flow and Solute Transport in a Single Fracture

2013 ◽  
Vol 316-317 ◽  
pp. 632-635
Author(s):  
Ye Fei Tan ◽  
Zhi Fang Zhou ◽  
Shi Qiang Wu ◽  
Xing Hua Xie ◽  
Bo Ning
Keyword(s):  
Finite Element Method ◽  
Drinking Water ◽  
Breakthrough Curve ◽  
Laboratory Experiments ◽  
Fractured Media ◽  
Single Fracture ◽  
The Finite Element Method ◽  
Dispersive Equation ◽  
One Dimensional ◽  
Channeling Flow

Groundwater in fractured media plays an important role in drinking water supply, and the understanding of its principle mechanisms is essential for securing the groundwater exploring and utilization. In this paper, a novel conceptual fracture model was presented on the basis of the reality of channeling flow in natural fractures and laboratory experiments were conducted for the purpose of getting a better understanding of the step-like breakthrough curve (BTC). Experimental results were fitted with convective dispersive equation (CDE) and compared with those of the finite element method (FEM) models. Results showed that the traditional one-dimensional CDE was invalid in the fitting of a step-like BTC and needed to be improved.

Line-by-Line Random-Number Database for Monte Carlo Simulations of Radiation in Combustion System

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Tao Ren ◽  
Michael F. Modest
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Heat ◽  
Random Number ◽  
Test Cases ◽  
Combustion System ◽  
Absorption Coefficients ◽  
One Dimensional ◽  
The Monte Carlo Method

With today's computational capabilities, it has become possible to conduct line-by-line (LBL) accurate radiative heat transfer calculations in spectrally highly nongray combustion systems using the Monte Carlo method. In these calculations, wavenumbers carried by photon bundles must be determined in a statistically meaningful way. The wavenumbers for the emitting photons are found from a database, which tabulates wavenumber–random number relations for each species. In order to cover most conditions found in industrial practices, a database tabulating these relations for CO2, H2O, CO, CH4, C2H4, and soot is constructed to determine emission wavenumbers and absorption coefficients for mixtures at temperatures up to 3000 K and total pressures up to 80 bar. The accuracy of the database is tested by reconstructing absorption coefficient spectra from the tabulated database. One-dimensional test cases are used to validate the database against analytical LBL solutions. Sample calculations are also conducted for a luminous flame and a gas turbine combustion burner. The database is available from the author's website upon request.

scholarly journals DESIGN OF MAIN BREAKWATER AT SINES HARBOUR

1976 ◽  
Vol 1 (15) ◽  
pp. 143 ◽  
Author(s):  
John Dorrington Mettam
Keyword(s):  
North Atlantic ◽  
Government Agency ◽  
Irregular Waves ◽  
Regular Waves ◽  
The West ◽  
The North ◽  
Flume Tests ◽  
Wide Range ◽  
The Subject ◽  
Engineering Conference

In March 1972 the author's firm in association with two Portuguese firms of consulting engineers, Consulmar and Lusotecna, were appointed by the Portuguese Government agency Gabinete da Area de Sines to prepare designs for the construction of a new harbour at Sines on the west coast of Portugal. The location is shown in Figure 1. The main breakwater, which is the subject of this paper, is probably the largest breakwater yet built, being 2 km long and in depths of water of up to 50 m. It is exposed to the North Atlantic and has been designed for a significant wave height of 11 m. Dolos units invented by Merrifield (ref. 1) form the main armour. The project programme required that studies be first made of a wide range of alternative layouts for the harbour. After the client had decided on the layout to be adopted, documents were to be prepared to enable tenders for construction to be invited in January 1973. This allowed little time for the design to be developed and only one series of flume tests, using regular waves, was completed during this period. Further tests in the regular flume were completed during the tender period and a thorough programme of testing with irregular waves was commenced later in the year, continuing until August 1974 when the root of the breakwater was complete and the construction of the main cross-section was about to start. The model tests, which were carried out at the Laboratorio Nacional de Engenharia Civil in Lisbon, were reported by Morals in a paper presented to the 14th International Coastal Engineering Conference in 1974. (ref. 2)

scholarly journals BREAKWATER ARMOR DISPLACEMENT THRESHOLDS: A POSSIBLE CORRELATION WITH CUMULATIVE WAVE ENERGY

1984 ◽  
Vol 1 (19) ◽  
pp. 186
Author(s):  
Daniel L. Behnke ◽  
Frederic Raichlen
Keyword(s):  
Wave Energy ◽  
Wave Train ◽  
Wave Length ◽  
Simple Wave ◽  
Wave Theory ◽  
Irregular Waves ◽  
Reconstruction Technique ◽  
Regular Wave ◽  
Regular Waves ◽  
Three Dimensional Model

An extensive program of stability experiments in a highly detailed three-dimensional model has recently been completed to define a reconstruction technique for a damaged breakwater (Lillevang, Raichlen, Cox, and Behnke, 1984). Tests were conducted with both regular waves and irregular waves from various directions incident upon the breakwater. In comparison of the results of the regular wave tests to those of the irregular wave tests, a relation appeared to exist between breakwater damage and the accumulated energy to which the structure had been exposed. The energy delivered per wave is defined, as an approximation, as relating to the product of H2 and L, where H is the significant height of a train of irregular waves and L is the wave length at a selected depth, calculated according to small amplitude wave theory using a wave period corresponding to the peak energy of the spectrum. As applied in regular wave testing, H is the uniform wave height and L is that associated with the period of the simple wave train. The damage in the model due to regular waves and that caused by irregular waves has been related through the use of the cumulative wave energy contained in those waves which have an energy greater than a threshold value for the breakwater.

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