A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves

1995 ◽  
Vol 294 ◽  
pp. 71-92 ◽  
Author(s):  
Ge Wei ◽  
James T. Kirby ◽  
Stephan T. Grilli ◽  
Ravishankar Subramanya
Keyword(s):  
Boussinesq Equations ◽  
Intermediate Water ◽  
Strong Nonlinearity ◽  
Boussinesq Model ◽  
Linear Dispersion ◽  
Fully Nonlinear ◽  
Surface Wave Propagation ◽  
Highly Nonlinear ◽  
Nonlinear Potential ◽  
Nonlinear Extensions

Fully nonlinear extensions of Boussinesq equations are derived to simulate surface wave propagation in coastal regions. By using the velocity at a certain depth as a dependent variable (Nwogu 1993), the resulting equations have significantly improved linear dispersion properties in intermediate water depths when compared to standard Boussinesq approximations. Since no assumption of small nonlinearity is made, the equations can be applied to simulate strong wave interactions prior to wave breaking. A high-order numerical model based on the equations is developed and applied to the study of two canonical problems: solitary wave shoaling on slopes and undular bore propagation over a horizontal bed. Results of the Boussinesq model with and without strong nonlinearity are compared in detail to those of a boundary element solution of the fully nonlinear potential flow problem developed by Grilli et al. (1989). The fully nonlinear variant of the Boussinesq model is found to predict wave heights, phase speeds and particle kinematics more accurately than the standard approximation.

scholarly journals MNLS simulations of surface wave groups with directional spreading in deep and finite depth waters

2021 ◽  
Author(s):  
Dylan Barratt ◽  
Ton Stefan van den Bremer ◽  
Thomas Alan Adcock Adcock
Keyword(s):  
Potential Flow ◽  
Finite Depth ◽  
Spectral Peak ◽  
Wave Group ◽  
Carrier Wave ◽  
Linear Dispersion ◽  
Wave Groups ◽  
Fully Nonlinear ◽  
Nonlinear Potential ◽  
The Impact

AbstractWe simulate focusing surface gravity wave groups with directional spreading using the modified nonlinear Schrödinger (MNLS) equation and compare the results with a fully-nonlinear potential flow code, OceanWave3D. We alter the direction and characteristic wavenumber of the MNLS carrier wave, to assess the impact on the simulation results. Both a truncated (fifth-order) and exact version of the linear dispersion operator are used for the MNLS equation. The wave groups are based on the theory of quasi-determinism and a narrow-banded Gaussian spectrum. We find that the truncated and exact dispersion operators both perform well if: (1) the direction of the carrier wave aligns with the direction of wave group propagation; (2) the characteristic wavenumber of the carrier wave coincides with the initial spectral peak. However, the MNLS simulations based on the exact linear dispersion operator perform significantly better if the direction of the carrier wave does not align with the wave group direction or if the characteristic wavenumber does not coincide with the initial spectral peak. We also perform finite-depth simulations with the MNLS equation for dimensionless depths ($$k_{\text {p}}d$$ k p d ) between 1.36 and 5.59, incorporating depth into the boundary conditions as well as the dispersion operator, and compare the results with those of fully-nonlinear potential flow code to assess the finite-depth limitations of the MNLS.

scholarly journals Limiting amplitudes of fully nonlinear interfacial tides and solitons

2016 ◽  
Vol 23 (4) ◽  
pp. 285-305
Author(s):  
Borja Aguiar-González ◽  
Theo Gerkema
Keyword(s):  
Numerical Solutions ◽  
Fluid Layer ◽  
Tidal Flow ◽  
Internal Tide ◽  
Boussinesq Equations ◽  
Strong Nonlinearity ◽  
Fully Nonlinear ◽  
Soliton Theory ◽  
Flow Over Topography ◽  
Linear Version

Abstract. A new two-fluid layer model consisting of forced rotation-modified Boussinesq equations is derived for studying tidally generated fully nonlinear, weakly nonhydrostatic dispersive interfacial waves. This set is a generalization of the Choi–Camassa equations, extended here with forcing terms and Coriolis effects. The forcing is represented by a horizontally oscillating sill, mimicking a barotropic tidal flow over topography. Solitons are generated by a disintegration of the interfacial tide. Because of strong nonlinearity, solitons may attain a limiting table-shaped form, in accordance with soliton theory. In addition, we use a quasi-linear version of the model (i.e. including barotropic advection but linear in the baroclinic fields) to investigate the role of the initial stages of the internal tide prior to its nonlinear disintegration. Numerical solutions reveal that the internal tide then reaches a limiting amplitude under increasing barotropic forcing. In the fully nonlinear regime, numerical experiments suggest that this limiting amplitude in the underlying internal tide extends to the nonlinear case in that internal solitons formed by a disintegration of the internal tide may not reach their table-shaped form with increased forcing, but appear limited well below that state.

A FULLY NONLINEAR BOUSSINESQ MODEL FOR WATER WAVE PROPAGATION

2011 ◽  
Vol 1 (32) ◽  
pp. 12
Author(s):  
Hong-sheng Zhang ◽  
Hua-wei Zhou ◽  
Guang-wen Hong ◽  
Jian-min Yang
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Nonlinear Boundary Conditions ◽  
Boussinesq Model ◽  
Linear Dispersion ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Sea Bed ◽  
Nonlinear Version ◽  
Nicolson Scheme

A set of high-order fully nonlinear Boussinesq-type equations is derived from the Laplace equation and the nonlinear boundary conditions. The derived equations include the dissipation terms and fully satisfy the sea bed boundary condition. The equations with the linear dispersion accurate up to [2,2] padé approximation is qualitatively and quantitatively studied in details. A numerical model for wave propagation is developed with the use of iterative Crank-Nicolson scheme, and the two-dimensional fourth-order filter formula is also derived. With two test cases numerically simulated, the modeled results of the fully nonlinear version of the numerical model are compared to those of the weakly nonlinear version.

Fully Nonlinear Potential/RANSE Simulation of Wave Interaction With Ships and Marine Structures

2008 ◽  
Author(s):  
Pierre Ferrant ◽  
Lionel Gentaz ◽  
Bertrand Alessandrini ◽  
Romain Luquet ◽  
Charles Monroy ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Irregular Waves ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Fully Nonlinear ◽  
Nonlinear Potential ◽  
6 Degrees Of Freedom

This paper documents recent advances of the SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach, a method for simulating fully nonlinear wave-body interactions including viscous effects. The methods efficiently combines a fully nonlinear potential flow description of undisturbed wave systems with a modified set of RANS with free surface equations accounting for the interaction with a ship or marine structure. Arbitrary incident wave systems may be described, including regular, irregular waves, multidirectional waves, focused wave events, etc. The model may be fixed or moving with arbitrary speed and 6 degrees of freedom motion. The extension of the SWENSE method to 6 DOF simulations in irregular waves as well as to manoeuvring simulations in waves are discussed in this paper. Different illlustative simulations are presented and discussed. Results of the present approach compare favorably with available reference results.

Development of 3-Dimensional Fully Nonlinear Potential Flow Planar Wave Tank in Framework of OpenFOAM

2019 ◽  
Author(s):  
Zaibin Lin ◽  
Ling Qian ◽  
Wei Bai ◽  
Zhihua Ma ◽  
Hao Chen ◽  
...  
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Wave Structure ◽  
Wave Model ◽  
Numerical Wave Tank ◽  
Wave Tank ◽  
Fully Nonlinear ◽  
3 Dimensional ◽  
Nonlinear Potential ◽  
Numerical Wave

Abstract A 3-Dimensional numerical wave tank based on the fully nonlinear potential flow theory has been developed in OpenFOAM, where the Laplace equation of velocity potential is discretized by Finite Volume Method. The water surface is tracked by the semi-Eulerian-Lagrangian method, where water particles on the free surface are allowed to move vertically only. The incident wave is generated by specifying velocity profiles at inlet boundary with a ramp function at the beginning of simulation to prevent initial transient disturbance. Additionally, an artificial damping zone is located at the end of wave tank to sufficiently absorb the outgoing waves before reaching downstream boundary. A five-point smoothing technique is applied at the free surface to eliminate the saw-tooth instability. The proposed wave model is validated against theoretical results and experimental data. The developed solver could be coupled with multiphase Navier-Stokes solvers in OpenFOAM in the future to establish an integrated versatile numerical wave tank for studying efficiently wave structure interaction problems.

Three-Dimensional Periodic Fully Nonlinear Potential Waves

2013 ◽  
Author(s):  
Dmitry Chalikov ◽  
Alexander V. Babanin
Keyword(s):  
Wave Field ◽  
Degrees Of Freedom ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Transform Method ◽  
Fully Nonlinear ◽  
Stokes Waves ◽  
Nonlinear Potential ◽  
The Fourier Transform

An exact numerical scheme for a long-term simulation of three-dimensional potential fully-nonlinear periodic gravity waves is suggested. The scheme is based on a surface-following non-orthogonal curvilinear coordinate system and does not use the technique based on expansion of the velocity potential. The Poisson equation for the velocity potential is solved iteratively. The Fourier transform method, the second-order accuracy approximation of the vertical derivatives on a stretched vertical grid and the fourth-order Runge-Kutta time stepping are used. The scheme is validated by simulation of steep Stokes waves. The model requires considerable computer resources, but the one-processor version of the model for PC allows us to simulate an evolution of a wave field with thousands degrees of freedom for hundreds of wave periods. The scheme is designed for investigation of the nonlinear two-dimensional surface waves, for generation of extreme waves as well as for the direct calculations of a nonlinear interaction rate. After implementation of the wave breaking parameterization and wind input, the model can be used for the direct simulation of a two-dimensional wave field evolution under the action of wind, nonlinear wave-wave interactions and dissipation. The model can be used for verification of different types of simplified models.

Wave Scattering Around a Vertical Cylinder: Fully Nonlinear Potential Flow Calculations Compared With Low Order Perturbation Results and Experiment

2002 ◽  
Author(s):  
Karsten Trulsen ◽  
Per Teigen
Keyword(s):  
Potential Flow ◽  
Wave Scattering ◽  
Vertical Cylinder ◽  
Wave Interaction ◽  
Perturbation Approach ◽  
Marine Structures ◽  
Fully Nonlinear ◽  
Nonlinear Potential ◽  
Specific Geometry ◽  
Truncated Cylinder

A detailed description of a fully nonlinear numerical method for computing wave interaction effects around arbitrary marine structures is presented. The paper highlights application to one specific geometry: A single, fixed vertical truncated cylinder. The fully nonlinear computations are compared with linear and second-order nonlinear results obtained with the perturbation approach, as well as with experiments.

Numerical Simulations of Large Deep Water Waves: The Application of a Boundary Element Method

2006 ◽  
Author(s):  
Caroline H. Hague ◽  
Chris Swan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Deep Water ◽  
Water Waves ◽  
Physical Space ◽  
Wave Model ◽  
Three Dimensions ◽  
Fully Nonlinear ◽  
Highly Nonlinear ◽  
Element Method

This paper concerns the description of extreme surface water waves in deep water. A fully nonlinear numerical wave model in three dimensions is presented, based on the Boundary Element Method (BEM), and is applied to nonlinear focusing of wave components with varying frequency and direction of propagation to form highly nonlinear groups. By using multiple fluxes at corners and edges of the numerical domain the “corner problem” associated with BEM-based models in physical space is overcome. A two-dimensional version of the method is also employed to model unidirectional cases, and examples presented include the focusing of Top Hat spectra in deep water to form highly nonlinear wave groups at or close to their breaking limit. The ability of the model to accurately simulate these sea states is highlighted by comparison to the fully nonlinear model of Bateman, Swan and Taylor (2001, 2003).

scholarly journals Did the Draupner wave occur in a crossing sea?

2011 ◽  
Vol 467 (2134) ◽  
pp. 3004-3021 ◽  
Author(s):  
T. A. A. Adcock ◽  
P. H. Taylor ◽  
S. Yan ◽  
Q. W. Ma ◽  
P. A. E. M. Janssen
Keyword(s):  
Low Frequency ◽  
Quality Measurement ◽  
Order Theory ◽  
Second Order ◽  
Flow Solver ◽  
The North ◽  
Highly Nonlinear ◽  
Nonlinear Potential ◽  
Wind Sea ◽  
Set Up

The ‘New Year Wave’ was recorded at the Draupner platform in the North Sea and is a rare high-quality measurement of a ‘freak’ or ‘rogue’ wave. The wave has been the subject of much interest and numerous studies. Despite this, the event has still not been satisfactorily explained. One piece of information that was not directly measured at the platform, but which is vital to understanding the nonlinear dynamics is the wave's directional spreading. This paper investigates the directionality of the Draupner wave and concludes it might have resulted from two wave-groups crossing, whose mean wave directions were separated by about 90 ° or more. This result has been deduced from a set-up of the low-frequency second-order difference waves under the giant wave, which can be explained only if two wave systems are propagating at such an angle. To check whether second-order theory is satisfactory for such a highly nonlinear event, we have run numerical simulations using a fully nonlinear potential flow solver, which confirm the conclusion deduced from the second-order theory. This is backed up by a hindcast from European Centre for Medium-Range Weather Forecasts that shows swell waves propagating at approximately 80 ° to the wind sea. Other evidence that supports our conclusion are the measured forces on the structure, the magnitude of the second-order sum waves and some other instances of freak waves occurring in crossing sea states.

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