Nonlinear refraction–diffraction of water waves: the complementary mild-slope equations

2009 ◽  
Vol 641 ◽  
pp. 509-520 ◽  
Author(s):  
YARON TOLEDO ◽  
YEHUDA AGNON
Keyword(s):  
Water Waves ◽  
Numerical Models ◽  
Nonlinear Refraction ◽  
Wave Interaction ◽  
Domain Model ◽  
Nonlinear Frequency ◽  
Class Iii ◽  
Mild Slope Equation ◽  
Bottom Boundary Condition ◽  
Analytical Perturbation

A second-order nonlinear frequency-domain model extending the linear complementary mild-slope equation (CMSE) is presented. The nonlinear model uses the same streamfunction formulation as the CMSE. This allows the vertical profile assumption to accurately satisfy the kinematic bottom boundary condition in the case of nonlinear triad interactions as well as for the linear refraction–diffraction part. The result is a model with higher accuracy of wave–bottom interactions including wave–wave interaction. The model's validity is confirmed by comparison with accurate numerical models, laboratory experiments over submerged obstacles and analytical perturbation solutions for class III Bragg resonance.

On a uniformly valid model for surface wave interaction

1993 ◽  
Vol 247 ◽  
pp. 589-601 ◽  
Author(s):  
Yehuda Agnon
Keyword(s):  
Surface Wave ◽  
Water Waves ◽  
Wave Train ◽  
Wave Interaction ◽  
Shallow Water Waves ◽  
First Order ◽  
Near Resonance ◽  
Wave Trains ◽  
Velocity Changes ◽  
Forced Waves

Nonlinear interaction of surface wave trains is studied. Zakharov's kernel is extended to include the vicinity of trio resonance. The forced wave amplitude and the wave velocity changes are then first order rather than second order. The model is applied to remove near-resonance singularities in expressions for the change of speed of one wave train in the presence of another. New results for Wilton ripples and the drift current and setdown in shallow water waves are readily derived. The ideas are applied to the derivation of forced waves in the vicinity of quartet and quintet resonance in an evolving wave field.

Numerical solutions to wave interaction with rubblemound breakwaters

1990 ◽  
Vol 17 (2) ◽  
pp. 252-261 ◽  
Author(s):  
Kevin R. Hall
Keyword(s):  
Numerical Modelling ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Scale Effects ◽  
Numerical Models ◽  
Internal Flow ◽  
Wave Interaction ◽  
Theoretical Development ◽  
Porous Media Flow ◽  
Complex Flow

The interaction of a wave with a rubblemound breakwater results in a complex flow field which is both nonlinear and turbulent, particularly within a region close to the surface of the structure. Numerical models describing internal flow in a rubblemound breakwater are becoming increasingly important, particularly as the influence of scale effects on internal flow in physical hydraulic models are becoming understood as important. A number of numerical models to predict the internal breakwater flow kinematics have been produced in the past two decades. This paper provides a review of the state-of-the-art of numerical modelling of wave interaction with rubblemound breakwaters. Details of the theoretical development and the resulting numerical solution techniques are presented. Methods for incorporating secondary effects such as two-phase (air–water) flow, inertia, and unbalanced boundary conditions are discussed. Limitations of the models resulting from the validity of the assumptions made in order to effect a numerical solution are discussed. Key words: breakwaters, internal flow, porous media flow, numerical modelling, rubblemound breakwaters.

Optimal sponge layer for water waves numerical models

2018 ◽  
Vol 163 ◽  
pp. 169-182 ◽  
Author(s):  
Rémi A. Carmigniani ◽  
Damien Violeau
Keyword(s):  
Water Waves ◽  
Numerical Models ◽  
Sponge Layer

An Efficient Numerical Model of Hyperbolic Mild-Slope Equation

2007 ◽  
Author(s):  
Zhiyao Song ◽  
Honggui Zhang ◽  
Jun Kong ◽  
Ruijie Li ◽  
Wei Zhang
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Water Waves ◽  
Computational Time ◽  
Transient Wave ◽  
Flat Bottom ◽  
The Real ◽  
Wave Elevation ◽  
Mild Slope Equation ◽  
Effective Wave

Introduction of an effective wave elevation function, the simplest time-dependent hyperbolic mild-slope equation has been presented and an effective numerical model for the water wave propagation has been established combined with different boundary conditions in this paper. Through computing the effective wave elevation and transforming into the real transient wave motion, then related wave heights are computed. Because the truncation errors of the presented model only induced by the dissipation terms, but those of Lin’s model (2004) contributed by the convection terms, dissipation terms and source terms, the error analysis shows that calculation stability of this model is enhanced obviously compared with Lin’s one. The tests show that this model succeeds to the merit in Lin’s one and the computer program simpler, computational time shorter because of calculation stability enhanced efficiently and computer memory decreased obviously. The presented model has the capability of simulating exactly the location of transient wave front by the speed of wave propagation in the first test, which is important for the real-time prediction of the arrival time of water waves generated in the deep sea. The model is validated against experimental data for combined wave refraction and diffraction over submerged circular shoal on a flat bottom in the second test. Good agreements are gained. The model can be applied to the theory research and engineering applications about the wave propagation in the coastal waters.

A Lattice Boltzmann Bluff Body Model for VIV Suppression

2006 ◽  
Author(s):  
Jannette B. Frandsen
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Lattice Boltzmann ◽  
Water Waves ◽  
Bluff Body ◽  
Numerical Models ◽  
Bluff Bodies ◽  
Free Surfaces ◽  
Viv Suppression ◽  
Reynolds Number Flows

In this paper, the suitability of a mesoscopic approach involving a single phase Lattice Boltzmann (LB) model is examined. In contrast, to continuum based numerical models, where only space and time are discrete, the discrete variables of the LB model are space, time and particle velocity. With reference to the Boltzmann equation of classical kinetic theory, the distribution of fluid molecules is represented by particle distribution functions. The LB method simulates fluid flow by tracking particle distributions. It is notable that the formulation avoids the need to include the Poisson equation. An elastic-collision scheme with no-slip walls is prescribed. The central idea behind proposing the present formulation is many fold. One goal is to capture smaller scales naturally, postponing the need of applying empirical turbulence models. Another goal is to get further insight into nonlinearities in steep and breaking free surfaces to improve current continuum mechanics solutions. Although the long term goal is to predict bluff-body high Reynolds number flows and breaking water waves, the present study is limited to laminar flow simulations and continuous free surfaces. The case studies presented include bluff bodies embedded in Reynolds number flows in the order of 100–200. The free surface test cases represent bore propagation past a single and multiple structures. The 2-D uniform grid solutions are compared with findings reported in the literature. Vortex patterns are studied when single or several objects are located in the bluff-body wakes. From a mitigation point of view, the model presents an easy means of re-arranging bluff bodies to study optimum solutions for VIV suppression with/without a free surface.

scholarly journals Statistical Parameters of the Air Turbulent Boundary Layer over Steep Water Waves Measured by the PIV Technique

2011 ◽  
Vol 41 (8) ◽  
pp. 1421-1454 ◽  
Author(s):  
Yu. Troitskaya ◽  
D. Sergeev ◽  
O. Ermakova ◽  
G. Balandina
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Interaction Parameter ◽  
Water Waves ◽  
Water Surface ◽  
Wind Wave ◽  
Wave Interaction ◽  
Statistical Parameters ◽  
Piv Technique ◽  
Wave Induced

Abstract A turbulent airflow with a centerline velocity of 4 m s−1 above 2.5-Hz mechanically generated gravity waves of different amplitudes has been studied in experiments using the particle image velocimetry (PIV) technique. Direct measurements of the instantaneous flow velocity fields above a curvilinear interface demonstrating flow separation are presented. Because the airflow above the wavy water surface is turbulent and nonstationary, the individual vector fields are conditionally averaged sampled on the phase of the water elevation. The flow patterns of the phase-averaged fields are relatively smooth. Because the averaged flow does not show any strongly nonlinear effects, the quasi-linear approximation can be used. The parameters obtained by the flow averaging are compared with the theoretical results obtained within the theoretical quasi-linear model of a turbulent boundary layer above the wavy water surface. The wave-induced pressure disturbances in the airflow are calculated using the retrieved statistical ensemble of wind flow velocities. The energy flux from the wind to waves and the wind–wave interaction parameter are estimated using the obtained wave-induced pressure disturbances. The estimated values of the wind–wave interaction parameter are in a good agreement with the theory.

On the analytical solutions for water waves generated by a prescribed landslide

2017 ◽  
Vol 821 ◽  
pp. 85-116 ◽  
Author(s):  
Hong-Yueh Lo ◽  
Philip L.-F. Liu
Keyword(s):  
Analytical Solutions ◽  
Water Waves ◽  
Initial Conditions ◽  
Numerical Models ◽  
Wave Model ◽  
Dispersive Wave ◽  
Forcing Function ◽  
Resonance Solution ◽  
The Difference ◽  
The One

This paper presents a suite of analytical solutions, for both the free-surface elevation and the flow velocity, for landslide-generated water waves. The one-dimensional (horizontal, 1DH) analytical solutions for water waves generated by a solid landslide moving at a constant speed in constant water depth were obtained for the linear and weakly dispersive wave model as well as the linear and fully dispersive wave model. The area enclosed by the landslide was shown to have stronger lasting effects on the generated water waves than the exact landslide shape. In addition, the resonance solution based on the fully dispersive wave model was examined, and the growth rate was derived. For the 1DH linear shallow water equations (LSWEs) on a constant slope, a closed-form analytical solution, which could serve as a useful benchmark for numerical models, was found for a special landslide forcing function. For the two-dimensional (horizontal, 2DH) LSWEs on a plane beach, we rederived the solutions using the quiescent water initial conditions. The difference between the initial conditions used in the new solutions and those used in previous studies was found to have a permanent effect on the generated waves. We further noted that convergence rate of the 2DH LSWE analytical solutions varies greatly, and advised that case-by-case convergence tests be conducted whenever the modal analytical solutions are numerically evaluated using a finite number of modes.

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