Large-Wave Simulation of Spilling Breakers Over Constant-Slope Bed

2008 ◽  
Author(s):  
Aggelos S. Dimakopoulos ◽  
Athanassios A. Dimas
Keyword(s):  
Free Surface ◽  
Euler Equations ◽  
Surf Zone ◽  
Surface Elevation ◽  
Scale Model ◽  
Free Surface Elevation ◽  
Large Wave ◽  
Wave Simulation ◽  
Subgrid Scales ◽  
Constant Slope

A subgrid scale model is presented for the large-wave simulation (LWS) of spilling breaking waves over bottom of arbitrary shape and finite depth. According to LWS formulation, large velocity and free-surface scales are fully resolved, while subgrid scales are accounted for by an eddy viscosity model, similar to large-eddy simulation (LES). The LWS-based model is applied on the two-dimensional wave propagation over a constant-slope bed. Fluid motion is described by the Euler equations for inviscid but rotational flow, subject to the fully non-linear free-surface boundary conditions. The application of LWS is facilitated by a boundary-fitted transformation, which introduces free-surface elevation terms in the Euler equations and simplifies the numerical implementation. Subgrid velocity scales are modeled similarly to LES, while the effect of free-surface subgrid scales are modeled by wave SGS stresses model. The resulting equations are solved numerically by a two-stage fractional time-step scheme, while an absorption zone is placed in the outflow region to minimize reflection by the outgoing waves. The simulation is carried out for the propagation and breaking of waves over a flat bed with constant slope 1/35 and results are compared to available experimental data. The numerical predictions for the breaking height, the breaking depth and the free-surface elevation dissipation in the surf zone agree very well with the corresponding measurements. The model predicts the vorticity generation in the breaking face of the wave and the appearance of the undertow current in the surf zone. The predicted shear of the undertow current is higher than the measured one.

scholarly journals LARGE-WAVE SIMULATION OF TURBULENT FLOW INDUCED BY WAVE PROPAGATION AND BREAKING OVER CONSTANT SLOPE BED

2012 ◽  
Vol 1 (33) ◽  
pp. 65
Author(s):  
Gerasimos Kolokythas ◽  
Aggelos Dimakopoulos ◽  
Athanassios Dimas
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Wave Breaking ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Large Wave ◽  
Wave Simulation ◽  
Constant Slope ◽  
Good Agreement

In the present study, the three-dimensional, incompressible, turbulent, free-surface flow, developing by the propagation of nonlinear breaking waves over a rigid bed of constant slope, is numerically simulated. The main objective is to investigate the process of spilling wave breaking and the characteristics of the developing undertow current employing the large-wave simulation (LWS) method. According to LWS methodology, large velocity and free-surface scales are fully resolved, and subgrid scales are treated by an eddy viscosity model, similar to large-eddy simulation (LES) methodology. The simulations are based on the numerical solution of the unsteady, three-dimensional, Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow boundary conditions. The case of incoming second-order Stokes waves, normal to the shore, with wavelength to inflow depth ratio λ/dΙ = 6.6, wave steepness H/λ = 0.025, bed slope tanβ = 1/35 and Reynolds number (based on inflow water depth) Red = 250,000 is investigated. The predictions of the LWS model for the incipient wave breaking parameters - breaking depth and height - are in very good agreement with published experimental measurements. Profiles of the time-averaged horizontal velocity in the surf zone are also in good agreement with the corresponding measured ones, verifying the ability of the model to capture adequately the undertow current.

Numerical Simulation of Oblique Wave Breaking and Wave-Induced Currents in the Surf Zone

2014 ◽  
Author(s):  
Gerasimos A. Kolokythas ◽  
Athanassios A. Dimas
Keyword(s):  
Free Surface ◽  
Wave Breaking ◽  
Surf Zone ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Maximum Magnitude ◽  
Longshore Current ◽  
Large Wave ◽  
Constant Slope

In the present study, the three-dimensional, incompressible, turbulent, free-surface flow, developing by the propagation and breaking of nonlinear gravity waves over a constant-slope beach, is numerically simulated. The main objective is to investigate the flow structure in the surf zone as a result of the interaction between the longshore and the undertow current, induced by spilling wave breaking, oblique to the shoreline. The simulations are performed employing the so-called large-wave simulation (LWS) method coupled with a numerical solver for the Navier-Stokes equations. According to the employed LWS methodology, large velocity and free-surface scales are fully resolved, while the effect of subgrid scales is modeled by eddy-viscosity stresses, similar to large-eddy simulation (LES) methodology. In order to validate our model, the case of incoming Stokes waves with wavelength to inflow depth ratio λ/dI ≈ 6.6 and wave steepness H/λ ≈ 0.025, propagating normal to the shore over a bed of constant slope 1/35, is investigated. Our results are compared to published experimental measurements, and it is found that the LWS model predicts adequately the wave breaking parameters — breaking height and depth — and the distribution of the undertow current in the surf zone. Two cases of oblique breaking waves, with inflow angles φI = 20° and 30°, and all other parameters identical to that of the validation case, are considered. The gradual breaking of the refracted waves is captured, as well as the three-dimensional structure of the flow in the surf zone. LWS-predicted profiles of the undertow and the longshore current at several positions in the surf zone, are presented. It is indicated that the undertow prevails in the outer surf zone, while the longshore current becomes stronger in the inner surf zone and reaches its maximum magnitude close to the shore.

Numerical Investigation of Focused Waves and Their Interaction With a Vertical Cylinder Using REEF3D

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Hans Bihs ◽  
Mayilvahanan Alagan Chella ◽  
Arun Kamath ◽  
Øivind Asgeir Arntsen
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Surface Elevation ◽  
Numerical Wave Tank ◽  
Free Surface Elevation ◽  
Wave Tank ◽  
Numerical Wave ◽  
Focused Wave ◽  
The Impact

For the stability of offshore structures, such as offshore wind foundations, extreme wave conditions need to be taken into account. Waves from extreme events are critical from the design perspective. In a numerical wave tank, extreme waves can be modeled using focused waves. Here, linear waves are generated from a wave spectrum. The wave crests of the generated waves coincide at a preselected location and time. Focused wave generation is implemented in the numerical wave tank module of REEF3D, which has been extensively and successfully tested for various wave hydrodynamics and wave–structure interaction problems in particular and for free surface flows in general. The open-source computational fluid dynamics (CFD) code REEF3D solves the three-dimensional Navier–Stokes equations on a staggered Cartesian grid. Higher order numerical schemes are used for time and spatial discretization. For the interface capturing, the level set method is selected. In order to test the generated waves, the time series of the free surface elevation are compared with experimental benchmark cases. The numerically simulated free surface elevation shows good agreement with experimental data. In further computations, the impact of the focused waves on a vertical circular cylinder is investigated. A breaking focused wave is simulated and the associated kinematics is investigated. Free surface flow features during the interaction of nonbreaking focused waves with a cylinder and during the breaking process of a focused wave are also investigated along with the numerically captured free surface.

Nonlinear Wave Crest Distribution on a Vertical Breakwater

2018 ◽  
Author(s):  
Valentina Laface ◽  
Giovanni Malara ◽  
Felice Arena ◽  
Ioannis A. Kougioumtzoglou ◽  
Alessandra Romolo
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Vertical Wall ◽  
Surface Elevation ◽  
Wave Crest ◽  
Height Distribution ◽  
Free Surface Elevation ◽  
Pressure Transducers ◽  
Pressure Time ◽  
Time Histories

The paper addresses the problem of deriving the nonlinear, up to the second order, crest wave height probability distribution in front of a vertical wall under the assumption of finite spectral bandwidth, finite water depth and long-crested waves. The distribution is derived by relying on the Quasi-Deterministic representation of the free surface elevation in front of the vertical wall. The theoretical results are compared against experimental data obtained by utilizing a compressive sensing algorithm for reconstructing the free surface elevation in front of the wall. The reconstruction is pursued by starting from recorded wave pressure time histories obtained by utilizing a row of pressure transducers located at various levels. The comparison shows that there is an excellent agreement between the proposed distribution and the experimental data and confirm the deviation of the crest height distribution from the Rayleigh one.

scholarly journals Relation between orbital velocities, pressure and surface elevation in non-linear nearshore water waves

2021 ◽  
Author(s):  
Kévin Martins ◽  
Philippe Bonneton ◽  
David Lannes ◽  
Hervé Michallet
Keyword(s):  
Free Surface ◽  
Surface Energy ◽  
Water Waves ◽  
Energy Levels ◽  
Sea Surface ◽  
Surface Elevation ◽  
Linear Wave ◽  
Free Surface Elevation ◽  
High Frequencies ◽  
Non Linear

AbstractThe inability of the linear wave dispersion relation to characterize the dispersive properties of non-linear shoaling and breaking waves in the nearshore has long been recognised. Yet, it remains widely used with linear wave theory to convert between sub-surface pressure, wave orbital velocities and the free surface elevation associated with non-linear nearshore waves. Here, we present a non-linear fully dispersive method for reconstructing the free surface elevation from sub-surface hydrodynamic measurements. This reconstruction requires knowledge of the dispersive properties of the wave field through the dominant wavenumbers magnitude κ, representative in an energy-averaged sense of a mixed sea-state composed of both free and forced components. The present approach is effective starting from intermediate water depths - where non-linear interactions between triads intensify - up to the surf zone, where most wave components are forced and travel approximately at the speed of non-dispersive shallow-water waves. In laboratory conditions, where measurements of κ are available, the non-linear fully dispersive method successfully reconstructs sea-surface energy levels at high frequencies in diverse non-linear and dispersive conditions. In the field, we investigate the potential of a reconstruction that uses a Boussinesq approximation of κ, since such measurements are generally lacking. Overall, the proposed approach offers great potential for collecting more accurate measurements under storm conditions, both in terms of sea-surface energy levels at high frequencies and wave-by-wave statistics (e.g. wave extrema). Through its control on the efficiency of non-linear energy transfers between triads, the spectral bandwidth is shown to greatly influence non-linear effects in the transfer functions between sub-surface hydrodynamics and the sea-surface elevation.

scholarly journals On generation and propagation of tsunamis in a shallow running ocean

1978 ◽  
Vol 1 (3) ◽  
pp. 373-390
Author(s):  
Lokenath Debnath ◽  
Uma Basu
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Relative Magnitude ◽  
Ocean Floor ◽  
Surface Elevation ◽  
Free Surface Elevation ◽  
Surface Disturbance ◽  
Fourier And Laplace Transforms ◽  
The Given ◽  
Integral Solutions

A theory is presented of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance. Integral solutions for both two and three dimensional problems are obtained by using the generalized Fourier and Laplace transforms. An asymptotic analysis is carried out for the investigation of the principal features of the free surface elevation. It is found that the propagation of the tsunamis depends on the relative magnitude of the given speed of the running ocean and the wave speed of the shallow ocean. When the speed of the running ocean is less than the speed of the shallow ocean wave, both the two and the three dimensional free surface elevation represent the generation and propagation of surface waves which decay asymptotically ast−12for the two dimensional case and ast−1for the three dimensional tsunamis. Several important features of the solution are discussed in some detail. As an application of the general theory, some physically realistic ocean floor disturbances are included in this paper.

Focused Plunging Breaking Waves Impact on Cylinder Group in Deep Water

2021 ◽  
Author(s):  
Ting Cui ◽  
Arun Kamath ◽  
Weizhi Wang ◽  
Lihao Yuan ◽  
Duanfeng Han ◽  
...  
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Breaking Waves ◽  
Surface Elevation ◽  
Relative Distance ◽  
Structural Safety ◽  
Wave Forces ◽  
Free Surface Elevation ◽  
Single Cylinder ◽  
Numerical Wave

Abstract The correct estimation of wave loading on a cylinder in a cylinder group under different impact scenarios is essential to determine the structural safety of coastal and offshore structures. This scenario differs from the interaction of waves with a single cylinder but not a lot of studies focus on cylinder groups under different arrangements. In this study, the interaction between plunging breaking waves and cylinder groups in deep water is investigated using the two-phase flow model in REEF3D, an open-source computational fluid dynamics program. The Reynolds-averaged Navier-Stokes equation with the two equation k–Ω turbulence model is adopted to resolve the numerical wave tank, with free surface calculated using the level set method. In this study, focused waves in deep water were modeled with a fixed wave steepness method. Wave breaking occurs when the steepness of the wave crest front satisfies the breaking criteria. The model is validated by comparing the numerical wave forces and free surface elevation with measurements from experiments. The computational results show fairly good agreement with experimental data for both free surface elevation and wave forces. Four cases are simulated to investigate the interaction of breaking waves with a cylinder group with different relative distance, number of cylinders and arrangement. Results show that breaking wave forces on the upstream cylinder are smaller than on a single cylinder with a relative distance of one cylinder diameter. The wave forces on cylinders in the pile group are effected by the relative distance between cylinders. The staggered arrangement has a significant influence on the wave forces on the first and second cylinder. The interaction inside a cylinder group mostly happens between the neighbouring cylinders. These interactions are also effected by the relative distance and the numbers of the neighbouring cylinders.

Numerical Simulation of Nonlinear Wave Propagation and Breaking Over Constant-Slope Bottom

2006 ◽  
Author(s):  
Aggelos S. Dimakopoulos ◽  
Athanassios A. Dimas
Keyword(s):  
Numerical Simulation ◽  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Surface Boundary ◽  
Nonlinear Wave Propagation ◽  
Large Wave ◽  
Slope Bottom ◽  
Wave Heights ◽  
Constant Slope

The numerical simulation of the two-dimensional free-surface flow resulting from the propagation of nonlinear gravity waves over constant-slope bottom is presented. The simulation is based on the numerical solution of the Euler equations subject to the fully nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow conditions using a hybrid finite-differences and spectral-method scheme. Wave breaking is accounted for by a surface roller model. The formulation includes a boundary-fitted transformation and is suitable for future extension to incorporate large-eddy and large-wave simulation terms. Results are presented for the simulation of the free-surface flow over two different bottom topographies, with constant slope values of 1:10 and 1:50, and three different inflow wave heights. Over the bottom slope, waves of small wave heights are modified according to linear theory. For nonlinear waves, wavelengths are becoming shorter, the free surface elevation deviates from its initial sinusoidal shape and wave heights increase with decreasing depth. Breaking is observed for the cases with the larger initial wave height and the smaller outflow depth.

On uniqueness and solvability in the linearized two-dimensional problem of a supercritical stream about a surface-piercing body

1995 ◽  
Vol 450 (1939) ◽  
pp. 233-253 ◽  
Keyword(s):  
Free Surface ◽  
Linear Relation ◽  
Existence Of Solutions ◽  
Surface Elevation ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Free Surface Elevation ◽  
Unique Existence ◽  
Velocity Circulation ◽  
Well Posed

Uniqueness and solvability theorems are proved for a well-posed formulation of the two-dimensional Neumann-Kelvin problem (the modified Neumann-Kelvin problem) in the case, when a body is partly immersed in a supercritical stream. Uniqueness is provided by two supplementary conditions which prescribe (i) additional flux at infinity downstream due to presence of body and (ii) a linear relation between the free-surface elevation at stern point and the velocity circulation along wetted contour. Two versions of source method are developed to find a solution. The first version is simpler, but it fails for some irregular values of the body’s velocity. In the second ver­sion complex sources’ strengths are used, avoiding irregular values and establishing the unique existence of solutions.

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