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.

The mechanism of vortex connection at a free surface

1999 ◽  
Vol 384 ◽  
pp. 207-241 ◽  
Author(s):  
CHIONG ZHANG ◽  
LIAN SHEN ◽  
DICK K. P. YUE
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Vortex Ring ◽  
Stokes Equations ◽  
Incidence Angle ◽  
Surface Boundary ◽  
Viscous Layer ◽  
Vertical Vorticity ◽  
Vorticity Component ◽  
Stress Boundary Conditions

Vortex connections at the surface are fundamental and prominent features in free-surface vortical flows. To understand the detailed mechanism of such connection, we consider, as a canonical problem, the laminar vortex connections at a free surface when an oblique vortex ring impinges upon that surface. We perform numerical simulations of the Navier–Stokes equations with viscous free-surface boundary conditions. It is found that the key to understanding the mechanism of vortex connection at a free surface is the surface layers: a viscous layer resulting from the dynamic zero-stress boundary conditions at the free surface, and a thicker blockage layer which is due to the kinematic boundary condition at the surface. In the blockage layer, the vertical vorticity component increases due to vortex stretching and vortex turning (from the transverse vorticity component). The vertical vorticity is then transported to the free surface through viscous diffusion and vortex stretching in the viscous layer leading to increased surface-normal vorticity. These mechanisms take place at the aft-shoulder regions of the vortex ring. Connection at the free surface is different from that at a free-slip wall owing to the generation of surface secondary vorticity. We study the components of this surface vorticity in detail and find that the presence of a free surface accelerates the connection process. We investigate the connection time scale and its dependence on initial incidence angle, Froude and Reynolds numbers. It is found that a criterion based on the streamline topology provides a precise definition for connection time, and may be preferred over existing definitions, e.g. those based on free-surface elevation or net circulation.

scholarly journals Linear pulse structure and signalling in a film flow on an inclined plane

1999 ◽  
Vol 396 ◽  
pp. 37-71 ◽  
Author(s):  
LEONID BREVDO ◽  
PATRICE LAURE ◽  
FREDERIC DIAS ◽  
THOMAS J. BRIDGES
Keyword(s):  
Free Surface ◽  
Saddle Point ◽  
Convective Instability ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Results ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Surface Boundary Conditions

The film flow down an inclined plane has several features that make it an interesting prototype for studying transition in a shear flow: the basic parallel state is an exact explicit solution of the Navier–Stokes equations; the experimentally observed transition of this flow shows many properties in common with boundary-layer transition; and it has a free surface, leading to more than one class of modes. In this paper, unstable wavepackets – associated with the full Navier–Stokes equations with viscous free-surface boundary conditions – are analysed by using the formalism of absolute and convective instabilities based on the exact Briggs collision criterion for multiple k-roots of D(k, ω) = 0; where k is a wavenumber, ω is a frequency and D(k, ω) is the dispersion relation function.The main results of this paper are threefold. First, we work with the full Navier–Stokes equations with viscous free-surface boundary conditions, rather than a model partial differential equation, and, guided by experiments, explore a large region of the parameter space to see if absolute instability – as predicted by some model equations – is possible. Secondly, our numerical results find only convective instability, in complete agreement with experiments. Thirdly, we find a curious saddle-point bifurcation which affects dramatically the interpretation of the convective instability. This is the first finding of this type of bifurcation in a fluids problem and it may have implications for the analysis of wavepackets in other flows, in particular for three-dimensional instabilities. The numerical results of the wavepacket analysis compare well with the available experimental data, confirming the importance of convective instability for this problem.The numerical results on the position of a dominant saddle point obtained by using the exact collision criterion are also compared to the results based on a steepest-descent method coupled with a continuation procedure for tracking convective instability that until now was considered as reliable. While for two-dimensional instabilities a numerical implementation of the collision criterion is readily available, the only existing numerical procedure for studying three-dimensional wavepackets is based on the tracking technique. For the present flow, the comparison shows a failure of the tracking treatment to recover a subinterval of the interval of unstable ray velocities V whose length constitutes 29% of the length of the entire unstable interval of V. The failure occurs due to a bifurcation of the saddle point, where V is a bifurcation parameter. We argue that this bifurcation of unstable ray velocities should be observable in experiments because of the abrupt increase by a factor of about 5.3 of the wavelength across the wavepacket associated with the appearance of the bifurcating branch. Further implications for experiments including the effect on spatial amplification rate are also discussed.

Numerical Simulation of Nonlinear Water Wave Propagation Over Rippled Bed

2007 ◽  
Author(s):  
Gerasimos A. Kolokythas ◽  
Athanassios A. Dimas
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Water Waves ◽  
Stokes Equations ◽  
Surface Flow ◽  
Surface Boundary ◽  
Computational Domain ◽  
Time Step ◽  
Outflow Boundary ◽  
Rippled Bed

In the present study, numerical simulations of the free-surface flow, developing by the propagation of nonlinear water waves over a rippled bottom, are performed assuming that the corresponding flow is two-dimensional, incompressible and viscous. The simulations are based on the numerical solution of the Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and the suitable bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. For the spatial discretization, a hybrid scheme with finite-differences and Chebyshev polynomials is applied, while a fractional time-step scheme is used for the temporal discretization. A wave absorption zone is placed at the outflow region in order to efficiently minimize reflection of waves by the outflow boundary. The numerical model is validated by comparison to the analytical solution for the laminar, oscillatory, current flow which develops a uniform boundary layer over a horizontal bottom. For the propagation of finite-amplitude waves over a rigid rippled bed, the case with wavelength to water depth ratio λ/d0 = 6 and wave height to wavelength ratio H0/λ = 0.05 is considered. The ripples have parabolic shape, while their dimensions — length and height — are chosen accordingly to fit laboratory and field data. Results indicate that the wall shear stress over the ripples and the form drag forces on the ripples increase with increasing ripple height, while the corresponding friction force is insensitive to this increase. Therefore, the percentage of friction in the total drag force decreases with increasing ripple height.

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.

scholarly journals Numerical Study of Violent Impact Flow Using a CIP-Based Model

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Qiao-ling Ji ◽  
Xi-zeng Zhao ◽  
Sheng Dong
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Large Scale ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Small Scale ◽  
Surface Boundary ◽  
Two Phase ◽  
Constrained Interpolation

A two-phase flow model is developed to study violent impact flow problem. The model governed by the Navier-Stokes equations with free surface boundary conditions is solved by a Constrained Interpolation Profile (CIP)-based high-order finite difference method on a fixed Cartesian grid system. The free surface is immersed in the computation domain and expressed by a one-fluid density function. An accurate Volume of Fluid (VOF)-type scheme, the Tangent of Hyperbola for Interface Capturing (THINC), is combined for the free surface treatment. Results of another two free surface capturing methods, the original VOF and CIP, are also presented for comparison. The validity and utility of the numerical model are demonstrated by applying it to two dam-break problems: a small-scale two-dimensional (2D) and three-dimensional (3D) full scale simulations and a large-scale 2D simulation. Main attention is paid to the water elevations and impact pressure, and the numerical results show relatively good agreement with available experimental measurements. It is shown that the present numerical model can give a satisfactory prediction for violent impact flow.

A Comparative Study of Wave Breaking Models in a High-Order Spectral Model

2017 ◽  
Author(s):  
Betsy R. Seiffert ◽  
Guillaume Ducrozet
Keyword(s):  
Free Surface ◽  
Energy Dissipation ◽  
Boundary Conditions ◽  
Wave Breaking ◽  
Water Surface ◽  
Eddy Viscosity ◽  
Breaking Waves ◽  
Surface Boundary ◽  
Diffusion Term ◽  
Surface Boundary Conditions

We examine the implementation of two different wave breaking models into the nonlinear potential flow solver HOS-NWT. HOS-NWT is a computationally efficient, open source code that solves for surface elevation in a numerical wave tank using the High-Order Spectral (HOS) method [1]. The first model is a combination of a kinematic wave breaking onset criteria proposed by Barthelemey, et al. [2] and validated by Saket, et al. [3], and an energy dissipation mechanism proposed by Tian, et al. [4, 5]. The wave breaking onset parameter is based on the ratio of local energy flux velocity to the local crest velocity. Once breaking is initiated, an eddy viscosity parameter is estimated based on the pre-breaking local wave geometry, as described in [4, 5]. This eddy viscosity is then added as a diffusion term to the kinematic and dynamic free surface boundary conditions for the duration of wave breaking. Results implementing this wave breaking mechanism in HOS-NWT have shown that the model can successfully calculate the surface elevation and corresponding frequency spectra, as well as the energy dissipation associated with breaking waves [6–8]. The second model implemented to account for wave breaking in HOS-NWT is based on the method proposed by Chalikov, et al. [9–11]. This model defines wave breaking onset by the curvature of the water surface and defines the wave as broken if it exceeds a certain value. A diffusion term is added to the kinematic and dynamic free surface boundary conditions which dissipates energy based on the local curvature of the water surface, which is consequently not constant in space nor time. Calculations made using the two models are compared with large scale experimental measurements conducted at the Hydrodynamics, Energetics and Atmospheric Environment Lab (LHEEA) at Ecole Centrale de Nantes. Comparison of calculations with measurements suggest that both models are successful at predicting wave breaking onset and energy dissipation. However, the model proposed by Barthelemy, et al. [2] and Tian, et al. [4] can be applied without knowing anything about the breaking waves a priori, whereas the model proposed by Chalikov [9] requires tuning to specific conditions.

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.

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