scholarly journals On an eddy viscosity model for energetic deep-water surface gravity wave breaking

2021 ◽  
Vol 929 ◽  
Author(s):  
Anatoliy Khait ◽  
Zhihua Ma
Keyword(s):  
Gravity Wave ◽  
Deep Water ◽  
Wave Breaking ◽  
Eddy Viscosity ◽  
Flow Model ◽  
Numerical Solutions ◽  
Numerical Models ◽  
Modulational Instability ◽  
Amplitude Spectrum ◽  
Surface Elevation

We present an investigation of the fundamental physical processes involved in deep-water gravity wave breaking. Our motivation is to identify the underlying reason causing the deficiency of the eddy viscosity breaking model (EVBM) in predicting surface elevation for strongly nonlinear waves. Owing to the limitation of experimental methods in the provision of high-resolution flow information, we propose a numerical methodology by developing an EVBM enclosed standalone fully nonlinear quasi-potential (FNP) flow model and a coupled FNP plus Navier–Stokes flow model. The numerical models were firstly verified with a wave train subject to modulational instability, then used to simulate a series of broad-banded focusing wave trains under non-, moderate- and strong-breaking conditions. A systematic analysis was carried out to investigate the discrepancies of numerical solutions produced by the two models in surface elevation and other important physical properties. It is found that EVBM predicts accurately the energy dissipated by breaking and the amplitude spectrum of free waves in terms of magnitude, but fails to capture accurately breaking induced phase shifting. The shift of phase grows with breaking intensity and is especially strong for high-wavenumber components. This is identified as a cause of the upshift of the wave dispersion relation, which increases the frequencies of large-wavenumber components. Such a variation drives large-wavenumber components to propagate at nearly the same speed, which is significantly higher than the linear dispersion levels. This suppresses the instant dispersive spreading of harmonics after the focal point, prolonging the lifespan of focused waves and expanding their propagation space.

Generation and Propagation of Long-Crested Finite-Depth Surface Waves: Comparison Between the Corresponding Results From Numerical Models and a Wave Tank

2008 ◽  
Author(s):  
M. Hasanat Zaman ◽  
Wade Parsons ◽  
Okey Nwogu ◽  
Wooyoung Choi ◽  
R. Emile Baddour ◽  
...  
Keyword(s):  
Surface Waves ◽  
Numerical Solutions ◽  
Numerical Models ◽  
Finite Depth ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Surface Elevation ◽  
Ocean Engineering ◽  
Measured Time ◽  
Wave Maker

The evolution of long-crested surface waves subject to side-band perturbations is investigated with two different numerical models: a direct solver for the Euler equations using a non-orthogonal boundary-fitted curvilinear coordinate system and an FFT-accelerated boundary integral method. The numerical solutions are then validated with laboratory experiments performed in the NRC-IOT Ocean Engineering Basin with a segmented wave-maker operating in piston mode. The numerical models are forced by a point measurement of the free surface elevation at a wave probe close to the wave-maker and the numerical solutions are compared with the measured time-series of the surface elevation at a few wave probe locations downstream.

CFD Simulation of Nonlinear Deep-Water Wave Instabilities Involving Wave Breaking

2021 ◽  
Author(s):  
Yuzhu Li ◽  
David R. Fuhrman
Keyword(s):  
Deep Water ◽  
Wave Breaking ◽  
Water Wave ◽  
Modulational Instability ◽  
Class Ii ◽  
Class I ◽  
Initial Growth ◽  
Extreme Waves ◽  
Wave Instabilities ◽  
Deep Water Wave

Abstract Extreme waves at the sea surface can have severe impacts on marine structures. One of the theoretical mechanisms leading to extreme waves is the instability of deep-water wave trains subject to initially small perturbations, which then grow exponentially. The present study focuses on the two-dimensional Benjamin–Feir (or modulational) instability and the three-dimensional crescent (or horseshoe) waves, also known as Class I and Class II instabilities, respectively. Numerical studies on Class I and Class II wave instabilities to date have been limited to models founded on potential flow theory, thus they could only properly investigate the process from initial growth of the perturbations to the initial breaking point. The present study conducts numerical simulations to investigate the generation and development of wave instabilities involving the wave breaking process. A CFD model solving Reynolds-averaged Navier-Stokes (RANS) equations coupled with turbulence closure in terms of the anisotropic Reynolds stress model is applied. Wave form evolutions, Fourier amplitudes, and the turbulence beneath the broken waves are investigated.

Focusing deep-water surface gravity wave packets: wave breaking criterion in a simplified model

2019 ◽  
Vol 873 ◽  
pp. 238-259 ◽  
Author(s):  
Nick Pizzo ◽  
W. Kendall Melville
Keyword(s):  
Gravity Wave ◽  
Deep Water ◽  
Wave Breaking ◽  
Water Surface ◽  
Dynamic Properties ◽  
Wave Packets ◽  
Surface Gravity ◽  
Simplified Model ◽  
Surface Gravity Wave ◽  
Maximum Slope

Geometric, kinematic and dynamic properties of focusing deep-water surface gravity wave packets are examined in a simplified model with the intent of deriving a wave breaking threshold parameter. The model is based on the spatial modified nonlinear Schrödinger equation of Dysthe (Proc. R. Soc. Lond. A, vol. 369 (1736), 1979, pp. 105–114). The evolution of initially narrow-banded and weakly nonlinear chirped Gaussian wave packets are examined, by means of a trial function and a variational procedure, yielding analytic solutions describing the approximate evolution of the packet width, amplitude, asymmetry and phase during focusing. A model for the maximum free surface gradient, as a function of $\unicode[STIX]{x1D716}$ and $\unicode[STIX]{x1D6E5}$, for $\unicode[STIX]{x1D716}$ the linear prediction of the maximum slope at focusing and $\unicode[STIX]{x1D6E5}$ the non-dimensional packet bandwidth, is proposed and numerically examined, indicating a quasi-self-similarity of these focusing events. The equations of motion for the fully nonlinear potential flow equations are then integrated to further investigate these predictions. It is found that a model of this form can characterize the bulk partitioning of $\unicode[STIX]{x1D716}-\unicode[STIX]{x1D6E5}$ phase space, between non-breaking and breaking waves, serving as a breaking criterion. Application of this result to better understanding air–sea interaction processes is discussed.

scholarly journals Five-Wave Resonances in Deep Water Gravity Waves: Integrability, Numerical Simulations and Experiments

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 205
Author(s):  
Dan Lucas ◽  
Marc Perlin ◽  
Dian-Yong Liu ◽  
Shane Walsh ◽  
Rossen Ivanov ◽  
...  
Keyword(s):  
Normal Form ◽  
Numerical Simulations ◽  
Gravity Waves ◽  
Deep Water ◽  
Plane Waves ◽  
Surface Elevation ◽  
Wave Interactions ◽  
Frequency Space ◽  
Target Mode ◽  
The Hilbert Transform

In this work we consider the problem of finding the simplest arrangement of resonant deep-water gravity waves in one-dimensional propagation, from three perspectives: Theoretical, numerical and experimental. Theoretically this requires using a normal-form Hamiltonian that focuses on 5-wave resonances. The simplest arrangement is based on a triad of wavevectors K1+K2=K3 (satisfying specific ratios) along with their negatives, corresponding to a scenario of encountering wavepackets, amenable to experiments and numerical simulations. The normal-form equations for these encountering waves in resonance are shown to be non-integrable, but they admit an integrable reduction in a symmetric configuration. Numerical simulations of the governing equations in natural variables using pseudospectral methods require the inclusion of up to 6-wave interactions, which imposes a strong dealiasing cut-off in order to properly resolve the evolving waves. We study the resonance numerically by looking at a target mode in the base triad and showing that the energy transfer to this mode is more efficient when the system is close to satisfying the resonant conditions. We first look at encountering plane waves with base frequencies in the range 1.32–2.35 Hz and steepnesses below 0.1, and show that the time evolution of the target mode’s energy is dramatically changed at the resonance. We then look at a scenario that is closer to experiments: Encountering wavepackets in a 400-m long numerical tank, where the interaction time is reduced with respect to the plane-wave case but the resonance is still observed; by mimicking a probe measurement of surface elevation we obtain efficiencies of up to 10% in frequency space after including near-resonant contributions. Finally, we perform preliminary experiments of encountering wavepackets in a 35-m long tank, which seem to show that the resonance exists physically. The measured efficiencies via probe measurements of surface elevation are relatively small, indicating that a finer search is needed along with longer wave flumes with much larger amplitudes and lower frequency waves. A further analysis of phases generated from probe data via the analytic signal approach (using the Hilbert transform) shows a strong triad phase synchronisation at the resonance, thus providing independent experimental evidence of the resonance.

scholarly journals MULTI-SCALE INFRA-GRAVITY WAVE DYNAMICS - THE FRENCH BASQUE COAST

2020 ◽  
pp. 46
Author(s):  
Volker Roeber ◽  
J. Dylan Nestler ◽  
Jonas Pinault ◽  
Assaf Azouri ◽  
Florian Bellafont
Keyword(s):  
Water Level ◽  
Gravity Wave ◽  
Numerical Study ◽  
Numerical Models ◽  
Wave Direction ◽  
Wave Dynamics ◽  
Multi Scale ◽  
Offshore Wave ◽  
A Site ◽  
Basque Coast

Phase-resolving numerical models are a powerful tool to identify and analyze dominant wave processes along a site of interest. We have carried out a numerical study related to infra-gravity wave dynamics along the French Basque coast. The computed scenarios are representative for the swell conditions at the site of interest and include variations in offshore wave height, direction, and water level. Several statistical methods were employed that illustrate that the irregular bathymetry is a key component for the strong variations in sea-swell and IG-wave energy. The water level is demonstrated to substantially affect the IG-wave behavior, more than the wave direction. Swash oscillations in the IG-frequency band are greater than or equal to sea-swell swash oscillations at nearly all locations along the studied shoreline.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/ELZwJCokkX0

scholarly journals Dissociation and recombination in the electrolyte flow model

2021 ◽  
Vol 2090 (1) ◽  
pp. 012076
Author(s):  
A Shobukhov ◽  
H Koibuchi
Keyword(s):  
Flow Model ◽  
Numerical Solutions ◽  
Stable Equilibrium ◽  
Steady State Solution ◽  
System Of Equations ◽  
Constant Flow ◽  
Dimensional Model ◽  
Electrolyte Flow ◽  
One Dimensional ◽  
Dilute Aqueous Solution

Abstract We propose a one-dimensional model for the dilute aqueous solution of NaCl which is treated as an incompressible fluid placed in the external electric field. This model is based on the Poisson-Nernst-Planck system of equations, which also contains the constant flow velocity as a parameter and considers the dissociation and the recombination of ions. We study the steady-state solution analytically and prove that it is a stable equilibrium. Analyzing the numerical solutions, we demonstrate the importance of dissociation and recombination for the physical meaningfulness of the model.

scholarly journals Computational Fluid Dynamics Simulation of Deep-Water Wave Instabilities Involving Wave Breaking

2021 ◽  
Vol 144 (2) ◽  
Author(s):  
Yuzhu Li ◽  
David R. Fuhrman
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Deep Water ◽  
Wave Breaking ◽  
Water Wave ◽  
Class Ii ◽  
Dynamics Simulation ◽  
Class I ◽  
Wave Instabilities ◽  
Deep Water Wave

Abstract Instabilities of deep-water wave trains subject to initially small perturbations (which then grow exponentially) can lead to extreme waves in offshore regions. The present study focuses on the two-dimensional Benjamin–Feir (or modulational) instability and the three-dimensional crescent (or horseshoe) waves, also known as Class I and Class II instabilities, respectively. Numerical studies on Class I and Class II wave instabilities to date have been mostly limited to models founded on potential flow theory; thus, they could only properly investigate the process from initial growth of the perturbations to the initial breaking point. The present study conducts numerical simulations to investigate the generation and development of wave instabilities involving the wave breaking process. A computational fluid dynamics (CFD) model solving Reynolds-averaged Navier–Stokes (RANS) equations coupled with a turbulence closure model in terms of the Reynolds stress model is applied. Wave form evolutions, Fourier amplitudes, and the turbulence beneath the broken waves are investigated.

scholarly journals Steep unidirectional wave groups – fully nonlinear simulations vs. experiments

2015 ◽  
Vol 2 (4) ◽  
pp. 1159-1195 ◽  
Author(s):  
L. Shemer ◽  
B. K. Ee
Keyword(s):  
Wave Breaking ◽  
Surface Elevation ◽  
Computational Results ◽  
Local Surface ◽  
Qualitative Comparison ◽  
Wave Groups ◽  
Fully Nonlinear ◽  
Nonlinear Simulations ◽  
Velocity Of Propagation ◽  
Steep Waves

Abstract. A method was developed to carry out detailed qualitative comparison of fully nonlinear computations with the measurements of unidirectional wave groups. Computational results on evolving wave groups were compared with the available experiments. The local surface elevation variation, evolution of envelope shapes, the velocity of propagation of the steepest crests in the group and their relation to the height of the crests were obtained numerically and experimentally. Conditions corresponding to incipient wave breaking were investigated in greater detail. The results shed additional light on the limits of applicability of the computational results, as well as on mechanisms leading to the breaking of steep waves.

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