Late Stages in the Development of Modulation Instability of Waves

2018 ◽  
Author(s):  
Igor Shugan ◽  
Sergey Kuznetsov ◽  
Yana Saprykina ◽  
Yang-Yih Chen
Keyword(s):  
Numerical Simulations ◽  
Wave Breaking ◽  
Spectral Width ◽  
Near Neighbor ◽  
Spectral Maximum ◽  
Resonance Model ◽  
Discrete Energy ◽  
Narrow Side ◽  
Steep Waves ◽  
Late Stages

We conducted experimental and theoretical studies on Benjamin-Feir (BF) instability and revealed a number of new features of the development of instability on the late stages of wave’s evolution. We employ the reduced (truncated) version of Zakharov equations — the multi-wave near-neighbor resonance model (NN model), which takes into account the most effective quasi-resonances with minimum detuning from exact resonance conditions. We show that near-neighbor model for wave interactions can adequately describe the number of new prominent features of BF instability observed in experiments and it is much simpler than Zakharov equation for computation and analysis. Numerical simulations of the full Zakharov equations confirm the main predictions obtained by the NN modeling and both reasonably correspond to the results of available physical experiments. Strong permanent downshifting of spectral maximum for gentle waves without wave breaking is revealed for twice as narrow side band spectral width in comparison with the most unstable case. Regime of multiple downshifting accompanied by wave breaking is discovered for steep waves. Discrete energy flow to higher spectral components takes a place in breaking and no breaking regimes. Results of numerical simulations of Zakharov and NN models reasonably correspond to each other and to our experimental and field observations on wave modulation.

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.

Numerical Simulations of Ship Bow and Shoulder Wave Breaking in Different Advancing Speeds

2018 ◽  
Author(s):  
Zhen Ren ◽  
Jianhua Wang ◽  
Decheng Wan
Keyword(s):  
Free Surface ◽  
Numerical Simulations ◽  
Wave Breaking ◽  
Wave Pattern ◽  
Breaking Wave ◽  
Wake Field ◽  
Bow Wave ◽  
Calm Water ◽  
Wave Phenomena ◽  
Good Agreement

The KCS model is employed for the numerical simulations to investigate the wave breaking phenomena of the bow and shoulder wave. RANS approach coupled with high resolution VOF technique is used to resolve the free surface. In order to study the speed effects on the phenomena of ship wave breaking, four different speeds, i.e. Fr = 0.26, 0.30, 0.32, 0.35, are investigated in calm water. Predicted resistance and wave patterns under Fr = 0.26 are validated with the available experiment data, and good agreement is achieved. For the Fr = 0.26 case, the wave pattern is steady, and the alternate variation of vorticity appear near the free surface is associated with the wake field. The breaking wave phenomena can be observed when the Froude number is over 0.32 and the Fr = 0.35 case shows most violent breaking bow wave. For the Fr = 0.35 case, the process of overturning and breaking of bow wave is observed clearly, and at the tail of bow wave, some breaking features of free surface are also captured. The reconnection of the initial plunger with the free surface results in a pair of counter-rotating vortex that is responsible for the second plunger and scar.

Stability of electron inertia Alfvén solitons

1992 ◽  
Vol 48 (2) ◽  
pp. 335-343 ◽  
Author(s):  
P. Frycz ◽  
R. Rankin ◽  
J. C. Samson
Keyword(s):  
Magnetic Field ◽  
Numerical Simulations ◽  
Final Stage ◽  
Wave Breaking ◽  
Characteristic Length ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Dimensional Electron ◽  
Electron Inertia ◽  
Nonlinear Phase

Das, Kamp and Sluijter have proposed equations describing three-dimensional electron inertia Alfvén waves for which the characteristic length scales in directions parallel and perpendicular to the ambient magnetic field are of the same order. Planar, obliquely propagating soliton solutions of these equations are known to be linearly unstable. Numerical simulations reveal the nonlinear phase of the evolution of these solitons: a transition from flat to cylindrical solitons is observed, followed by breaking-up into three-dimensional localized cavities. The final stage corresponds to wave breaking; no final stable structure is achieved within the model.

scholarly journals Modelling of tsunami wave run-up, breaking and impact on vertical wall by SPH method

2013 ◽  
Vol 1 (3) ◽  
pp. 2831-2857
Author(s):  
M. H. Dao ◽  
H. Xu ◽  
E. S. Chan ◽  
P. Tkalich
Keyword(s):  
Wave Breaking ◽  
Vertical Wall ◽  
Sph Method ◽  
Particle Hydrodynamics ◽  
Potential Applications ◽  
Sph Model ◽  
Smoothed Particle ◽  
Run Up ◽  
Steep Waves ◽  
Tunami N2

Abstract. Accurate predictions of wave run-up and run-down are important for coastal impact assessment of relatively long waves such as tsunami or storm waves. Wave run-up is, however, a complex process involving nonlinear build-up of the wave front, intensive wave breaking and strong turbulent flow, making the numerical approximation challenging. Recent advanced modeling methodologies could help to overcome these numerical challenges. For a demonstration, we study run-up of non-breaking and breaking solitary waves on vertical wall using two methods, the enhanced Smoothed Particle Hydrodynamics (SPH) method and the traditional non-breaking nonlinear model Tunami-N2. The Tunami-N2 model fails to capture the evolution of steep waves at the proximity of breaking that observed in the experiments. Whereas, the SPH method successfully simulate the wave propagation, breaking, impact on structure and the reform and breaking processes of wave run-down. The study also indicates that inadequate approximation of the wave breaking could lead to significant under-predictions of wave height and impact pressure on structures. The SPH model shows potential applications for accurate impact assessments of wave run-up onto coastal structures.

scholarly journals On kinematics of very steep waves

2013 ◽  
Vol 13 (8) ◽  
pp. 2101-2107 ◽  
Author(s):  
L. Shemer
Keyword(s):  
Wave Breaking ◽  
Wide Spectrum ◽  
Wave Train ◽  
Vertical Acceleration ◽  
Wave Group ◽  
Third Order ◽  
Large Wave ◽  
The Third ◽  
Steep Waves ◽  
Group Velocities

Abstract. Experiments on extremely steep deterministic waves generated in a large wave tank by focusing of a broad-banded wave train serve as a motivation for the theoretical analysis of the conditions leading to wave breaking. Particular attention is given to the crest of the steepest wave where both the horizontal velocity and the vertical acceleration attain their maxima. Analysis is carried out up to the third order in wave steepness. The apparent, Eulerian and Lagrangian accelerations are computed for wave parameters observed in experiments. It is demonstrated that for a wave group with a wide spectrum, the crest propagation velocity differs significantly from both the phase and the group velocities of the peak wave. Conclusions are drawn regarding the applicability of various criteria for wave breaking.

scholarly journals The Characteristic Transient Response of a Pressurized Cantilever Pipe Subjected to Transverse Impact at Its Tip

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Feng Liu ◽  
Yuchao Yang ◽  
Yuelei Wu
Keyword(s):  
Internal Pressure ◽  
Numerical Simulations ◽  
Present Model ◽  
Bending Moment ◽  
Transverse Impact ◽  
Pure Bending ◽  
Softening Behavior ◽  
Critical Curvature ◽  
Plastic Hardening ◽  
Late Stages

This paper describes an experimental study on the pure bending mechanical behavior of a pressurized pipe and adoption of a measured moment-curvature relationship under different working conditions in numerical simulations for transient pipe-whip prediction. To describe the effects of pipe contents and internal pressure, the governing equations were derived based on large deformation theory. Bending moment and axial force were uncoupled in the constitutive equation, and an experiment-based relationship between moment and curvature was adopted. The numerical simulations show that the present model can simulate the mechanical processes of elasticity, plastic hardening, and softening behavior in the initial, middle, and late stages of whole response, respectively. In addition, it was shown that kinks may occur at several positions along an empty cantilever pipe due to the collapse of sections under intense dynamic loading. However, this behavior did not occur for the full pressurized pipe, indicating that the contents and internal pressure are able to effectively impede the partial flattening of the pipe section, improving its critical curvature and changing its plastic dynamic response behavior.

scholarly journals VALIDATION OF A BUOYANCY-MODIFIED TURBULENCE MODEL BY NUMERICAL SIMULATIONS OF BREAKING WAVES OVER A FIXED BAR

2018 ◽  
pp. 71
Author(s):  
Brecht Devolder ◽  
Peter Troch ◽  
Pieter Rauwoens
Keyword(s):  
Numerical Simulations ◽  
Wave Breaking ◽  
Surf Zone ◽  
Breaking Waves ◽  
Navier Stokes ◽  
Two Phase ◽  
Numerical Wave Flume ◽  
Wave Flume ◽  
Nearshore Sediment Transport ◽  
Run Up

The surf zone dynamics are governed by important processes such as turbulence generation , nearshore sediment transport , wave run-up and wave overtopping at a coastal structure. During field observations , it is very challenging to measure and quantify wave breaking turbulence . Complementary to experimental laboratory studies in a more controlled environment , numerical simulations are highly suitable to understand and quantify surf zone processes more accurately. In this study, wave propagation and wave breaking over a fixed barred beach profile is investigated using a two­ phase Navier-Stokes flow solver. We show that accurate predictions of the turbulent two-phase flow field require special attention regarding turbulence modelling. The numerical wave flume is implemented in the open­ source OpenFOAM library. The computed results (surface elevations , velocity profiles and turbulence levels) are compared against experimental measurements in a wave flume (van der A et al., 2017) .

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