Nonlinear interactions between deep-water waves and currents

2011 ◽  
Vol 691 ◽  
pp. 1-25 ◽  
Author(s):  
R. M. Moreira ◽  
D. H. Peregrine
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Surface Velocity ◽  
Fully Nonlinear ◽  
Individual Wave ◽  
Waves And Currents ◽  
Wave Blocking ◽  
The Individual

AbstractThe effects of nonlinearity on a train of linear water waves in deep water interacting with underlying currents are investigated numerically via a boundary-integral method. The current is assumed to be two-dimensional and stationary, being induced by a distribution of singularities located beneath the free surface, which impose sharp and gentle surface velocity gradients. For ‘slowly’ varying currents, the fully nonlinear results confirm that opposing currents induce wave steepening and breaking within the region where a high convergence of rays occurs. For ‘rapidly’ varying currents, wave blocking and breaking are more prominent. In this case reflection was observed when sufficiently strong adverse currents are imposed, confirming that at least part of the wave energy that builds up within the caustic can be released in the form of partial reflection and wave breaking. For bichromatic waves, the fully nonlinear results show that partial wave blocking occurs at the individual wave components in the wave groups and that waves become almost monochromatic upstream of the blocking region.

Vorticity effects on nonlinear wave–current interactions in deep water

2015 ◽  
Vol 778 ◽  
pp. 314-334 ◽  
Author(s):  
R. M. Moreira ◽  
J. T. A. Chacaltana
Keyword(s):  
Shear Flow ◽  
Nonlinear Wave ◽  
Deep Water ◽  
Water Waves ◽  
Wave Breaking ◽  
Surface Profile ◽  
Boundary Integral ◽  
Progressive Waves ◽  
Wave Blocking ◽  
Deep Water Waves

The effects of uniform vorticity on a train of ‘gentle’ and ‘steep’ deep-water waves interacting with underlying flows are investigated through a fully nonlinear boundary integral method. It is shown that wave blocking and breaking can be more prominent depending on the magnitude and direction of the shear flow. Reflection continues to occur when sufficiently strong adverse currents are imposed on ‘gentle’ deep-water waves, though now affected by vorticity. For increasingly positive values of vorticity, the induced shear flow reduces the speed of right-going progressive waves, introducing significant changes to the free-surface profile until waves are completely blocked by the underlying current. A plunging breaker is formed at the blocking point when ‘steep’ deep-water waves interact with strong adverse currents. Conversely negative vorticities augment the speed of right-going progressive waves, with wave breaking being detected for strong opposing currents. The time of breaking is sensitive to the vorticity’s sign and magnitude, with wave breaking occurring later for negative values of vorticity. Stopping velocities according to nonlinear wave theory proved to be sufficient to cause wave blocking and breaking.

Fully nonlinear solution of bi-chromatic deep-water waves

2014 ◽  
Vol 91 ◽  
pp. 290-299 ◽  
Author(s):  
Zhiliang Lin ◽  
Longbin Tao ◽  
Yongchang Pu ◽  
Alan J. Murphy
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Fully Nonlinear ◽  
Nonlinear Solution ◽  
Deep Water Waves

Numerical Simulations of Large Deep Water Waves: The Application of a Boundary Element Method

2006 ◽  
Author(s):  
Caroline H. Hague ◽  
Chris Swan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Deep Water ◽  
Water Waves ◽  
Physical Space ◽  
Wave Model ◽  
Three Dimensions ◽  
Fully Nonlinear ◽  
Highly Nonlinear ◽  
Element Method

This paper concerns the description of extreme surface water waves in deep water. A fully nonlinear numerical wave model in three dimensions is presented, based on the Boundary Element Method (BEM), and is applied to nonlinear focusing of wave components with varying frequency and direction of propagation to form highly nonlinear groups. By using multiple fluxes at corners and edges of the numerical domain the “corner problem” associated with BEM-based models in physical space is overcome. A two-dimensional version of the method is also employed to model unidirectional cases, and examples presented include the focusing of Top Hat spectra in deep water to form highly nonlinear wave groups at or close to their breaking limit. The ability of the model to accurately simulate these sea states is highlighted by comparison to the fully nonlinear model of Bateman, Swan and Taylor (2001, 2003).

scholarly journals Convergence of a Boundary Integral Method for Water Waves

1996 ◽  
Vol 33 (5) ◽  
pp. 1797-1843 ◽  
Author(s):  
J. Thomas Beale ◽  
Thomas Y. Hou ◽  
John Lowengrub
Keyword(s):  
Water Waves ◽  
Integral Method ◽  
Boundary Integral ◽  
Boundary Integral Method

Highly nonlinear standing water waves with small capillary effect

1998 ◽  
Vol 369 ◽  
pp. 253-272 ◽  
Author(s):  
WILLIAM W. SCHULTZ ◽  
JEAN-MARC VANDEN-BROECK ◽  
LEI JIANG ◽  
MARC PERLIN
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Standing Waves ◽  
High Amplitude ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Ripple Formation ◽  
Node Distribution ◽  
Highly Nonlinear ◽  
Periodic Standing Waves

We calculate spatially and temporally periodic standing waves using a spectral boundary integral method combined with Newton iteration. When surface tension is neglected, the non-monotonic behaviour of global wave properties agrees with previous computations by Mercer & Roberts (1992). New accurate results near the limiting form of gravity waves are obtained by using a non-uniform node distribution. It is shown that the crest angle is smaller than 90° at the largest calculated crest curvature. When a small amount of surface tension is included, the crest form is changed significantly. It is necessary to include surface tension to numerically reproduce the steep standing waves in Taylor's (1953) experiments. Faraday-wave experiments in a large-aspect-ratio rectangular container agree with our computations. This is the first time such high-amplitude, periodic waves appear to have been observed in laboratory conditions. Ripple formation and temporal symmetry breaking in the experiments are discussed.

A comparison of numerical predictions and experimental measurements of the internal kinematics of a deep-water plunging wave

1996 ◽  
Vol 315 ◽  
pp. 51-64 ◽  
Author(s):  
David Skyner
Keyword(s):  
Numerical Model ◽  
Deep Water ◽  
Numerical Data ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Wave Crest ◽  
Breaking Wave ◽  
Small Shift ◽  
Wave Flume ◽  
Numerical Predictions

A deep-water long-crested breaking wave is generated from a time-stepping numerical model, then replicated in a wave flume. The numerical model is based on the boundary integral method and measurements of the internal kinematics are made during the breaking process with Particle Image Velocimetry (PIV). Velocity measurements are obtained throughout the wave crest, including the plunging spout. After a small shift of the numerical data to match the surface profiles, the predicted and measured kinematics are found to be in good agreement, within the limits of experimental error.

scholarly journals Singularities in the complex physical plane for deep water waves

2011 ◽  
Vol 685 ◽  
pp. 83-116 ◽  
Author(s):  
Gregory R. Baker ◽  
Chao Xie
Keyword(s):  
Standing Wave ◽  
Real Axis ◽  
Deep Water ◽  
Finite Time ◽  
Water Waves ◽  
Boundary Integral ◽  
Stokes Wave ◽  
Breaking Wave ◽  
The Real ◽  
Deep Water Waves

AbstractDeep water waves in two-dimensional flow can have curvature singularities on the surface profile; for example, the limiting Stokes wave has a corner of $2\lrm{\pi} / 3$ radians and the limiting standing wave momentarily forms a corner of $\lrm{\pi} / 2$ radians. Much less is known about the possible formation of curvature singularities in general. A novel way of exploring this possibility is to consider the curvature as a complex function of the complex arclength variable and to seek the existence and nature of any singularities in the complex arclength plane. Highly accurate boundary integral methods produce a Fourier spectrum of the curvature that allows the identification of the nearest singularity to the real axis of the complex arclength plane. This singularity is in general a pole singularity that moves about the complex arclength plane. It approaches the real axis very closely when waves break and is associated with the high curvature at the tip of the breaking wave. The behaviour of these singularities is more complex for standing waves, where two singularities can be identified that may collide and separate. One of them approaches the real axis very closely when a standing wave forms a very narrow collapsing column of water almost under free fall. In studies so far, no singularity reaches the real axis in finite time. On the other hand, the surface elevation $y(x)$ has square-root singularities in the complex $x$ plane that do reach the real axis in finite time, the moment when a wave first starts to break. These singularities have a profound effect on the wave spectra.

Geometric Modeling for Fully Nonlinear Ship-Wave Interactions

1997 ◽  
Vol 41 (01) ◽  
pp. 17-25
Author(s):  
M.S. Celebi ◽  
R.F. Beck
Keyword(s):  
Body Surface ◽  
Geometric Modeling ◽  
Mixed Boundary ◽  
Boundary Integral ◽  
The Body ◽  
Boundary Integral Method ◽  
Lagrange Equations ◽  
Time Step ◽  
Fully Nonlinear ◽  
Node Placement

Using the desingularized boundary integral method to solve transient nonlinear water-wave problems requires the solution of a mixed boundary value problem at each time step. The problem is solved at nodes (or collocation points) distributed on an ever-changing body surface. In this paper, a dynamic node allocation technique is developed to distribute efficiently nodes on the body surface. A B-spline surface representation is employed to generate an arbitrary ship hull form in parametric space. A variational adaptive curve grid generation method is then applied on the hull station curves to generate effective node placement. The numerical algorithm uses a conservative form of the parametric variational Euler-Lagrange equations to perform adaptive gridding on each station. Numerical examples of node placement on typical hull cross sections and for fully nonlinear wave resistance computations are presented.

Sign in / Sign up

Export Citation Format

Share Document