286 research outputs found
A nonlinear Schr\"odinger equation for water waves on finite depth with constant vorticity
A nonlinear Schr\"odinger equation for the envelope of two dimensional
surface water waves on finite depth with non zero constant vorticity is
derived, and the influence of this constant vorticity on the well known
stability properties of weakly nonlinear wave packets is studied. It is
demonstrated that vorticity modifies significantly the modulational instability
properties of weakly nonlinear plane waves, namely the growth rate and
bandwidth. At third order we have shown the importance of the coupling between
the mean flow induced by the modulation and the vorticity. Furthermore, it is
shown that these plane wave solutions may be linearly stable to modulational
instability for an opposite shear current independently of the dimensionless
parameter kh, where k and h are the carrier wavenumber and depth respectively
Head-on collision of two solitary waves and residual falling jet formation
The head-on collision of two equal and two unequal steep solitary waves is investigated numerically. The former case is equivalent to the reflection of one solitary wave by a vertical wall when viscosity is neglected. We have performed a series of numerical simulations based on a Boundary Integral Equation Method (BIEM) on finite depth to investigate during the collision the maximum runup, phase shift, wall residence time and acceleration field for arbitrary values of the non-linearity parameter a/h, where a is the amplitude of initial solitary waves and h the constant water depth. The initial solitary waves are calculated numerically from the fully nonlinear equations. The present work extends previous results on the runup and wall residence time calculation to the collision of very steep counter propagating solitary waves. Furthermore, a new phenomenon corresponding to the occurrence of a residual jet is found for wave amplitudes larger than a threshold value
Experiments on wind-perturbed rogue wave hydrodynamics using the Peregrine breather model
International audienceBeing considered as a prototype for description of oceanic rogue waves (RWs), the Peregrine breather solution of the nonlinear Schrodinger equation (NLS) has been recently observed and intensely investigated experimentally in particular within the context of water waves. Here, we report the experimental results showing the evolution of the Peregrine solution in the presence of wind forcing in the direction of wave propagation. The results show the persistence of the breather evolution dynamics even in the presence of strong wind and chaotic wave eld generated by it. Furthermore, we have shown that characteristic spectrum of the Peregrine breather persists even at the highest values of the generated wind velocities thus making it a viable characteristic for prediction of rogue waves
Shallow water waves generated by subaerial solid landslides
Subaerial landslides are common events, which may generate very large water waves. The numerical modelling and simulation of these events are thus of primary interest for forecasting and mitigation of tsunami disasters. In this paper, we aim at describing these extreme events using a simplified shallow water model to derive relevant scaling laws. To cope with the problem, two different numerical codes are employed: one, SPHysics, is based on a Lagrangian meshless approach to accurately describe the impact stage whereas the other, Gerris, based on a two-phase finite-volume method is used to study the propagation of the wave. To validate Gerris for this very particular problem, two numerical cases of the literature are reproduced: a vertical sinking box and a 2-D wedge sliding down a slope. Then, to get insights into the problem of subaerial landslide-generated tsunamis and to further validate the codes for this case of landslides, a series of experiments is conducted in a water wave tank and successfully compared with the results of both codes. Based on a simplified approach, we derive different scaling laws in excellent agreement with the experiments and numerical simulation
Soliton spectra of random water waves in shallow basins
Interpretation of random wave field on a shallow water in terms of Fourier
spectra is not adequate, when wave amplitudes are not infinitesimally small. A
nonlinearity of wave fields leads to the harmonic interactions and random
variation of Fourier spectra. As has been shown by Osborne and his co-authors,
a more adequate analysis can be performed in terms of nonlinear modes
representing cnoidal waves; a spectrum of such modes remains unchanged even in
the process of nonlinear mode interactions. Here we show that there is an
alternative and more simple analysis of random wave fields on shallow water,
which can be presented in terms of interacting Korteweg - de Vries solitons.
The data processing of random wave field is developed on the basis of inverse
scattering method. The soliton component obscured in a random wave field is
determined and a corresponding distribution function of number of solitons on
their amplitudes is constructed. The approach developed is illustrated by means
of artificially generated quasi-random wave field and applied to the real data
interpretation of wind waves generated in the laboratory wind tank.Comment: 23 pages, 15 figure
Transverse instability of gravity–capillary solitary waves on deep water in the presence of constant vorticity
International audienc
A nonlinear Schr\"odinger equation for gravity-capillary water waves on arbitrary depth with constant vorticity: Part I
A nonlinear Schr\"odinger equation for the envelope of two-dimensional
gravity-capillary waves propagating at the free surface of a vertically sheared
current of constant vorticity is derived. In this paper we extend to
gravity-capillary wave trains the results of \citet{thomas2012pof} and complete
the stability analysis and stability diagram of \citet{Djordjevic1977} in the
presence of vorticity. Vorticity effect on the modulational instability of
weakly nonlinear gravity-capillary wave packets is investigated. It is shown
that the vorticity modifies significantly the modulational instability of
gravity-capillary wave trains, namely the growth rate and instability
bandwidth. It is found that the rate of growth of modulational instability of
short gravity waves influenced by surface tension behaves like pure gravity
waves: (i) in infinite depth, the growth rate is reduced in the presence of
positive vorticity and amplified in the presence of negative vorticity, (ii) in
finite depth, it is reduced when the vorticity is positive and amplified and
finally reduced when the vorticity is negative. The combined effect of
vorticity and surface tension is to increase the rate of growth of modulational
instability of short gravity waves influenced by surface tension, namely when
the vorticity is negative. The rate of growth of modulational instability of
capillary waves is amplified by negative vorticity and attenuated by positive
vorticity. Stability diagrams are plotted and it is shown that they are
significantly modified by the introduction of the vorticity
Transverse instability of gravity–capillary solitary waves on deep water in the presence of constant vorticity
International audienc
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