118 research outputs found
Run-up characterstics of symmetrical solitary tsunami waves of unknown shapes
The problem of tsunami wave run-up on a beach is discussed in the framework
of the rigorous solutions of the nonlinear shallow-water theory. We present an
analysis of the run-up characteristics for various shapes of the incoming
symmetrical solitary tsunami waves. It will be demonstrated that the extreme
(maximal) wave characteristics on a beach (run-up and draw-down heights, run-up
and draw-down velocities and breaking parameter) are weakly dependent on the
shape of incident wave if the definition of the significant wave length
determined on the 2/3 level of the maximum height is used. The universal
analytical expressions for the extreme wave characteristics are derived for the
run-up of the solitary pulses. They can be directly applicable for tsunami
warning because in many case the shape of the incident tsunami wave is unknown.Comment: Submitted to PAGEOP
Numerical simulation of a solitonic gas in KdV and KdV-BBM equations
19 pages, 11 figures, 47 references. Other author's papers can be found at http://www.denys-dutykh.com/The collective behaviour of soliton ensembles (i.e. the solitonic gas) is studied using the methods of the direct numerical simulation. Traditionally this problem was addressed in the context of integrable models such as the celebrated KdV equation. We extend this analysis to non-integrable KdV-BBM type models. Some high resolution numerical results are presented in both integrable and nonintegrable cases. Moreover, the free surface elevation probability distribution is shown to be quasi-stationary. Finally, we employ the asymptotic methods along with the Monte-Carlo simulations in order to study quantitatively the dependence of some important statistical characteristics (such as the kurtosis and skewness) on the Stokes-Ursell number (which measures the relative importance of nonlinear effects compared to the dispersion) and also on the magnitude of the BBM term
Physical Mechanisms of the Rogue Wave Phenomenon
A review of physical mechanisms of the rogue wave phenomenon is given. The data of marine observations as well as laboratory experiments are briefly discussed. They demonstrate that freak waves may appear in deep and shallow waters. Simple statistical analysis of the rogue wave probability based on the assumption of a Gaussian wave field is reproduced. In the context of water wave theories the probabilistic approach shows that numerical simulations of freak waves should be made for very long times on large spatial domains and large number of realizations. As linear models of freak waves the following mechanisms are considered: dispersion enhancement of transient wave groups, geometrical focusing in basins of variable depth, and wave-current interaction. Taking into account nonlinearity of the water waves, these mechanisms remain valid but should be modified. Also, the influence of the nonlinear modulational instability (Benjamin-Feir instability) on the rogue wave occurence is discussed. Specific numerical simulations were performed in the framework of classical nonlinear evolution equations: the nonlinear Schrodinger equation, the Davey - Stewartson system, the Korteweg - de Vries equation, the Kadomtsev - Petviashvili equation, the Zakharov equation, and the fully nonlinear potential equations. Their results show the main features of the physical mechanisms of rogue wave phenomenon
Solitary wave interactions with a periodic forcing: the extended Korteweg-de Vries framework
The aim of this work is to study numerically the interaction of large
amplitude solitary waves with an external periodic forcing using the forced
extended Korteweg-de Vries equation (feKdV). Regarding these interactions, we
find that a solitary wave can bounce back and forth remaining close to its
initial position when the forcing and the solitary wave are near resonant or it
can move away from its initial position without reversing their direction.
Additionally, we verify that the numerical results agree well within the
asymptotic approximation for broad the forcings
Soliton interactions with an external forcing: the modified Korteweg-de Vries framework
The aim of this work is to study asymptotically and numerically the
interaction of solitons with an external forcing with variable speed using the
forced modified Korteweg-de Vries equation (mKdV). We show that the asymptotic
predictions agree well with numerical solutions for forcing with constant speed
and linear variable speed. Regarding forcing with linear variable speed, we
find regimes in which the solitons are trapped at the external forcing and its
amplitude increases or decreases in time depending on whether the forcing
accelerates or decelerates
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