5,321 research outputs found
Simulations and experiments of short intense envelope solitons of surface water waves
The problem of existence of stable nonlinear groups of gravity waves in deep
water is revised by means of laboratory and numerical simulations with the
focus on intense waves. Wave groups with steepness up to are reproduced in laboratory experiments ( is the wave
crest amplitude, is the mean angular frequency and is the
gravity acceleration). We show that the groups remain stable and exhibit
neither noticeable radiation nor structural transformation for more than 60
wave lengths or about 15-30 group lengths. These solitary wave patterns differ
from the conventional envelope solitons, as only a few individual waves are
contained in the group. Very good agreement is obtained between the laboratory
results and strongly nonlinear numerical simulations of the potential Euler
equations. The envelope soliton solution of the nonlinear Schr\"odinger
equation is shown to be a reasonable first approximation for specifying the
wavemaker driving signal. The short intense envelope solitons possess vertical
asymmetry similar to regular Stokes waves with the same frequency and crest
amplitude. Nonlinearity is found to have remarkably stronger effect on the
speed of envelope solitons in comparison to the nonlinear correction to the
Stokes wave velocity.Comment: Under review in Physics of Fluid
Wave mitigation in ordered networks of granular chains
We study the propagation of stress waves through ordered 2D networks of
granular chains. The quasi-particle continuum theory employed captures the
acoustic pulse splitting, bending, and recombination through the network and is
used to derive its effective acoustic properties. The strong wave mitigation
properties of the network predicted theoretically are confirmed through both
numerical simulations and experimental tests. In particular, the leading pulse
amplitude propagating through the system is shown to decay exponentially with
the propagation distance and the spatial structure of the transmitted wave
shows an exponential localization along the direction of the incident wave. The
length scales that characterized these exponential decays are studied and
determined as a function of the geometrical properties of the network. These
results open avenues for the design of efficient impact mitigating structures
and provide new insights into the mechanisms of wave propagation in granular
matter.Comment: submitted to Journal of the Mechanics and Physics of Solid
Numerical study on diverging probability density function of flat-top solitons in an extended Korteweg-de Vries equation
We consider an extended Korteweg-de Vries (eKdV) equation, the usual
Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity.
We investigate the statistical behaviour of flat-top solitary waves described
by an eKdV equation in the presence of weak dissipative disorder in the linear
growth/damping term. With the weak disorder in the system, the amplitude of
solitary wave randomly fluctuates during evolution. We demonstrate numerically
that the probability density function of a solitary wave parameter
which characterizes the soliton amplitude exhibits loglognormal divergence near
the maximum possible value.Comment: 8 pages, 4 figure
Coupled Ostrovsky equations for internal waves in a shear flow
In the context of fluid flows, the coupled Ostrovsky equations arise when two
distinct linear long wave modes have nearly coincident phase speeds in the
presence of background rotation. In this paper, nonlinear waves in a stratified
fluid in the presence of shear flow are investigated both analytically, using
techniques from asymptotic perturbation theory, and through numerical
simulations. The dispersion relation of the system, based on a three-layer
model of a stratified shear flow, reveals various dynamical behaviours,
including the existence of unsteady and steady envelope wave packets.Comment: 47 pages, 39 figures, accepted to Physics of Fluid
Remarks on nonlinear relation among phases and frequencies in modulational instabilities of parallel propagating Alfven waves
Nonlinear relations among frequencies and phases in modulational instability
of circularly polarized Alfven waves are discussed, within the context of one
dimensional, dissipation-less, unforced fluid system. We show that generation
of phase coherence is a natural consequence of the modulational instability of
Alfven waves. Furthermore, we quantitatively evaluate intensity of wave-wave
interaction by using bi-coherence, and also by computing energy flow among wave
modes, and demonstrate that the energy flow is directly related to the phase
coherence generation.Comment: 17 pages, Nonlinear Processes in Geophysics (published), the paper
with full resolution images is
http://www.copernicus.org/EGU/npg/13/npg-13-425.pd
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