82 research outputs found
Nonconservative higher-order hydrodynamic modulation instability
The modulation instability (MI) is a universal mechanism that is responsible
for the disintegration of weakly nonlinear narrow-banded wave fields and the
emergence of localized extreme events in dispersive media. The instability
dynamics is naturally triggered, when unstable energy side-bands located around
the main energy peak are excited and then follow an exponential growth law. As
a consequence of four wave mixing effect, these primary side-bands generate an
infinite number of additional side-bands, forming a triangular side-band
cascade. After saturation, it is expected that the system experiences a return
to initial conditions followed by a spectral recurrence dynamics. Much complex
nonlinear wave field motion is expected, when the secondary or successive
side-band pair that are created are also located in the finite instability gain
range around the main carrier frequency peak. This latter process is referred
to as higher-order MI. We report a numerical and experimental study that
confirm observation of higher-order MI dynamics in water waves. Furthermore, we
show that the presence of weak dissipation may counter-intuitively enhance wave
focusing in the second recurrent cycle of wave amplification. The
interdisciplinary weakly nonlinear approach in addressing the evolution of
unstable nonlinear waves dynamics may find significant resonance in other
nonlinear dispersive media in physics, such as optics, solids, superfluids and
plasma
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
Spectral up- and downshifting of Akhmediev breathers under wind forcing
We experimentally and numerically investigate the effect of wind forcing on
the spectral dynamics of Akhmediev breathers, a wave-type known to model the
modulation instability. We develop the wind model to the same order in
steepness as the higher order modifcation of the nonlinear Schroedinger
equation, also referred to as the Dysthe equation. This results in an
asymmetric wind term in the higher order, in addition to the leading order wind
forcing term. The derived model is in good agreement with laboratory
experiments within the range of the facility's length. We show that the leading
order forcing term amplifies all frequencies equally and therefore induces only
a broadening of the spectrum while the asymmetric higher order term in the
model enhances higher frequencies more than lower ones. Thus, the latter term
induces a permanent upshift of the spectral mean. On the other hand, in
contrast to the direct effect of wind forcing, wind can indirectly lead to
frequency downshifts, due to dissipative effects such as wave breaking, or
through amplification of the intrinsic spectral asymmetry of the Dysthe
equation. Furthermore, the definitions of the up- and downshift in terms of
peak- and mean frequencies, that are critical to relate our work to previous
results, are highlighted and discussed.Comment: 30 pages, 11 figure
Numerical instability of the Akhmediev breather and a finite-gap model of it
In this paper we study the numerical instabilities of the NLS Akhmediev
breather, the simplest space periodic, one-mode perturbation of the unstable
background, limiting our considerations to the simplest case of one unstable
mode. In agreement with recent theoretical findings of the authors, in the
situation in which the round-off errors are negligible with respect to the
perturbations due to the discrete scheme used in the numerical experiments, the
split-step Fourier method (SSFM), the numerical output is well-described by a
suitable genus 2 finite-gap solution of NLS. This solution can be written in
terms of different elementary functions in different time regions and,
ultimately, it shows an exact recurrence of rogue waves described, at each
appearance, by the Akhmediev breather. We discover a remarkable empirical
formula connecting the recurrence time with the number of time steps used in
the SSFM and, via our recent theoretical findings, we establish that the SSFM
opens up a vertical unstable gap whose length can be computed with high
accuracy, and is proportional to the inverse of the square of the number of
time steps used in the SSFM. This neat picture essentially changes when the
round-off error is sufficiently large. Indeed experiments in standard double
precision show serious instabilities in both the periods and phases of the
recurrence. In contrast with it, as predicted by the theory, replacing the
exact Akhmediev Cauchy datum by its first harmonic approximation, we only
slightly modify the numerical output. Let us also remark, that the first rogue
wave appearance is completely stable in all experiments and is in perfect
agreement with the Akhmediev formula and with the theoretical prediction in
terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv
admin note: text overlap with arXiv:1707.0565
A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)
Meeting abstrac
Effects of dexmedetomidine and esmolol on systemic hemodynamics and exogenous lactate clearance in early experimental septic shock
An experimental and numerical study of the resonant flow between a hull and a wall
International audienceThe wave-induced resonant flow in a narrow gap between a stationary hull and a vertical wall is studied experimentally and numerically. Vortex shedding from the sharp bilge edge of the hull gives rise to a quadratically damped free surface response in the gap, where the damping coefficient is approximately independent of wave steepness and frequency. Particle image velocimetry and direct numerical simulations were used to characterise the shedding dynamics and explore the influence of discretisation in the measurements and computations. Secondary separation was identified as a particular feature which occurred at the hull bilge in these gap flows. This can result in the generation of a system with multiple vortical regions and asymmetries between the inflow and outflow. The shedding dynamics was found to exhibit a high degree of invariance to the amplitude in the gap and the spanwise position of the barge. The new measurements and the evaluation of numerical models of varying fidelity can assist in informing offshore operations such as the side by side offloading from floating liquefied natural gas facilities
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Tsunami generated by a granular collapse down a rough inclined plane
In this Letter, we experimentally investigate the collapse of initially dry
granular media into water and the subsequent impulse waves. We systematically
characterize the influence of the slope angle and the granular material on the
initial amplitude of the generated leading wave and the evolution of its
amplitude during the propagation. The experiments show that whereas the
evolution of the leading wave during the propagation is well predicted by a
solution of the linearized Korteweg-de Vries equation, the generation of the
wave is more complicated to describe. Our results suggest that the internal
properties of the granular media and the interplay with the surrounding fluid
are important parameters for the generation of waves at low velocity impacts.
Moreover, the amplitude of the leading wave reaches a maximum value at large
slope angle. The runout distance of the collapse is also shown to be smaller in
the presence of water than under totally dry conditions. This study provides a
first insight into tsunamis generated by subaerial landslides at low Froude
number
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