Can uneven bathymetry freeze water-wave breathers?

2020 ◽  
Author(s):  
Maura Brunetti ◽  
Alexis Gomel ◽  
Andrea Armaroli ◽  
Amin Chabchoub ◽  
Jérôme Kasparian
Keyword(s):  
Optical Fibers ◽  
Gravity Waves ◽  
Water Wave ◽  
Applied Mathematics ◽  
Wave Packets ◽  
Nonlinear Coefficient ◽  
Surface Gravity ◽  
Surface Gravity Wave ◽  
Wave Flume ◽  
The Impact

<p>The nonlinear Schrödinger equation is a robust model for describing the evolution of surface gravity wave-packets over arbitrary bathymetry. Both the dispersive and the nonlinear coefficients turn out to depend on the fluid depth [1,2]. Its variation along the propagation direction provides a new degree of freedom to tailor the wave-packet evolution, in analogy to what has been obtained in optical fibers with varying dispersion [3].</p><p>We investigate how the nonlinear stage of modulation instability can be frozen by varying the water bottom from intermediate to large depth giving rise to an increase of the magnitude of the nonlinear coefficient within the focusing regime. We consider the case of an abrupt bathymetry change at the maximal focusing point. With the help of a three-wave truncation, we provide analytical conditions on the occurrence of freezing. We present numerical simulations of the full model and the experimental confirmation in a water wave flume experiment. We show that the effects of high-order nonlinear terms and dissipation do not dominate the evolution, making the freezing quite a robust phenomenon.   </p><p>Our results help clarify how the breathing evolution of water wave-packets can be dynamically controlled and to understand the impact of bathymetry on extreme-wave lifetimes.</p><p>References</p><p>[1] H. Hasimoto, and Hiroaki Ono. "Nonlinear modulation of gravity waves." Journal of the Physical Society of Japan 33, 805-811 (1972)</p><p>[2] V. D. Djordjevic, and L. G. Redekopp, “On the development of packets of surface gravity waves moving over an uneven bottom” Journal of Applied Mathematics and Physics (ZAMP) 29, 950–962 (1978)</p><p>[3] A. Bendahmane et al., “Experimental dynamics of Akhmediev breathers in a dispersion varying optical fiber” Optics Letters 39, 4490-4493 (2014)</p><p> </p>

scholarly journals Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 96 ◽  
Author(s):  
Georgi Gary Rozenman ◽  
Shenhe Fu ◽  
Ady Arie ◽  
Lev Shemer
Keyword(s):  
Quantum Mechanics ◽  
Gravity Waves ◽  
Water Waves ◽  
Water Wave ◽  
Wave Packets ◽  
Theoretical Models ◽  
Surface Gravity ◽  
Finite Width ◽  
Self Healing ◽  
Surface Gravity Waves

We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.

Surfing surface gravity waves

2017 ◽  
Vol 823 ◽  
pp. 316-328 ◽  
Author(s):  
Nick E. Pizzo
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Water Wave ◽  
Phase Speed ◽  
Surface Gravity ◽  
Simple Criterion ◽  
Surface Gravity Wave ◽  
Surface Gravity Waves

A simple criterion for water particles to surf an underlying surface gravity wave is presented. It is found that particles travelling near the phase speed of the wave, in a geometrically confined region on the forward face of the crest, increase in speed. The criterion is derived using the equation of John (Commun. Pure Appl. Maths, vol. 6, 1953, pp. 497–503) for the motion of a zero-stress free surface under the action of gravity. As an example, a breaking water wave is theoretically and numerically examined. Implications for upper-ocean processes, for both shallow- and deep-water waves, are discussed.

scholarly journals VISIR-1.b: ocean surface gravity waves and currents for energy-efficient navigation

2019 ◽  
Vol 12 (8) ◽  
pp. 3449-3480 ◽  
Author(s):  
Gianandrea Mannarini ◽  
Lorenzo Carelli
Keyword(s):  
Energy Efficiency ◽  
Gravity Waves ◽  
Ocean Surface ◽  
Surface Gravity ◽  
Ocean Current ◽  
Ship Routing ◽  
Surface Gravity Waves ◽  
Waves And Currents ◽  
The Impact

Abstract. The latest development of the ship-routing model published in Mannarini et al. (2016a) is VISIR-1.b, which is presented here. The new version of the model targets large ocean-going vessels by considering both ocean surface gravity waves and currents. To effectively analyse currents in a graph-search method, new equations are derived and validated against an analytical benchmark. A case study in the Atlantic Ocean is presented, focussing on a route from the Chesapeake Bay to the Mediterranean Sea and vice versa. Ocean analysis fields from data-assimilative models (for both ocean state and hydrodynamics) are used. The impact of waves and currents on transatlantic crossings is assessed through mapping of the spatial variability in the tracks, an analysis of their kinematics, and their impact on the Energy Efficiency Operational Indicator (EEOI) of the International Maritime Organization. Sailing with or against the main ocean current is distinguished. The seasonal dependence of the EEOI savings is evaluated, and greater savings with a higher intra-monthly variability during winter crossings are indicated in the case study. The total monthly mean savings are between 2 % and 12 %, while the contribution of ocean currents is between 1 % and 4 %. Several other ocean routes are also considered, providing a pan-Atlantic scenario assessment of the potential gains in energy efficiency from optimal tracks, linking them to regional meteo-oceanographic features.

scholarly journals Simulation of Inertia–Gravity Waves in a Poleward-Breaking Rossby Wave

2006 ◽  
Vol 63 (12) ◽  
pp. 3253-3276 ◽  
Author(s):  
Christoph Zülicke ◽  
Dieter Peters
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Rossby Wave ◽  
Rossby Waves ◽  
Mesoscale Model ◽  
Wave Packets ◽  
The Impact ◽  
Jet Streak ◽  
Horizontal Wavelength ◽  
Inertia Gravity Waves

Poleward-breaking Rossby waves often induce an upper-level jet streak over northern Europe. Dominant inertia–gravity wave packets are observed downstream of this jet. The physical processes of their generation and propagation, in such a configuration, are investigated with a mesoscale model. The study is focused on an observational campaign from 17 to 19 December 1999 over northern Germany. Different simulations with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) have been performed. For a high-resolution process study, three domains were set up that encompass the evolution of Rossby waves and that of inertia–gravity waves. To minimize the impact of model damping, the horizontal and vertical resolution has been adjusted appropriately. With a novel statistical approach, the properties of inertia–gravity wave packets have been estimated. This method uses the horizontal divergence field and takes into account the spatial extension of a wave packet. It avoids the explicit treatment of the background field and works for arbitrary wavelength. Two classes of inertia–gravity waves were found: subsynoptic waves with a horizontal wavelength of about 500 km and mesoscale waves with a horizontal wavelength of about 200 km. The subsynoptic structures were also detected in radiosonde observations during this campaign. The similarity between simulated and observed wavelengths and amplitudes suggests that the simulations can be considered as near realistic. Spontaneous radiation from unbalanced flow is an important process of inertia–gravity wave generation. Synoptic-scale imbalances in the exit region of the upper-tropospheric jet streak were identified with the smoothed cross-stream Lagrangian Rossby number. In a number of simulations with different physics, it was found that the inertia–gravity wave activity was related to the tropospheric jet, orography, and moist convection. The upward propagation of inertia–gravity waves was favored during this event of a poleward-breaking Rossby wave. The presence of the polar vortex induced background winds exceeding the critical line. Consequently, the activity of inertia–gravity waves in the lower stratosphere increased by an order of magnitude during the case study. The successful simulation of the complex processes of generation and propagation showed the important role of poleward Rossby wave breaking for the appearance of inertia–gravity waves in the midlatitudes.

Focusing deep-water surface gravity wave packets: wave breaking criterion in a simplified model

2019 ◽  
Vol 873 ◽  
pp. 238-259 ◽  
Author(s):  
Nick Pizzo ◽  
W. Kendall Melville
Keyword(s):  
Gravity Wave ◽  
Deep Water ◽  
Wave Breaking ◽  
Water Surface ◽  
Dynamic Properties ◽  
Wave Packets ◽  
Surface Gravity ◽  
Simplified Model ◽  
Surface Gravity Wave ◽  
Maximum Slope

Geometric, kinematic and dynamic properties of focusing deep-water surface gravity wave packets are examined in a simplified model with the intent of deriving a wave breaking threshold parameter. The model is based on the spatial modified nonlinear Schrödinger equation of Dysthe (Proc. R. Soc. Lond. A, vol. 369 (1736), 1979, pp. 105–114). The evolution of initially narrow-banded and weakly nonlinear chirped Gaussian wave packets are examined, by means of a trial function and a variational procedure, yielding analytic solutions describing the approximate evolution of the packet width, amplitude, asymmetry and phase during focusing. A model for the maximum free surface gradient, as a function of $\unicode[STIX]{x1D716}$ and $\unicode[STIX]{x1D6E5}$, for $\unicode[STIX]{x1D716}$ the linear prediction of the maximum slope at focusing and $\unicode[STIX]{x1D6E5}$ the non-dimensional packet bandwidth, is proposed and numerically examined, indicating a quasi-self-similarity of these focusing events. The equations of motion for the fully nonlinear potential flow equations are then integrated to further investigate these predictions. It is found that a model of this form can characterize the bulk partitioning of $\unicode[STIX]{x1D716}-\unicode[STIX]{x1D6E5}$ phase space, between non-breaking and breaking waves, serving as a breaking criterion. Application of this result to better understanding air–sea interaction processes is discussed.

scholarly journals Potential flow simulations of Peregrine-type deep water surface gravity wave packets

PAMM ◽  
2015 ◽  
Vol 15 (1) ◽  
pp. 537-538
Author(s):  
Arne Wenzel ◽  
Dennis Bünte ◽  
Norbert P. Hoffmann
Keyword(s):  
Gravity Wave ◽  
Deep Water ◽  
Potential Flow ◽  
Water Surface ◽  
Wave Packets ◽  
Surface Gravity ◽  
Surface Gravity Wave ◽  
Flow Simulations

scholarly journals Projectile motion of surface gravity water wave packets: An analogy to quantum mechanics

2021 ◽  
Author(s):  
Georgi Gary Rozenman ◽  
Matthias Zimmermann ◽  
Maxim A. Efremov ◽  
Wolfgang P. Schleich ◽  
William B. Case ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Water Wave ◽  
Wave Packets ◽  
Surface Gravity ◽  
Projectile Motion
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