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

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.

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>

Laboratory Observations on the Evolution of Deep-Water Wave Packets

2011 ◽  
Author(s):  
Yuxiang Ma ◽  
Guohai Dong ◽  
Xiaozhou Ma
Keyword(s):  
Experimental Data ◽  
Deep Water ◽  
Wave Breaking ◽  
Water Wave ◽  
Wave Packets ◽  
Local Maximum ◽  
Peak Frequency ◽  
Higher Harmonics ◽  
Stokes Waves ◽  
Deep Water Wave

New experimental data for the evolution of deep-water wave packets has been presented. The present experimental data shows that the local maximum steepness for extreme waves is significantly above the criterion of the limiting Stokes waves. The wavelet spectra of the wave groups around the breaking locations indicate that the energy of higher harmonics can be generated quickly before wave breaking and mainly concentrate at the part of the wave fronts. After wave breaking, however, these higher harmonics energy is dissipated immediately. Furthermore, the variations of local peak frequency have also been examined. It is found that frequency downshift increases with the increase of initial steepness and wave packet size.

TOPOLOGICAL EFFECTS IN QUANTUM MECHANICS AND HIGH VELOCITY ESTIMATES

2011 ◽  
Vol 20 (05) ◽  
pp. 951-961 ◽  
Author(s):  
RICARDO WEDER
Keyword(s):  
Exact Solution ◽  
Quantum Mechanics ◽  
Error Bounds ◽  
High Velocity ◽  
Wave Packets ◽  
Finite Energy ◽  
Time Dependent ◽  
Rigorous Proof ◽  
Bohm Effect ◽  
Aharonov Bohm

We consider the problem of obtaining high-velocity estimates for finite energy solutions (wave packets) to Schrödinger equations for N-body systems. We discuss a time-dependent method that allows us to obtain precise estimates with error bounds that decay as a power of the velocity. We apply this method to the electric Aharonov–Bohm effect. We give the first rigorous proof that quantum mechanics predicts the existence of this effect. Our result follows from an estimate in norm, uniform in time, that proves that the Aharonov–Bohm Ansatz is a good approximation to the exact solution to the Schrödinger equation for high velocity.

Surface Gravity Water Wave Airy Wavepacket

2015 ◽  
Author(s):  
Shenhe Fu ◽  
Yuval Tsur ◽  
Jianying Zhou ◽  
Lev Shemer ◽  
Ady Arie
Keyword(s):  
Water Wave ◽  
Surface Gravity
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