A new triad resonance between co-propagating surface and interfacial waves

2011 ◽  
Vol 691 ◽  
pp. 267-278 ◽  
Author(s):  
Mohammad-Reza Alam
Keyword(s):  
Theoretical Analysis ◽  
Surface Waves ◽  
Wave Train ◽  
Stratified Fluid ◽  
Direct Simulation ◽  
Interfacial Wave ◽  
Higher Harmonics ◽  
New Class ◽  
Near Resonance ◽  
Littoral Zones

AbstractIn a two-layer density-stratified fluid it is known, due to Ball (J. Fluid Mech., vol. 19, 1964, p. 465), that two oppositely travelling surface waves may form a triad resonance with an interfacial wave. Ball claims ‘there are no other interactions’ between two surface waves and one interfacial wave. Contrary to this, here we present a new class of triad resonance that occurs between two co-propagating surface waves and one interfacial wave. While in Ball’s resonance the interfacial wave has a wavelength of about half of two surface waves, in the new resonance presented here the interfacial wave has a much higher wavelength compared to those of surface waves. This, together with the unidirectionality of the participant triplet, makes the realization of the new resonance more likely in real ocean scenarios. We further show, via theoretical analysis and direct simulation, that, unique to this new class of resonance, the triad inevitably undergoes a cascade of (near-) resonance interaction that spreads the energy of initial waves to a number of lower and higher harmonics. The significance of the resonance studied here is, particularly, more emphasized in the littoral zones, where the spectrum refracts toward a unidirectional wave train.

scholarly journals Suppression of Wind Ripples and Microwave Backscattering Due to Turbulence Generated by Breaking Surface Waves

2020 ◽  
Vol 12 (21) ◽  
pp. 3618
Author(s):  
Stanislav Ermakov ◽  
Vladimir Dobrokhotov ◽  
Irina Sergievskaya ◽  
Ivan Kapustin
Keyword(s):  
Remote Sensing ◽  
Surface Waves ◽  
Wave Breaking ◽  
Wave Train ◽  
Wind Waves ◽  
Breaking Waves ◽  
Doppler Spectrum ◽  
Strong Wave ◽  
Wave Maker ◽  
Radar Backscattering

The role of wave breaking in microwave backscattering from the sea surface is a problem of great importance for the development of theories and methods on ocean remote sensing, in particular for oil spill remote sensing. Recently it has been shown that microwave radar return is determined by both Bragg and non-Bragg (non-polarized) scattering mechanisms and some evidence has been given that the latter is associated with wave breaking, in particular, with strong breaking such as spilling or plunging. However, our understanding of mechanisms of the action of strong wave breaking on small-scale wind waves (ripples) and thus on the radar return is still insufficient. In this paper an effect of suppression of radar backscattering after strong wave breaking has been revealed experimentally and has been attributed to the wind ripple suppression due to turbulence generated by strong wave breaking. The experiments were carried out in a wind wave tank where a frequency modulated wave train of intense meter-decimeter-scale surface waves was generated by a mechanical wave maker. The wave train was compressed according to the gravity wave dispersion relation (“dispersive focusing”) into a short-wave packet at a given distance from the wave maker. Strong wave breaking with wave crest overturning (spilling) occurred for one or two highest waves in the packet. Short decimeter-centimeter-scale wind waves were generated at gentle winds, simultaneously with the long breaking waves. A Ka-band scatterometer was used to study microwave backscattering from the surface waves in the tank. The scatterometer looking at the area of wave breaking was mounted over the tank at a height of about 1 m above the mean water level, the incidence angle of the microwave radiation was about 50 degrees. It has been obtained that the radar return in the presence of short wind waves is characterized by the radar Doppler spectrum with a peak roughly centered in the vicinity of Bragg wave frequencies. The radar return was strongly enhanced in a wide frequency range of the radar Doppler spectrum when a packet of long breaking waves arrived at the area irradiated by the radar. After the passage of breaking waves, the radar return strongly dropped and then slowly recovered to the initial level. Measurements of velocities in the upper water layer have confirmed that the attenuation of radar backscattering after wave breaking is due to suppression of short wind waves by turbulence generated in the breaking zone. A physical analysis of the effect has been presented.

On a uniformly valid model for surface wave interaction

1993 ◽  
Vol 247 ◽  
pp. 589-601 ◽  
Author(s):  
Yehuda Agnon
Keyword(s):  
Surface Wave ◽  
Water Waves ◽  
Wave Train ◽  
Wave Interaction ◽  
Shallow Water Waves ◽  
First Order ◽  
Near Resonance ◽  
Wave Trains ◽  
Velocity Changes ◽  
Forced Waves

Nonlinear interaction of surface wave trains is studied. Zakharov's kernel is extended to include the vicinity of trio resonance. The forced wave amplitude and the wave velocity changes are then first order rather than second order. The model is applied to remove near-resonance singularities in expressions for the change of speed of one wave train in the presence of another. New results for Wilton ripples and the drift current and setdown in shallow water waves are readily derived. The ideas are applied to the derivation of forced waves in the vicinity of quartet and quintet resonance in an evolving wave field.

Dissipative effects on the resonant flow of a stratified fluid over topography

1988 ◽  
Vol 192 ◽  
pp. 287-312 ◽  
Author(s):  
N. F. Smyth
Keyword(s):  
Bottom Topography ◽  
Stratified Fluid ◽  
Flow Speed ◽  
Resonant Condition ◽  
Weakly Nonlinear ◽  
Dissipative Effects ◽  
Long Wave ◽  
Near Resonance ◽  
Wave Limit ◽  
Wave Modes

The effect of dissipation on the flow of a stratified fluid over topography is considered in the weakly nonlinear, long-wave limit for the case when the flow is near resonance, i.e. the basic flow speed is close to a linear long-wave speed for one of the long-wave modes. The two types of dissipation considered are the dissipation due to viscosity acting in boundary layers and/or interfaces and the dissipation due to viscosity acting in the fluid as a whole. The effect of changing bottom topography on the flow produced by a force moving at a resonant velocity is also considered. In this case, the resonant condition is that the force velocity is close to a linear long-wave velocity for one of the long-wave modes. It is found that in most cases, these extra effects result in the formation of a steady state, in contrast to the flow without these effects, which remains unsteady for all time. The flow resulting under the action of boundary-layer dissipation is compared with recent experimental results.

The generation of surface waves over a sloping beach by an oscillating line-source. I. The general solution

1974 ◽  
Vol 76 (3) ◽  
pp. 545-554 ◽  
Author(s):  
Clare A. N. Morris
Keyword(s):  
General Solution ◽  
Integral Representation ◽  
Surface Waves ◽  
Line Source ◽  
Wave Train ◽  
Wave Generation ◽  
Outgoing Wave ◽  
Arbitrary Angle ◽  
Laplace Integral Representation ◽  
Sloping Beach

AbstractThe problem of wave generation by a line source of sinusoidally varying strength situated in water above a beach of arbitrary angle α(0 < α ≤ π) is solved by the use of a Laplace-integral representation of the solution. It is shown that a solution can be constructed which is regular at the shoreline and gives an outgoing wave-train at infinity.

scholarly journals Understanding the Value of Fulfillment Flexibility in an Online Retailing Environment

2021 ◽  
Author(s):  
Levi DeValve ◽  
Yehua Wei ◽  
Di Wu ◽  
Rong Yuan
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Problem Definition ◽  
Order Fulfillment ◽  
Distribution Centers ◽  
Online Retailing ◽  
New Class ◽  
Managerial Implications ◽  
The Cost ◽  
Improve Service Quality

Problem definition: Fulfillment flexibility, the ability of distribution centers (DCs) to fulfill demand originating from other DCs, can help e-retailers reduce lost sales and improve service quality. Because the cost of full flexibility is prohibitive, we seek to understand the value of partially flexible fulfillment networks under simple and effective fulfillment policies. Academic/practical relevance: We propose a general method for understanding the practical value of (partial) fulfillment flexibility using a data-driven model, theoretical analysis, and numerical simulations. Our method applies to settings with local fulfillment (i.e., order fulfillment from the originating DC) prioritization and possible customer abandonment, two features that are new to the fulfillment literature. We then apply this method for a large e-retailer. We also introduce a new class of spillover limit fulfillment policies with attractive theoretical and practical features. Methodology: Our analysis uses dynamic and stochastic optimization, applied probability, and numerical simulations. Results: We derive optimal fulfillment policies in stylized settings, as well as bounds on the performance under an optimal policy using theoretical analysis, to provide guidelines on which policies to test in numerical simulations. We then use simulations to estimate for our industrial partner that a proposed fulfillment network with additional flexibility equates to a profit improvement on the order of tens of millions of U.S. dollars. Managerial implications: We provide an approach for e-retailers to understand when fulfillment flexibility is most valuable. We find that fulfillment flexibility provides the most benefit for our collaborator when gross profits are high relative to fulfillment costs or centrally held inventory is low. Also, we identify the risks of myopic fulfillment with additional flexibility and demonstrate that an effective spillover limit policy mitigates these risks.

scholarly journals Asymmetric behavior of surface waves induced by an underlying interfacial wave

2019 ◽  
Vol 17 (5) ◽  
pp. 1333-1351
Author(s):  
Shixiao W. Jiang ◽  
Gregor Kovačič ◽  
Douglas Zhou
Keyword(s):  
Surface Waves ◽  
Interfacial Wave ◽  
Asymmetric Behavior

THEORETICAL ANALYSIS OF SURFACE WAVES ON A ROUND LIQUID JET IN A GASEOUS CROSSFLOW

2014 ◽  
Vol 24 (1) ◽  
pp. 23-40 ◽  
Author(s):  
Shaolin Wang ◽  
Y. Huang ◽  
Z. L. Liu
Keyword(s):  
Theoretical Analysis ◽  
Surface Waves ◽  
Liquid Jet

The transmission of surface waves under surface obstacles

1961 ◽  
Vol 57 (3) ◽  
pp. 638-668 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Transmission Coefficient ◽  
Cross Section ◽  
Water Waves ◽  
Wave Train ◽  
Circular Cross Section ◽  
Great Distance ◽  
The Body ◽  
Radius Of Curvature

ABSTRACTA train of surface waves (water waves under gravity) is normally incident on a cylinder with horizontal generators fixed near the free surface, and is partially transmitted and partially reflected. At a great distance behind the cylinder the wave motion tends to a regular wave train travelling towards infinity; the ratio of its amplitude to the amplitude of the incident wave is the transmission coefficient . The transmission coefficient is studied when the wavelength is short compared to the dimensions of the body; physically (though not for engineering applications) this is the most interesting range of wavelengths, which corresponds to the range of shadow formation and ray propagation in optics and acoustics. The waves are then confined to a thin layer near the free surface, and the transmission under a partially immersed obstacle is then small. In the calculation the boundary condition at the free surface is linearized, viscosity is neglected, and the motion is assumed to be irrotational.At present the transmission coefficient is known only for a few configurations, all of them relating to infinitely thin plane barriers. A method is now given which is applicable to cylinders of finite cross-section and which is worked out in detail for a half-immersed cylinder of circular cross-section. The solution of the problem is made to depend on the solution of an integral equation which is solved by iteration. Only the first two terms can be obtained with any accuracy, and it appears at first that this is not sufficient to give the leading term in the transmission coefficient at short wavelengths; this difficulty is characteristic of transmission problems. By various mathematical devices which throw light on the mechanism of wave transmission, it is, nevertheless, found possible to prove that the transmission coefficient for waves of short wavelength λ and period 2π/ω incident on a half-immersed circular cylinder of radius a is asymptotically given bywhen N = 2πα/λ = ω2α/g is large. Earlier evidence had pointed towards an exponential law. It is suggested that transmission coefficients of order N−4 are typical for obstacles having vertical tangents and finite non-zero radius of curvature at the points where they meet the horizontal mean free surface. For obstacles having both front and rear face plane vertical to a depth a, is probably of order e−2N approximately; if only one of the two faces is plane vertical, is probably of order e−N approximately. Thus is seen to depend critically on the details of the cross-section.

Low-dimensional chaos in surface waves: Theoretical analysis of an experiment

1986 ◽  
Vol 34 (4) ◽  
pp. 3221-3237 ◽  
Author(s):  
Ehud Meron ◽  
Itamar Procaccia
Keyword(s):  
Theoretical Analysis ◽  
Surface Waves ◽  
Low Dimensional
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