Stability of water waves

1986 ◽  
Vol 406 (1830) ◽  
pp. 115-125 ◽  
Keyword(s):  
Hamiltonian Systems ◽  
Water Waves ◽  
Water Wave ◽  
Loss Of Stability ◽  
Imaginary Eigenvalue ◽  
Linearized Problem ◽  
Stability Of Water ◽  
Permanent Form

We apply some general results for Hamiltonian systems, depending on the notion of signature of eigenvalues, to determine the circumstances under which collisions of imaginary eigenvalue for the linearized problem about a travelling water wave of permanent form are avoided or lead to loss of stability, up to non-degeneracy assumptions. A new superharmonic instability is predicted and verified.

Reflexion of water waves by a permeable barrier

1979 ◽  
Vol 95 (1) ◽  
pp. 141-157 ◽  
Author(s):  
C. Macaskill
Keyword(s):  
Water Waves ◽  
Water Wave ◽  
Finite Depth ◽  
Infinite Depth ◽  
Permeable Barrier ◽  
Impermeable Barrier ◽  
Linearized Problem ◽  
Special Case ◽  
Thin Barrier ◽  
Standard Techniques

The linearized problem of water-wave reflexion by a thin barrier of arbitrary permeability is considered with the restriction that the flow be two-dimensional. The formulation includes the special case of transmission through one or more gaps in an otherwise impermeable barrier. The general problem is reduced to a set of integral equations using standard techniques. These equations are then solved using a special decomposition of the finite depth source potential which allows accurate solutions to be obtained economically. A representative range of solutions is obtained numerically for both finite and infinite depth problems.

scholarly journals An alternative approach to study irrotational periodic gravity water waves

2021 ◽  
Vol 72 (4) ◽  
Author(s):  
Biswajit Basu ◽  
Calin I. Martin
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Water Wave ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Stagnation Points ◽  
Alternative Approach ◽  
New Formulation ◽  
Bounded Below ◽  
Surface Dynamic

AbstractWe are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.

Shallow water wave generation by unsteady flow

1968 ◽  
Vol 31 (4) ◽  
pp. 779-788 ◽  
Author(s):  
J. E. Ffowcs Williams ◽  
D. L. Hawkings
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Water Wave ◽  
Small Amplitude ◽  
Point Of View ◽  
Sound Waves ◽  
Aerodynamic Sound ◽  
Shallow Layer ◽  
Sound Theory ◽  
Water Simulation

Small amplitude waves on a shallow layer of water are studied from the point of view used in aerodynamic sound theory. It is shown that many aspects of the generation and propagation of water waves are similar to those of sound waves in air. Certain differences are also discussed. It is concluded that shallow water simulation can be employed in the study of some aspects of aerodynamically generated sound.

scholarly journals A Spherical Hybrid Triboelectric Nanogenerator for Enhanced Water Wave Energy Harvesting

Micromachines ◽  
2018 ◽  
Vol 9 (11) ◽  
pp. 598 ◽  
Author(s):  
Kwangseok Lee ◽  
Jeong-won Lee ◽  
Kihwan Kim ◽  
Donghyeon Yoo ◽  
Dong Kim ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
Water Waves ◽  
Water Wave ◽  
Degrees Of Freedom ◽  
Low Frequency ◽  
Random Motion ◽  
Triboelectric Nanogenerator ◽  
Hybrid Energy ◽  
Pollution Levels ◽  
Self Powered

Water waves are a continuously generated renewable source of energy. However, their random motion and low frequency pose significant challenges for harvesting their energy. Herein, we propose a spherical hybrid triboelectric nanogenerator (SH-TENG) that efficiently harvests the energy of low frequency, random water waves. The SH-TENG converts the kinetic energy of the water wave into solid–solid and solid–liquid triboelectric energy simultaneously using a single electrode. The electrical output of the SH-TENG for six degrees of freedom of motion in water was investigated. Further, in order to demonstrate hybrid energy harvesting from multiple energy sources using a single electrode on the SH-TENG, the charging performance of a capacitor was evaluated. The experimental results indicate that SH-TENGs have great potential for use in self-powered environmental monitoring systems that monitor factors such as water temperature, water wave height, and pollution levels in oceans.

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.

Numerical simulation of viscous, nonlinear and progressive water waves

2009 ◽  
Vol 637 ◽  
pp. 443-473 ◽  
Author(s):  
ASHISH RAVAL ◽  
XIANYUN WEN ◽  
MICHAEL H. SMITH
Keyword(s):  
Numerical Simulation ◽  
Shear Stress ◽  
Deep Water ◽  
Water Waves ◽  
Water Wave ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Energy Decay Rate ◽  
Average Wind ◽  
Anticlockwise Rotation

A numerical simulation is performed to study the velocity, streamlines, vorticity and shear stress distributions in viscous water waves with different wave steepness in intermediate and deep water depth when the average wind velocity is zero. The numerical results present evidence of ‘clockwise’ and ‘anticlockwise’ rotation of the fluid at the trough and crest of the water waves. These results show thicker vorticity layers near the surface of water wave than that predicted by the theories of inviscid rotational flow and the low Reynolds number viscous flow. Moreover, the magnitude of vorticity near the free surface is much larger than that predicted by these theories. The analysis of the shear stress under water waves show a thick shear layer near the water surface where large shear stress exists. Negative and positive shear stresses are observed near the surface below the crest and trough of the waves, while the maximum positive shear stress is inside the water and below the crest of the water wave. Comparison of wave energy decay rate in intermediate depth and deep water waves with laboratory and theoretical results are also presented.

Transmission of water waves through small apertures

1971 ◽  
Vol 49 (1) ◽  
pp. 65-74 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Transmission Coefficient ◽  
Asymptotic Expansions ◽  
Water Waves ◽  
Water Wave ◽  
Approximate Formula ◽  
Matched Asymptotic Expansions ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Method Of Solution

A method of solution is proposed for flows through small apertures in otherwise impermeable barriers. This method, which is an application of the method of matched asymptotic expansions, is used to solve a specific water-wave problem, yielding an approximate formula for the transmission coefficient.

NONLINEAR LOW FREQUENCY WATER WAVES IN A CYLINDRICAL SHELL

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1615-1618 ◽  
Author(s):  
H. W. PENG ◽  
D. J. WANG ◽  
C. B. LEE
Keyword(s):  
High Frequency ◽  
Water Waves ◽  
Water Wave ◽  
Excitation Frequency ◽  
Low Frequency ◽  
Viscous Effect ◽  
First Approximation ◽  
Quantitative Results ◽  
High Frequency Excitation ◽  
Frequency Excitation

The experiment was carried out to study the low frequency surface waves due to the horizontal high frequency excitation. The feature of the phenomenon was that the big amplitude axisymmetric surface wave frequency was typically about 1/50 of the excitation frequency. The viscous effect of water was neglected as a first approximation in the earlier papers on this subject. In contrast, we found the viscosity was important to achieve the low frequency water wave with the cooperation of hundreds of "finger" waves. Photographs were taken with stroboscopic lighting and thereafter relevant quantitative results were obtained based on the measurements with Polytec Scanning Vibrometer PSV 400.

scholarly journals Super compact equation for water waves

2017 ◽  
Vol 828 ◽  
pp. 661-679 ◽  
Author(s):  
A. I. Dyachenko ◽  
D. I. Kachulin ◽  
V. E. Zakharov
Keyword(s):  
Wave Equation ◽  
Water Waves ◽  
Wave Breaking ◽  
Water Wave ◽  
Rogue Waves ◽  
Resonant Interaction ◽  
Zakharov Equation ◽  
Advection Term ◽  
New Equation ◽  
The Many

Mathematicians and physicists have long been interested in the subject of water waves. The problems formulated in this subject can be considered fundamental, but many questions remain unanswered. For instance, a satisfactory analytic theory of such a common and important phenomenon as wave breaking has yet to be developed. Our knowledge of the formation of rogue waves is also fairly poor despite the many efforts devoted to this subject. One of the most important tasks of the theory of water waves is the construction of simplified mathematical models that are applicable to the description of these complex events under the assumption of weak nonlinearity. The Zakharov equation, as well as the nonlinear Schrödinger equation (NLSE) and the Dysthe equation (which are actually its simplifications), are among them. In this article, we derive a new modification of the Zakharov equation based on the assumption of unidirectionality (the assumption that all waves propagate in the same direction). To derive the new equation, we use the Hamiltonian form of the Euler equation for an ideal fluid and perform a very specific canonical transformation. This transformation is possible due to the ‘miraculous’ cancellation of the non-trivial four-wave resonant interaction in the one-dimensional wave field. The obtained equation is remarkably simple. We call the equation the ‘super compact water wave equation’. This equation includes a nonlinear wave term (à la NLSE) together with an advection term that can describe the initial stage of wave breaking. The NLSE and the Dysthe equations (DystheProc. R. Soc. Lond.A, vol. 369, 1979, pp. 105–114) can be easily derived from the super compact equation. This equation is also suitable for analytical studies as well as for numerical simulation. Moreover, this equation also allows one to derive a spatial version of the water wave equation that describes experiments in flumes and canals.

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