Attenuation of short surface waves by the sea floor via nonlinear sub-harmonic interaction

2011 ◽  
Vol 689 ◽  
pp. 529-540 ◽  
Author(s):  
Mohammad-Reza Alam ◽  
Yuming Liu ◽  
Dick K. P. Yue
Keyword(s):  
Surface Waves ◽  
Harmonic Wave ◽  
Harmonic Waves ◽  
Sea Floor ◽  
Resonant Interactions ◽  
Long Wave ◽  
Direct Perturbation ◽  
Harmonic Interaction ◽  
Interaction Problem ◽  
Energy Argument

AbstractWe consider the indirect mechanism for dissipation of short surface waves through their near-resonant interactions with long sub-harmonic waves that are dissipated by the bottom. Using direct perturbation analysis and an energy argument, we obtain analytic predictions of the evolution of the amplitudes of two short primary waves and the long sub-harmonic wave which form a near-resonant triad, elucidating the energy transfer, from the short waves to the long wave, which may be significant over time. We obtain expressions for the rate of total energy loss of the system and show that this rate has an extremum corresponding to a specific value of the (bottom) damping coefficient (for a given pair of short wavelengths relative to water depth). These analytic results agree very well with direct numerical simulations developed for the general nonlinear wave–wave and wave–bottom interaction problem.

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

A model study of elastic waves in a layered sphere

1967 ◽  
Vol 57 (5) ◽  
pp. 959-981
Author(s):  
Victor Gregson
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Elastic Waves ◽  
Wave Dispersion ◽  
Flat Space ◽  
Dispersion Curves ◽  
Body Waves ◽  
Surface Wave Dispersion ◽  
Steel Sphere ◽  
Long Wave

abstract Elastic waves produced by an impact were recorded at the surface of a solid 12.0 inch diameter steel sphere coated with a 0.3 inch copper layer. Conventional modeling techniques employing both compressional and shear piezoelectric transducers were used to record elastic waves for one millisecond at various points around the great circle of the sphere. Body, PL, and surface waves were observed. Density, layer thickness, compressional and shear-wave velocities were measured so that accurate surface-wave dispersion curves could be computed. Surface-wave dispersion was measured as well as computed. Measured PL mode dispersion compared favorably with theoretical computations. In addition, dispersion curves for Rayleigh, Stoneley, and Love modes were computed. Measured surface-wave dispersion showed Rayleigh and Love modes were observed but not Stoneley modes. Measured dispersion compared favorably with theoretical computations. The curvature correction applied to dispersion calculations in a flat space has been estimated to correct dispersion values at long-wave lengths to about one per cent of correct dispersion in a spherical model. Measured dispersion compared with such flat space dispersion corrected for curvature proved accurate within one per cent at long wave lengths. Two sets of surface waves were observed. One set was associated with body waves radiating outward from impact. The other set was associated with body waves reflecting at the pole opposite impact. For each set of surface waves, measured dispersion compared favorably with computed dispersion.

Resonant Interactions and Chaotic Excitation in Nonlinear Surface Waves in Dense Plasma

2021 ◽  
pp. 1-12
Author(s):  
Amit Ghosh ◽  
Jyotirmoy Goswami ◽  
Swarniv Chandra ◽  
Chinmay Das ◽  
Yash Arya ◽  
...  
Keyword(s):  
Surface Waves ◽  
Dense Plasma ◽  
Resonant Interactions ◽  
Nonlinear Surface Waves ◽  
Nonlinear Surface

Cancellation of Non-Harmonic Waves Using a Cycloidal Turbine

2011 ◽  
Author(s):  
John T. Imamura ◽  
Stefan G. Siegel ◽  
Casey Fagley ◽  
Tom McLaughlin
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Linear Time ◽  
Harmonic Wave ◽  
Point Vortex ◽  
Harmonic Waves ◽  
Incoming Wave ◽  
Response Characteristics ◽  
Depth Water ◽  
Multi Component System

We computationally investigate the ability of a cycloidal turbine to cancel two-dimensional non-harmonic waves in deep water. A cycloidal turbine employs the same geometry as the well established Cycloidal or Voith-Schneider Propeller. It consists of a shaft and one or more hydrofoils that are attached eccentrically to the main shaft and can be independently adjusted in pitch angle as the cycloidal turbine rotates. We simulate the cycloidal turbine interaction with incoming waves by viewing the turbine as a wave generator superimposed with the incoming flow. The generated waves ideally are 180° out of phase and cancel the incoming wave downstream of the turbine. The upstream wave is very small as generation of single-sided waves is a characteristic of the cycloidal turbine as has been shown in prior work. The superposition of the incoming wave and generated wave is investigated in the far-field and we model the hydrofoil as a point vortex. This model has previously been used to successfully terminate regular deep water waves as well as intermediate depth water waves. We explore the ability of this model to cancel non-harmonic waves. Near complete cancellation is possible for a non-harmonic wave with components designed to match those generated by the cycloidal turbine for specified parameters. Cancellation of a specific wave component of a multi-component system is also shown. Also, step changes in the device operating parameters of circulation strength, rotation rate, and submergence depth are explored to give insight to the cycloidal turbine response characteristics and adaptability to changes in incoming waves. Based on these studies a linear, time-invarient (LTI) model is developed which captures the steady state wave frequency response. Such a model can be used for control development in future efforts to efficiently cancel more complex incoming waves.

scholarly journals A centre manifold approach to solitary waves in a sheared, stably stratified fluid layer

1996 ◽  
Vol 3 (2) ◽  
pp. 110-114 ◽  
Author(s):  
W. B. Zimmerman ◽  
M. G. Velarde
Keyword(s):  
Nonlinear Waves ◽  
Fluid Layer ◽  
Approximate Equation ◽  
Stratified Fluid ◽  
Material Surface ◽  
Centre Manifold ◽  
Wave Approximation ◽  
Long Wave ◽  
Long Wave Approximation ◽  
Energy Argument

Abstract. The centre manifold approach is used to derive an approximate equation for nonlinear waves propagating in a sheared, stably stratified fluid layer. The evolution equation matches limiting forms derived by other methods, including the inviscid, long wave approximation leading to the Korteweg- deVries equation. The model given here allows large modulations of the height of the waveguide. This permits the crude modelling of shear layer instabilities at the upper material surface of the waveguide which excite solitary internal waves in the waveguide. An energy argument is used to support the existence of these waves.

scholarly journals Searching for chaotic deterministic features in laboratory water surface waves

2000 ◽  
Vol 7 (1/2) ◽  
pp. 37-48 ◽  
Author(s):  
M. Joelson ◽  
Th. Dudok de Wit ◽  
Ph. Dussouillez ◽  
A. Ramamonjiarisoa
Keyword(s):  
Surface Waves ◽  
Water Surface ◽  
Wind Waves ◽  
Theoretical Models ◽  
Resonant Interactions ◽  
Mechanical Waves ◽  
Random Character ◽  
Nonlinear Features ◽  
Low Dimensional ◽  
Laboratory Water

Abstract. The dynamic evolution of laboratory water surface waves has been studied within the framework of dynamical systems with the aim to identify stochastic or deterministic nonlinear features. Three different regimes are considered: pure wind waves, pure mechanical waves and mixed (wind and mechanical) waves. These three regimes show different dynamics. The results on wind waves do not clearly support the recently proposed idea that a deterministic Stokes-like component dominate the evolution of such waves; they are more appropriately described by a similarity-like approach that includes a random character. Cubic resonant interactions are clearly identified in pure mechanical waves using tricoherence functions. However, detailed aspects of the interactions do not fully agree with existing theoretical models. Finally, a deterministic motion is observed in mixed waves, which therefore are best described by a low dimensional nonlinear deterministic process.

A nonlinear mechanism for the generation of sea waves

1969 ◽  
Vol 311 (1506) ◽  
pp. 371-389 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Waves ◽  
Orbital Motion ◽  
Long Waves ◽  
Shear Instability ◽  
Sea Waves ◽  
Short Waves ◽  
Long Wave ◽  
Nonlinear Mechanism ◽  
Surrounding Fluid

Recent observations of the growth of sea waves under the action of wind have established that the rate of growth is several times greater than has yet been accounted for. In this paper a new mechanism of wave generation is proposed, based on the idea of a maser-like action of the short waves on the longer waves. It is shown that when surface waves decay they impart their momentum to the surrounding fluid. Short waves are readily regenerated by shear instability. But a longer wave passing through shorter waves causes the short waves to steepen on the long-wave crests. Hence the short waves impart more of their momentum to the crests of the long waves, where the orbital motion of the long waves is in the direction of wave propagation. If the short waves are decaying only weakly (under the action of viscosity), the effect on the long waves is slight. But when the short waves are forced to decay strongly by breaking on the forward slopes of the long waves the gain of energy by the latter is greatly increased. Calculations suggest that the mechanism is capable of imparting energy to sea waves at the rate observed.

STUDIES ON SEISMIC WAVES: III. PROPAGATION OF ELASTIC WAVES IN THE NEIGHBORHOOD OF A FREE BOUNDARY

Geophysics ◽  
1947 ◽  
Vol 12 (1) ◽  
pp. 57-71 ◽  
Author(s):  
C. Y. Fu
Keyword(s):  
Surface Waves ◽  
Elastic Waves ◽  
Seismic Waves ◽  
Classical Method ◽  
Epicentral Distance ◽  
Harmonic Waves ◽  
Inhomogeneous Waves ◽  
Different Types ◽  
Propagation Of Elastic Waves ◽  
The Waves

Continuous and spherical harmonic waves are generated at an internal point of the medium. By use of the classical method of Sommerfeld, the different modes of propagation near a free surface after the arrival of the waves are examined. From the approximate evaluations of the integrals, it is found that in addition to the ordinary types of body and surface waves, there are also inhomogeneous waves and surface waves which are not of the Rayleigh type. The amplitude factors of these latter waves vary inversely as the square instead of as the square root of the epicentral distance. Altogether, there are not less than five different types of waves and they are obtained from integrations in the neighborhood of the singularities of the integrals.

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