Wave Motion Control Over Submerged Horizontal Plates

The interaction of surface gravity waves with horizontal pitching plate for actively control waves is investigated based on the linearized theory of water waves. The three-dimensional (3D) problem is formulated for the submerged plate pitching about its middle point and the other plate is considered to be floating above the submerged plate. The submerged plate's thickness is considered negligible in comparison with the water depth and wavelength of the incident wave. The study is carried out using the matched eigenfunction expansion method and the analytical solution is developed for the interaction of the surface gravity waves with horizontal submerged structure. The performance is analyzed for both impermeable and porous submerged pitching plate. The numerical results for the reflection coefficient, transmission coefficient, and free-surface deflection are computed and analyzed. The study is carried to find the optimal value of the length and depth of the submerged plate at which the dissipation of the incident wave energy is observed. The reduction the wave transformation due to the pitching of the plate with the change in angle of incidence is also analyzed. The present study will be helpful in the analysis of proper functioning of submerged pitching plate to control wave motion for the protection of offshore structures.

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Wave Motion Control Over Submerged Horizontal Plates

Volume 7: Ocean Engineering ◽

10.1115/omae2015-42070 ◽

2015 ◽

Author(s):

D. Karmakar ◽

C. Guedes Soares

Keyword(s):

Gravity Waves ◽

Incident Wave ◽

Water Waves ◽

Wave Motion ◽

Offshore Structures ◽

Surface Gravity ◽

Wave Transformation ◽

Angle Of Incidence ◽

Surface Gravity Waves ◽

Submerged Plate

The interaction of surface gravity waves with horizontal pitching plate for actively control waves is investigated based on the linearized theory of water waves. The two dimensional problem is formulated for the submerged plate pitching about its middle point and the other plate is considered to be floating above the submerged plate. The submerged plate’s thickness is considered negligible in comparison with the water depth and wavelength of the incident wave. The study is carried out using the matched eigenfunction expansion method and the analytical solution is developed for the interaction of the surface gravity waves with horizontal submerged structure. The numerical results for the reflection coefficient, transmission coefficient and free surface deflection are computed and analyzed. The study is carried to find the optimal value of the length and depth of the submerged plate at which the dissipation of the incident wave energy is observed. The reduction the wave transformation due to the pitching of the plate with the change in angle of incidence is also analyzed. The present study will be helpful in the analysis of proper functioning of submerged pitching plate to control wave motion for the protection of offshore structures.

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Surface Gravity Waves

Rays, Waves, and Scattering ◽

10.23943/princeton/9780691148373.003.0011 ◽

2017 ◽

Author(s):

John A. Adam

Keyword(s):

Gravity Waves ◽

Water Waves ◽

Water Surface ◽

Wave Pattern ◽

The Body ◽

Surface Gravity ◽

Shallow Water Waves ◽

Ship Waves ◽

Surface Gravity Waves ◽

Basic Fluid

This chapter deals with the underlying mathematics of surface gravity waves, defined as gravity waves observed on an air–sea interface of the ocean. Surface gravity waves, or surface waves, differ from internal waves, gravity waves that occur within the body of the water (such as between parts of different densities). Examples of gravity waves are wind-generated waves on the water surface, as well tsunamis and ocean tides. Wind-generated gravity waves on the free surface of the Earth's seas, oceans, ponds, and lakes have a period of between 0.3 and 30 seconds. The chapter first describes the basic fluid equations before discussing the dispersion relations, with a particular focus on deep water waves, shallow water waves, and wavepackets. It also considers ship waves and how dispersion affects the wave pattern produced by a moving object, along with long and short waves.

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Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves

Fluids ◽

10.3390/fluids4020096 ◽

2019 ◽

Vol 4 (2) ◽

pp. 96 ◽

Cited By ~ 2

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.

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Scattering of Surface Gravity Waves by Islands, Reefs, and Barriers

Rays, Waves, and Scattering ◽

10.23943/princeton/9780691148373.003.0017 ◽

2017 ◽

Author(s):

John A. Adam

Keyword(s):

Gravity Waves ◽

Water Waves ◽

Surface Displacement ◽

Deep Ocean ◽

Surface Gravity ◽

Edge Waves ◽

Surface Gravity Waves ◽

Present Context ◽

Constant Slope ◽

Sloping Beach

This chapter focuses on the scattering of surface gravity waves by islands, reefs, and barriers. Surface gravity waves that propagate from the deep ocean to coastal regions may be strongly amplified by reflection, refraction, diffraction, and shoaling due to variation in water depth. Analytical solutions provide an attractive approach to studies on wave scattering, but they are obtainable for only special topographies and simple governing equations. The chapter considers long surface gravity waves (linear shallow water waves) such that the depth of the water is much greater than the vertical free surface displacement and the wavelength is much larger than the depth. The fluid equations are derived directly for the present context. The discussion covers trapped waves, the scattering or S-matrix, submerged circular islands, edge waves on a sloping beach, one-dimensional edge waves on a constant slope, and wave amplication by a sloping beach.

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A note on the uniqueness of small-amplitude water waves travelling in a region of varying depth

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100056371 ◽

1979 ◽

Vol 86 (3) ◽

pp. 511-519 ◽

Cited By ~ 1

Author(s):

G. F. Fitz-Gerald ◽

R. H. J. Grimshaw

Keyword(s):

Linear Theory ◽

Gravity Waves ◽

Water Waves ◽

Small Amplitude ◽

Velocity Potential ◽

Surface Gravity ◽

Two Dimensional ◽

Physical Interest ◽

Surface Gravity Waves ◽

Convexity Conditions

The two-dimensional, irrotational, linear theory used in the investigation of the propagation of monochromatic surface gravity waves in a region of varying depth is considered. Uniqueness of the velocity potential is established for bottom profiles satisfying certain convexity conditions. These include the majority of profiles of physical interest.

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Surfing surface gravity waves

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.314 ◽

2017 ◽

Vol 823 ◽

pp. 316-328 ◽

Cited By ~ 8

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.

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