Surfing surface gravity waves

2017 ◽  
Vol 823 ◽  
pp. 316-328 ◽  
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.

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.

Surface Gravity Waves

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.

A note on the divergence effect and the Lagrangian-mean surface elevation in periodic water waves

1988 ◽  
Vol 189 ◽  
pp. 235-242 ◽  
Author(s):  
M. E. Mcintyre
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Gravity Waves ◽  
Water Waves ◽  
Wave Amplitude ◽  
Exact Expression ◽  
Mean Velocity ◽  
Surface Gravity Waves ◽  
Generalized Lagrangian ◽  
Divergence Effect

Longuet-Higgins’ exact expression for the increase in the Lagrangian-mean elevation of the free surface due to the presence of periodic, irrotational surface gravity waves is rederived from generalized Lagrangian-mean theory. The raising of the Lagrangian-mean surface as wave amplitude builds up illustrates the non-zero divergence of the Lagrangian-mean velocity field in an incompressible fluid.

scholarly journals The effect of randomness on the stability of deep water surface gravity waves in the presence of a thin thermocline

1998 ◽  
Vol 40 (2) ◽  
pp. 190-206
Author(s):  
Sudebi Bhattacharyya ◽  
K. P. Das
Keyword(s):  
Growth Rate ◽  
Evolution Equation ◽  
Gravity Waves ◽  
Fourth Order ◽  
Deep Water ◽  
Water Surface ◽  
Spectral Width ◽  
Surface Gravity ◽  
Surface Gravity Waves ◽  
The Stability

AbstractThe effect of randomness on the stability of deep water surface gravity waves in the presence of a thin thermocline is studied. A previously derived fourth order nonlinear evolution equation is used to find a spectral transport equation for a narrow band of surface gravity wave trains. This equation is used to study the stability of an initially homogeneous Lorentz shape of spectrum to small long wave-length perturbations for a range of spectral widths. The growth rate of the instability is found to decrease with the increase of spectral widths. It is found that the fourth order term in the evolution equation produces a decrease in the growth rate of the instability. There is stability if the spectral width exceeds a certain critical value. For a vanishing bandwidth the deterministic growth rate of the instability is recovered. Graphs have been plotted showing the variations of the growth rate of the instability against the wavenumber of the perturbation for some different values of spectral width, thermocline depth, angle of perturbation and wave steepness.

Array measurements of atmospheric pressure fluctuations above surface gravity waves

1981 ◽  
Vol 102 ◽  
pp. 1-59 ◽  
Author(s):  
R. L. Snyder ◽  
F. W. Dobson ◽  
J. A. Elliott ◽  
R. B. Long
Keyword(s):  
Gravity Waves ◽  
Atmospheric Pressure ◽  
Pressure Sensors ◽  
Phase Speed ◽  
Limited Range ◽  
Surface Gravity ◽  
Wave Number ◽  
Surface Gravity Waves ◽  
Array Measurements ◽  
Wave Induced

A joint experiment to study microscale fluctuations of atmospheric pressure above surface gravity waves was conducted in the Bight of Abaco, Bahamas, during November and December 1974. Field hardware included a three-dimensional array of six wave sensors and seven air-pressure sensors, one of which was mounted on a wave follower. The primary objectives of the study were to resolve differences in previous field measurements by Dobson (1971), Elliott (1972b) and Snyder (1974), and to estimate the vertical profile of wave-induced pressure and the corresponding input of energy and momentum to the wave field.Analysis of a pre-experiment intercalibration of instruments and of 30 h of field data partially removes the discrepancy between the previous measurements of the wave-induced component of the pressure and gives a consistent picture of the profile of this pressure over a limited range of dimensionless height and wind speed. Over this range the pressure decays approximately exponentially without change of phase; the decay is slightly less steep than predicted by potential theory. The corresponding momentum transfer is positive for wind speeds exceeding the phase speed. Extrapolation of present results to higher frequencies suggests that the total transfer is a significant fraction of the wind stress (0·1 to 1·0, depending on dimensionless fetch).Analysis of the turbulent component of the atmospheric pressure shows that the ‘intrinsic’ downwind coherence scale is typically an order-of-magnitude greater than the crosswind scale, consistent with a ‘frozen’ turbulence hypothesis. These and earlier data of Priestley (1965) and Elliott (1972c) suggest a horizontally isotropic ‘intrinsic’ turbulent pressure spectrum which decays ask−νwherekis the (horizontal) wave-number and ν is typically −2 to −3; estimates of this spectrum are computed for the present data. The implications of these findings for Phillips’ (1957) theory of wave growth are examined.

scholarly journals Experimental study of particle trajectories below deep-water surface gravity wave groups

2019 ◽  
Vol 879 ◽  
pp. 168-186 ◽  
Author(s):  
T. S. van den Bremer ◽  
C. Whittaker ◽  
R. Calvert ◽  
A. Raby ◽  
P. H. Taylor
Keyword(s):  
Gravity Wave ◽  
Deep Water ◽  
Water Waves ◽  
Wave Equations ◽  
Stokes Drift ◽  
Surface Gravity ◽  
Return Flow ◽  
Surface Gravity Wave ◽  
Wave Groups ◽  
Wave Induced

Owing to the interplay between the forward Stokes drift and the backward wave-induced Eulerian return flow, Lagrangian particles underneath surface gravity wave groups can follow different trajectories depending on their initial depth below the surface. The motion of particles near the free surface is dominated by the waves and their Stokes drift, whereas particles at large depths follow horseshoe-shaped trajectories dominated by the Eulerian return flow. For unidirectional wave groups, a small net displacement in the direction of travel of the group results near the surface, and is accompanied by a net particle displacement in the opposite direction at depth. For deep-water waves, we study these trajectories experimentally by means of particle tracking velocimetry in a two-dimensional flume. In doing so, we provide visual illustration of Lagrangian trajectories under groups, including the contributions of both the Stokes drift and the Eulerian return flow to both the horizontal and the vertical Lagrangian displacements. We compare our experimental results to leading-order solutions of the irrotational water wave equations, finding good agreement.

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