scholarly journals DEEP WATER WAVES GENERATED BY HURRICANE "AUDREY" OF 1957

2011 ◽  
Vol 1 (8) ◽  
pp. 31
Author(s):  
Basil W. Wilson
Keyword(s):  
Gulf Of Mexico ◽  
Deep Water ◽  
Water Waves ◽  
Numerical Technique ◽  
Wave Generation ◽  
Weather Data ◽  
Wind Fields ◽  
Directional Wave ◽  
The Waves ◽  
Meteorological Analysis

A post-mortem analysis of Hurricane Audrey of June 24-27, 1957, in the Gulf of Mexico, is described using all available ship reports and weather data from USA and Mexican sources. A detailed meteorological analysis defines the changing surface pressure and wind systems at 3-hour intervals, from which the space-time wind-fields have been derived for selected paths of wave generation bearing on the Louisiana coastline. A numerical technique of moving-fetch wave-prediction has been used to determine the characteristics of the waves in deep water that would have been prevalent in various parts of the Gulf of Mexico during passage of the hurricane. For two deep water locations in particular the effects of multi-directional wave generation are considered.

scholarly journals Reflection of nonlinear deep-water waves incident onto a wedge of arbitrary angle

1990 ◽  
Vol 32 (1) ◽  
pp. 61-96 ◽  
Author(s):  
T. R. Marchant ◽  
A. J. Roberts
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Wave Reflection ◽  
Mach Reflection ◽  
Wedge Angle ◽  
Arbitrary Angle ◽  
Weakly Nonlinear ◽  
Progressive Waves ◽  
The Waves ◽  
Wave Properties

AbstractWave reflection by a wedge in deep water is examined, where the wedge can represent a breakwater of finite length or the bow of a ship heading directly into the waves. In addition, the form of the solution allows the results to apply to ships heading at an angle into the waves. We consider a deep-water wavetrain approaching the wedge head on from infinity and being reflected. Far from the wedge there is a field of progressive waves (the incident wavetrain) while close to the wedge there is a short-crested wavefield (the incident and reflected wavetrains). A weakly-nonlinear slowly-varying averaged Lagrangian theory is used to describe the problem (see Whitham [16]) as the theory includes the nonlinear interaction between the incident and reflected wavetrains. This modelling of a short-crested wavefield allows the nonlinear wavefield to be found for broad wedges, as opposed to previous theories which are applicable to thin wedges only.It is shown that the governing partial differential equations are hyperbolic and that the solution comprises two regions, within which the wave properties are constant separated by a wave jump. Given the wedge angle and the incident wavefield, the jump angle and the wave steepness and wavenumber of the short-crested wave-field behind the wave jump can be determined. Two solution branches are found to exist: one corresponds to regular reflection, while for small amplitudes the other is similar to Mach-reflection and so it is called near Mach-reflection. Results are presented describing both solution branches and the transition between them.

scholarly journals THE DEVELOPMENT OF A SAND BEACH BY DEEP-WATER WAVES

2000 ◽  
Vol 1 (4) ◽  
pp. 12
Author(s):  
Harold Flinsch
Keyword(s):  
Grain Size ◽  
Deep Water ◽  
Water Waves ◽  
Equilibrium Theory ◽  
Sand Beach ◽  
Shore Line ◽  
Natural Development ◽  
Accurate Forecast ◽  
Sand And Gravel ◽  
The Waves

In a previous paper**, it was shown that the mechanism of the trochoidal waves can be used to determine the equilibrium slope of a sand beach under any wave conditions. As a start it was assumed that the beach material was of uniform grain size, and that the waves approached the beach directly with all motion in planes at right angles to the shore line. In the present paper, the application of the theory is shown in the development of various sand and gravel beaches. The equilibrium theory is studied in the light of the fact that there is usually considerable transportation of material along the shore. In particular, attention is called to the characteristics of beaches with rounded or pointed contours, of beaches whose ends are closed off by rocks or cliffs, or whose ends are open and extend into deep water without barriers of any kind. A method of study and analysis is demonstrated which can be applied to all beaches. Finally, it is shown that an accurate forecast of the natural development of a beach can be made on the basis of the equilibrium slope equation, as well as a forecast of the effect of any structure placed in a naturally developing beach.

scholarly journals Equations for Deep Water Counter Streaming Waves and New Integrals of Motion

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 47 ◽  
Author(s):  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Water Waves ◽  
Integrals Of Motion ◽  
Wave Interactions ◽  
The Right ◽  
The Waves

The waves on a free surface of 2D deep water can be split into two groups: the waves moving to the right, and the waves moving to the left. A specific feature of the four-wave interactions of water waves allows to describe the evolution of the two groups as a system of two equations. The fundamental consequence of this decomposition is the conservation of the “number of waves” in each particular group. The envelope approximation for the waves in each group of counter streaming waves is obtained.

Water waves in a deep square basin

1995 ◽  
Vol 302 ◽  
pp. 65-90 ◽  
Author(s):  
Peter J. Bryant ◽  
Michael Stiassnie
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Three Dimensional ◽  
Standing Waves ◽  
Two Dimensional ◽  
Initial State ◽  
Dimensional Properties ◽  
Periodic Standing Waves ◽  
The Waves ◽  
Small Disturbances

The form and evolution of three-dimensional standing waves in deep water are calculated analytically from Zakharov's equation and computationally from the full nonlinear bounddary value problem. The water is contained in a basin with a square cross-cection, when three-dimensional properties to pairs of sides are the same. It is found that non-periodic standing waves commonly follow forms of cyclic recurrence over times. The two-dimensional Stokes type of periodic standing waves (dominated by the fundamental harmonic) are shown to be unstable to three dimensional disturbances, but over long times the waves return cyclically close to their initial state. In contrast, the three-dimensional Stokes type of periodic standing waves are found to be stabel to small disturbances. New two-dimensional periodic standing waves with amplitude maxima at other than the fundamental harmonic have been investigated recently (Bryant & Stiassnie 1994). The equivalent three-dimensional standing waves are described here. The new two-dimensional periodic standing waves, like the two-dimensional Stokes standing waves, are found to be unstable to three-dimensional disturbances, and to exhibit cyclic recurrence over long times. Only some of the new three-dimensional periodic standing waves are found to be stable to small disturbances.

scholarly journals On the formation of water waves by wind (second paper)

1926 ◽  
Vol 110 (754) ◽  
pp. 241-247 ◽  
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Deep Water ◽  
Water Waves ◽  
Velocity Potential ◽  
Systematic Difference ◽  
Small Extent ◽  
Short Waves ◽  
First Approximation ◽  
The Waves

In a previous paper I investigated the problem of the formation of waves on deep water by wind, and found that the available data were consistent with the hypothesis that the growth of the waves is due principally to a systematic difference between the pressures of the air on the front and rear slopes. Lamb had already discussed the maintenance of waves against viscosity by an approximate method, but without obtaining numerical results. Being under the incorrect impression that Lamb’s approximation would not hold for the short waves I was chiefly considering, I proceeded on more elaborate lines. It now appears, however, that Lamb’s method is not only applicable to the problem of waves on deep water, but is readily extended to cover the case when the water is comparatively shallow, and to allow for surface tension. The fundamental approximations are first, the usual one that squares of the displacements from the steady state can be neglected, and second, that viscosity modifies the motion of the water to only a small extent. The motion of the water can then, to a first approximation, be considered as irrotational. With the previous notation, let ζ be the elevation of the free surface x, y, z the position co-ordinates, t the time, U the undisturbed velocity of the water, h the depth, and φ the velocity potential. Also let σ, p, q , and ϑ denote respectively ∂/∂ t , ∂/∂ x , ∂/∂ y , and ∂/∂ z , and write p 2 + q 2 = - r 2 .

Refraction of finite-amplitude water waves: deep-water waves approaching circular caustics

1981 ◽  
Vol 109 ◽  
pp. 63-74 ◽  
Author(s):  
D. H. Peregrine
Keyword(s):  
Wave Field ◽  
Deep Water ◽  
Water Waves ◽  
Finite Amplitude ◽  
Ray Theory ◽  
Wave Approximation ◽  
Comparison With Experiment ◽  
Straight Lines ◽  
The Waves ◽  
Deep Water Waves

The ‘numerically exact’ properties of plane periodic deep-water waves are used in a slowly-varying-wave approximation for a steady axisymmetric wave field. The linear ‘ray’ theory for such a wave field corresponds to waves approaching a circular caustic. A parameter, C, characterizes each solution. If C is smaller than 20 the wave behaviour is dominated by the convergence of wave energy and waves are expected to break. Comparison with experiment for C = 0 indicates that breaking may be accurately predicted. If C is greater than 50 then the waves propagate closer to the caustic and, since it is of Peregrine & Smith's (1979) type R, it is likely that the waves do not break. These solutions show that wave action does not flow along the straight lines of the linear rays.

scholarly journals Bound Coherent Structures Propagating on the Free Surface of Deep Water

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 115
Author(s):  
Dmitry Kachulin ◽  
Sergey Dremov ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Nonlinear Models ◽  
Ideal Incompressible Fluid ◽  
Equation Model ◽  
System Of Nonlinear Equations ◽  
Potential Flows ◽  
Deep Water Waves

This article presents a study of bound periodically oscillating coherent structures arising on the free surface of deep water. Such structures resemble the well known bi-soliton solution of the nonlinear Schrödinger equation. The research was carried out in the super-compact Dyachenko-Zakharov equation model for unidirectional deep water waves and the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. The special numerical algorithm that includes a damping procedure of radiation and velocity adjusting was used for obtaining such bound structures. The results showed that in both nonlinear models for deep water waves after the damping is turned off, a periodically oscillating bound structure remains on the fluid surface and propagates stably over hundreds of thousands of characteristic wave periods without losing energy.

scholarly journals Wave Directions in a Narrow Bay

2010 ◽  
Vol 40 (1) ◽  
pp. 155-169 ◽  
Author(s):  
Heidi Pettersson ◽  
Kimmo K. Kahma ◽  
Laura Tuomi
Keyword(s):  
Wave Model ◽  
Wave Climate ◽  
Spectral Peak ◽  
Step Size ◽  
Weakly Nonlinear ◽  
Spectral Wave Model ◽  
Directional Coupling ◽  
Directional Wave ◽  
The Baltic ◽  
The Waves

Abstract In slanting fetch conditions the direction of actively growing waves is strongly controlled by the fetch geometry. The effect was found to be pronounced in the long and narrow Gulf of Finland in the Baltic Sea, where it significantly modifies the directional wave climate. Three models with different assumptions on the directional coupling between the wave components were used to analyze the physics responsible for the directional behavior of the waves in the gulf. The directionally decoupled model produced the direction at the spectral peak correctly when the slanting fetch geometry was narrow but gave a weaker steering than observed when the fetch geometry was broader. The method of Donelan estimated well the direction at the spectral peak in well-defined slanting fetch conditions, but overestimated the longer fetch components during wave growth from a more complex shoreline. Neither the decoupled nor the Donelan model reproduced the observed shifting of direction with the frequency. The performance of the third-generation spectral wave model (WAM) in estimating the wave directions was strongly dependent on the grid resolution of the model. The dominant wave directions were estimated satisfactorily when the grid-step size was dropped to 5 km in the gulf, which is 70 km in its narrowest part. A mechanism based on the weakly nonlinear interactions is proposed to explain the strong steering effect in slanting fetch conditions.

scholarly journals Impact of the Deepwater Horizon oil spill on a deep-water coral community in the Gulf of Mexico

2012 ◽  
Vol 109 (50) ◽  
pp. 20303-20308 ◽  
Author(s):  
H. K. White ◽  
P.-Y. Hsing ◽  
W. Cho ◽  
T. M. Shank ◽  
E. E. Cordes ◽  
...  
Keyword(s):  
Gulf Of Mexico ◽  
Oil Spill ◽  
Deep Water ◽  
Deepwater Horizon ◽  
Coral Community ◽  
Deepwater Horizon Oil Spill ◽  
Water Coral
Sign in / Sign up

Export Citation Format

Share Document