scholarly journals Traveling Waves in Deep Water with Gravity and Surface Tension

2010 ◽  
Vol 70 (7) ◽  
pp. 2373-2389 ◽  
Author(s):  
Benjamin Akers ◽  
David P. Nicholls
Keyword(s):  
Surface Tension ◽  
Deep Water ◽  
Traveling Waves

scholarly journals Traveling waves from the arclength parameterization: Vortex sheets with surface tension

2013 ◽  
Vol 15 (3) ◽  
pp. 359-380 ◽  
Author(s):  
Benjamin Akers ◽  
David Ambrose ◽  
J. Douglas Wright
Keyword(s):  
Surface Tension ◽  
Traveling Waves ◽  
Vortex Sheets

Capillary–gravity waves of solitary type and envelope solitons on deep water

1993 ◽  
Vol 252 ◽  
pp. 703-711 ◽  
Author(s):  
Michael S. Longuet-Higgins
Keyword(s):  
Surface Tension ◽  
Dispersion Relation ◽  
Gravity Waves ◽  
Deep Water ◽  
Small Amplitude ◽  
Finite Amplitude ◽  
Surface Slope ◽  
Carrier Wave ◽  
Envelope Solitons ◽  
Special Case

The existence of steady solitary waves on deep water was suggested on physical grounds by Longuet-Higgins (1988) and later confirmed by numerical computation (Longuet-Higgins 1989; Vanden-Broeck & Dias 1992). Their numerical methods are accurate only for waves of finite amplitude. In this paper we show that solitary capillary-gravity waves of small amplitude are in fact a special case of envelope solitons, namely those having a carrier wave of length 2π(T/ρg)1½2 (g = gravity, T = surface tension, ρ = density). The dispersion relation $c^2 = 2(1-\frac{11}{32}\alpha^2_{\max)$ between the speed c and the maximum surface slope αmax is derived from the nonlinear Schrödinger equation for deep-water solitons (Djordjevik & Redekopp 1977) and is found to provide a good asymptote for the numerical calculations.

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 .

Measurement of high frequency capillary waves on steep gravity waves

1978 ◽  
Vol 86 (3) ◽  
pp. 401-413 ◽  
Author(s):  
John H. Chang ◽  
Richard N. Wagner ◽  
Henry C. Yuen
Keyword(s):  
Surface Tension ◽  
High Resolution ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Deep Water ◽  
High Frequency ◽  
Qualitative Agreement ◽  
Capillary Wave ◽  
Capillary Waves ◽  
Good Qualitative Agreement

The properties of high frequency capillary waves generated by steep gravity waves on deep water have been measured with a high resolution laser optical slope gauge. The results have been compared with the steady theory of Longuet-Higgins (1963). Good qualitative agreement is obtained. However, the quantitative predictions of the capillary wave slopes cannot be verified by the data because the theory requires knowledge of an idealized quantity - the crest curvature of the gravity wave in the absence of surface tension - which cannot be measured experimentally.

Benthic foraminiferal zonation in deep-water carbonate platform margin environments, northern Little Bahama Bank

1988 ◽  
Vol 62 (01) ◽  
pp. 1-8 ◽  
Author(s):  
Ronald E. Martin
Keyword(s):  
Deep Water ◽  
Benthic Foraminifera ◽  
Carbonate Platform ◽  
Sedimentary Facies ◽  
Depositional Environments ◽  
Near Surface ◽  
Sediment Gravity Flows ◽  
Gravity Flows ◽  
Platform Margin ◽  
Water Carbonate

The utility of benthic foraminifera in bathymetric interpretation of clastic depositional environments is well established. In contrast, bathymetric distribution of benthic foraminifera in deep-water carbonate environments has been largely neglected. Approximately 260 species and morphotypes of benthic foraminifera were identified from 12 piston core tops and grab samples collected along two traverses 25 km apart across the northern windward margin of Little Bahama Bank at depths of 275-1,135 m. Certain species and operational taxonomic groups of benthic foraminifera correspond to major near-surface sedimentary facies of the windward margin of Little Bahama Bank and serve as reliable depth indicators. Globocassidulina subglobosa, Cibicides rugosus, and Cibicides wuellerstorfi are all reliable depth indicators, being most abundant at depths >1,000 m, and are found in lower slope periplatform aprons, which are primarily comprised of sediment gravity flows. Reef-dwelling peneroplids and soritids (suborder Miliolina) and rotaliines (suborder Rotaliina) are most abundant at depths <300 m, reflecting downslope bottom transport in proximity to bank-margin reefs. Small miliolines, rosalinids, and discorbids are abundant in periplatform ooze at depths <300 m and are winnowed from the carbonate platform. Increased variation in assemblage diversity below 900 m reflects mixing of shallow- and deep-water species by sediment gravity flows.

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