Small-amplitude equatorial water waves with constant vorticity: Dispersion relations and particle trajectories

2014 ◽  
Vol 34 (8) ◽  
pp. 3045-3060 ◽  
Author(s):  
Delia Ionescu-Kruse ◽  
◽  
Anca-Voichita Matioc
Keyword(s):  
Water Waves ◽  
Small Amplitude ◽  
Dispersion Relations ◽  
Particle Trajectories ◽  
Constant Vorticity

Particle trajectories in linear periodic capillary and capillary–gravity water waves

2007 ◽  
Vol 365 (1858) ◽  
pp. 2241-2251 ◽  
Author(s):  
David Henry
Keyword(s):  
Surface Tension ◽  
Linear Theory ◽  
Significant Role ◽  
Water Waves ◽  
Small Amplitude ◽  
Capillary Wave ◽  
Capillary Waves ◽  
Particle Trajectories ◽  
Particle Paths

Surface tension plays a significant role as a restoration force in the setting of small-amplitude waves, leading to pure capillary and gravity-capillary waves. We show that within the framework of linear theory, the particle paths in a periodic gravity–capillary or pure capillary wave propagating at the surface of water over a flat bed are not closed.

scholarly journals Traveling Quasi-periodic Water Waves with Constant Vorticity

2021 ◽  
Author(s):  
M. Berti ◽  
L. Franzoi ◽  
A. Maspero
Keyword(s):  
Periodic Solutions ◽  
Water Waves ◽  
Small Amplitude ◽  
Capillary Water ◽  
Flat Bottom ◽  
Borel Set ◽  
Free Interface ◽  
Constant Vorticity ◽  
Wave Solutions ◽  
Full Lebesgue Measure

AbstractWe prove the first bifurcation result of time quasi-periodic traveling wave solutions for space periodic water waves with vorticity. In particular, we prove the existence of small amplitude time quasi-periodic solutions of the gravity-capillary water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space-periodic free interface. These quasi-periodic solutions exist for all the values of depth, gravity and vorticity, and restrict the surface tension to a Borel set of asymptotically full Lebesgue measure.

Shallow water wave generation by unsteady flow

1968 ◽  
Vol 31 (4) ◽  
pp. 779-788 ◽  
Author(s):  
J. E. Ffowcs Williams ◽  
D. L. Hawkings
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Water Wave ◽  
Small Amplitude ◽  
Point Of View ◽  
Sound Waves ◽  
Aerodynamic Sound ◽  
Shallow Layer ◽  
Sound Theory ◽  
Water Simulation

Small amplitude waves on a shallow layer of water are studied from the point of view used in aerodynamic sound theory. It is shown that many aspects of the generation and propagation of water waves are similar to those of sound waves in air. Certain differences are also discussed. It is concluded that shallow water simulation can be employed in the study of some aspects of aerodynamically generated sound.

scholarly journals Particle trajectories in solitary water waves

2007 ◽  
Vol 44 (03) ◽  
pp. 423-432 ◽  
Author(s):  
Adrian Constantin ◽  
Joachim Escher
Keyword(s):  
Water Waves ◽  
Particle Trajectories
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