On the deep water wave motion

By Adrian Constantin. 2001

226 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Oceanography

View Paper: https://www.semanticscholar.org/paper/51e0a4ff5a302434413737db735e6fe1498c1425

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. David Henry
2. Erik Wahlén
3. Joachim Escher
4. Walter A. Strauss

In Oceanography

1. Adrian Constantin
2. Erik Wahlén
3. David Henry
4. Walter A. Strauss
5. Joachim Escher
6. Mats Ehrnström
7. Eugen Varvaruca
8. R. Johnson

Citations in the corpus

• Edge waves along a sloping beach (2001, methodology): “Due to the small displacements associated with these waves, the governing equations for water waves or the shallow-water equations are linearized (Minzoni & Whitham 1977 showed that both approximations are equally consistent) and this simplification permits a thorough analysis.”
• On Gerstner’s Water Wave (2008, methodology): “It is our aim in this paper to present an alternative approach to the analysis of Gerstner’s wave, mainly the use of degree theory, and in the process hope to simplify some of the proofs contained in [3].”
• Symmetry of steady periodic gravity water waves with vorticity (2007, background): “Notice that the only known explicit nontrivial gravity water wave (found by Gerstner [15] and later rediscovered independently by Rankine [21]) is for water of infinite depth with vorticity, and the surface profile is symmetric (see the discussion in [2]).”
• Exact steady periodic water waves with vorticity (2004, background): “In 1802 Gerstner [7, 15] constructed an explicit example of a periodic traveling wave in water of infinite depth with a particular nonzero vorticity.”
• The trajectories of particles in Stokes waves (2006, background): “(see [ 5 ]). Interestingly, for certain specific nonvanishing vorticities there are even nontrivial three-dimensional explicit solutions to the governing equations for water waves with all particle paths closed [6].”
• Steady periodic capillary waves with vorticity (2006, background): “In the last few years there has been an increasing amount of research in the area of water waves with vorticity, see [3], [4] regarding the symmetry of rotational water waves, [12], [15], [16], [24] for questions of uniqueness and [1], [2], [5], [6], [25], [26] for existence results.”
• Symmetry of steady periodic surface water waves with vorticity (2004, background): “In 1809 Gerstner constructed an explicit example of a periodic travelling wave in water of infinite depth with a particular non-zero vorticity – see (Constantin 2001) for a discussion.”