Edge waves along a sloping beach

By Adrian Constantin. 2001

174 citations recorded by the source corpus.

We construct a family of explicit rotational solutions to the nonlinear governing equations for water waves, describing edge waves propagating over a planesloping beach. A detailed analysis of the edge wave dynamics and of the run-up pattern is made possible by the use of the Lagrangian approach to the water motion.

Subfields: Earth-Surface Processes, Oceanography

View Paper: https://www.semanticscholar.org/paper/ff2f0fbb5f362cfe43348d3f2571925a68becf21

How researchers see this paper

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

In Earth-Surface Processes

1. David Henry
2. Adrian Constantin
3. Erik Wahlén
4. Eugen Varvaruca
5. Walter A. Strauss
6. R. Johnson
7. Yue Liu

In Oceanography

1. Adrian Constantin
2. David Henry
3. Erik Wahlén
4. Eugen Varvaruca
5. R. Johnson
6. Walter A. Strauss
7. Yue Liu
8. Bogdan–Vasile Matioc

Citations in the corpus

• 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 ].”
• On Gerstner’s Water Wave (2008, background): “It is interesting to note that the analysis presented here was adapted by the same author in [4] to present an explicit solution of the governing equations which describes the propagation of edge-waves along a sloping beach.”
• 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.”