Steady Periodic Water Waves with Constant Vorticity: Regularity and Local Bifurcation

By Adrian Constantin, Eugen Varvaruca. 2009

215 citations recorded by the source corpus.

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential equation for a periodic function of one variable. The new formulation leads to a regularity result and, by use of bifurcation theory, to the existence of waves of small amplitude even in the presence of stagnation points in the flow.

Subfields: Earth-Surface Processes, Numerical Analysis, Oceanography

View Paper: https://www.semanticscholar.org/paper/01e9b6732095787de9d8222ef81a9ba6df8d84e3

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. Adrian Constantin
2. Eugen Varvaruca
3. Walter A. Strauss
4. Georg S. Weiss
5. David Henry
6. R. Johnson
7. Rossen I. Ivanov
8. Yue Liu

In Numerical Analysis

1. Eugen Varvaruca
2. Adrian Constantin
3. Georg S. Weiss
4. Walter A. Strauss
5. Erik Wahlén

In Oceanography

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

Citations in the corpus

• Global bifurcation of steady gravity water waves with critical layers (2014, methodology): “Construction of small-amplitude waves via local bifurcation has already been accomplished in [49, 18].”
• A geometric approach to generalized Stokes conjectures (2009, background): “Also, for waves with non-zero vorticity, ψ need not be monotone in the y-direction [34, 10].”