Global bifurcation of steady gravity water waves with critical layers
By Adrian Constantin, Walter A. Strauss, Eugen Varvaruca. 2014
204 citations recorded by the source corpus.
We construct families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed, in particular establishing the existence of waves of large amplitude. A Riemann–Hilbert problem approach is used to recast the governing equations as a one-dimensional elliptic pseudodifferential equation with a scalar constraint. The structural properties of this formulation, which arises as the Euler–Lagrange equation of an energy functional, enable us to develop a theory of analytic global bifurcation.
Subfields: Applied Mathematics, Earth-Surface Processes, Oceanography
View Paper: https://www.semanticscholar.org/paper/ace4cc139edbda2a0f7bdb781533751b0954e9a6
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Rossen I. Ivanov
- Adrian Constantin
- Yue Liu
- Zhaoyang Yin
- Yong Zhou
- Joachim Escher
- David Henry
- Erik Wahlén
In Earth-Surface Processes
- Rossen I. Ivanov
- Adrian Constantin
- David Henry
- Eugen Varvaruca
- R. Johnson
- Walter A. Strauss
- Yue Liu
- Erik Wahlén
In Oceanography
- Rossen I. Ivanov
- Adrian Constantin
- David Henry
- Yue Liu
- Eugen Varvaruca
- Erik Wahlén
- R. Johnson
- Robin Ming Chen
Citations in the corpus
- Equatorial Wave–Current Interactions (2019, methodology): “It is therefore advisable to rely on the nonlinear alternative to the conventional linear viscous boundary-layer approach for the description of the flow in the neighbourhood of critical levels, where Kelvin ‘cat’s eye’ flow patterns appear (see the discussion in [9] for the somewhat simpler case of”