Symmetry of steady periodic surface water waves with vorticity
By Adrian Constantin, Joachim Escher. Journal of Fluid Mechanics, 2004
195 citations recorded by the source corpus.
For large classes of vorticities we prove that a steady periodic gravity water wave with a monotonic profile between crests and troughs must be symmetric. The analysis uses sharp maximum principles for elliptic partial differential equations.
View Paper: https://www.semanticscholar.org/paper/f19c0ffafca4b86404d697021dceeedcee4e8151
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- David Henry
- Erik Wahlén
- Mats Ehrnström
- Adrian Constantin
- Yue Liu
- Zhaoyang Yin
- Joachim Escher
- Zhiwu Lin
Citations in the corpus
- The trajectories of particles in Stokes waves (2006, background): “The symmetry of the free surface is actually guaranteed if we assume that the wave profile is monotone between crests and troughs [26, 7 ]. The only Stokes waves for which the free surface is not a continuously differentiable curve are the waves of greatest height in which case the curve is symmetr”
- Symmetry of steady periodic gravity water waves with vorticity (2007, background): “In [4, 5] monotonicity means strictly increasing from trough to crest, and vice versa.”
- Steady Periodic Water Waves with Constant Vorticity: Regularity and Local Bifurcation (2009, background): “The physical motivation for our study lies in the desire to understand wave-current interactions, since nonzero vorticity is the hallmark of a non-uniform underlying current [10, 12].”
- 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.”
- On Gerstner’s Water Wave (2008, background): “In recent years there has been growing interest in free surface water waves (see [1, 2, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 18, 20, 21, 22, 25, 35, 36]), but the current state of affairs regarding explicit solutions has not advanced much since the last century.”
- Global bifurcation of steady gravity water waves with critical layers (2014, unknown): “[12, 11].”