# Branch cuts of Stokes wave on deep water. Part II: Structure and location of branch points in infinite set of sheets of Riemann surface

@inproceedings{Lushnikov2015BranchCO, title={Branch cuts of Stokes wave on deep water. Part II: Structure and location of branch points in infinite set of sheets of Riemann surface}, author={Pavel M. Lushnikov}, year={2015} }

Stokes wave is a finite amplitude periodic gravity wave propagating with constant velocity in inviscid fluid. Complex analytical structure of Stokes wave is analyzed using a conformal mapping of a free fluid surface of Stokes wave into the real line with fluid domain mapped into the lower complex half-plane. There is one square root branch point per spatial period of Stokes located in the upper complex half-plane at the distance vc from the real axis. The increase of Stokes wave height results…

## 2 Citations

### Structure and location of branch point singularities for Stokes waves on deep water

- MathematicsJournal of Fluid Mechanics
- 2016

The Stokes wave is a finite-amplitude periodic gravity wave propagating with constant velocity in an inviscid fluid. The complex analytical structure of the Stokes wave is analysed using a conformal…

### New singularities for Stokes waves

- MathematicsJournal of Fluid Mechanics
- 2016

In 1880, Stokes famously demonstrated that the singularity that occurs at the crest of the steepest possible water wave in infinite depth must correspond to a corner of $120^{\circ }$ . Here, the…

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