# Complex singularity of a stokes wave

@article{Dyachenko2013ComplexSO, title={Complex singularity of a stokes wave}, author={Sergey A. Dyachenko and Pavel M. Lushnikov and A. O. Korotkevich}, journal={JETP Letters}, year={2013}, volume={98}, pages={675-679} }

Two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth can be described by a conformal map of the fluid domain into the complex lower half-plane. Stokes wave is the fully nonlinear gravity wave propagating with the constant velocity. The increase in the scaled wave height H/λ from the linear limit H/λ = 0 to the critical value Hmax/λ marks the transition from the limit of almost linear wave to a strongly nonlinear limiting Stokes wave. Here, H is…

## 33 Citations

### Branch Cuts of Stokes Wave on Deep Water. Part I: Numerical Solution and Padé Approximation

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Complex analytical structure of Stokes wave for two‐dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth is analyzed. Stokes wave is the fully nonlinear…

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

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- 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…

### Short branch cut approximation in two-dimensional hydrodynamics with free surface

- MathematicsProceedings of the Royal Society A
- 2021

A potential motion of ideal incompressible fluid with a free surface and infinite depth is considered in two-dimensional geometry. A time-dependent conformal mapping of the lower complex half-plane…

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

- Mathematics
- 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 surface in two-dimensional potential flow: singularities, invariants and virtual fluid

- MathematicsJournal of Fluid Mechanics
- 2022

Abstract We study a two-dimensional (2-D) potential flow of an ideal fluid with a free surface with decaying conditions at infinity. By using the conformal variables approach, we study a particular…

### Waves over Curved Bottom: The Method of Composite Conformal Mapping

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Abstract A compact and efficient numerical method is described for studying plane flows of an ideal fluid with a smooth free boundary over a curved and nonuniformly moving bottom. Exact equations of…

### Numerical Simulation of the Wave Breaking Process on the Surface of a Dielectric Liquid in a Tangential Electric Field

- Physics2019 IEEE 20th International Conference on Dielectric Liquids (ICDL)
- 2019

This work is devoted to numerical simulation of the process of interaction between nonlinear waves propagating along the free surface of dielectric liquid in a strong tangential electric field. The…

### Wave breaking on the surface of a dielectric liquid in a horizontal electric field

- PhysicsIEEE Transactions on Dielectrics and Electrical Insulation
- 2020

The weak nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the…

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

- Mathematics
- 2015

uid surface of Stokes wave into the real line with uid 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…

### 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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