# Poles and Branch Cuts in Free Surface Hydrodynamics

@article{Lushnikov2019PolesAB, title={Poles and Branch Cuts in Free Surface Hydrodynamics}, author={Pavel M. Lushnikov and V. E. Zakharov}, journal={Water Waves}, year={2019}, volume={3}, pages={251-266} }

We consider the motion of ideal incompressible fluid with free surface. We analyzed the exact fluid dynamics through the time-dependent conformal mapping $$z=x+iy=z(w,t)$$ z = x + i y = z ( w , t ) of the lower complex half plane of the conformal variable w into the area occupied by fluid. We established the exact results on the existence vs. nonexistence of the pole and power law branch point solutions for $$1/z_w$$ 1 / z w and the complex velocity. We also proved the nonexistence of the time…

## 3 Citations

Special Issue Dedicated to Walter Craig

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This volume is dedicated to the memory of our dear friend and colleagueWalter Craig who sadly passed away on January 18, 2019 in Hamilton, Ontario, Canada.Walter was a world renowned scholar for his…

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We study a 2D 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 solution of Euler equations…

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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…

## References

SHOWING 1-10 OF 51 REFERENCES

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…

Explosive Development of the Kelvin–Helmholtz Quantum Instability on the He-II Free Surface

- PhysicsJournal of Experimental and Theoretical Physics
- 2019

Exact Local Solutions for the Formation of Singularities on the Free Surface of an Ideal Fluid

- Mathematics, Physics
- 2018

A classical problem of the dynamics of the free surface of an ideal incompressible fluid with infinite depth has been considered. It has been found that the regime of motion of the fluid where the…

Numerical Modeling of Sea Waves

- Physics
- 2016

The paper describes characteristics of numerical models of surface waves based on full equations for the flow with free surface in potential approximation, as well as their efficiency and…

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…

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…

On the theory of oscillatory waves

- Physics
- 2009

I n the Report of the Fourteenth Meeting of the British Association for the Advancement of Science it is stated by Mr Russell, as a result of his experiments, that the velocity of propagation of a…

Generalized vortex methods for free-surface flow problems

- PhysicsJournal of Fluid Mechanics
- 1982

The motion of free surfaces in incompressible, irrotational, inviscid layered flows is studied by evolution equations for the position of the free surfaces and appropriate dipole (vortex) and source…

On the connection between thin vortex layers and vortex sheets

- PhysicsJournal of Fluid Mechanics
- 1990

The equations for the two-dimensional motion of a layer of uniform vorticity in an incompressible, inviscid fluid are examined in the limit of small thickness. Under the right circumstances, the…

A study of singularity formation in vortex-sheet motion by a spectrally accurate vortex method

- MathematicsJournal of Fluid Mechanics
- 1992

Moore's asymptotic analysis of vortex-sheet motion predicts that the Kelvin–Helmholtz instability leads to the formation of a weak singularity in the sheet profile at a finite time. The numerical…