Poles and branch cuts in free surface hydrodynamics

Abstract

We consider the motion of ideal incompressible fluid with free surface. We analyzed the exact fluid dynamics though the time-dependent conformal mapping $z=x+iy=z(w,t)$ 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 $1/z_w$ and the complex velocity. We also proved the nonexistence of the time-dependent rational solution of that problem for the second and the first order moving pole.

arXiv comment16 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1809.09584

References in corpus (9)

• Branch cuts of Stokes wave on deep water. Part I: Numerical solution and Padé approximation
• New conformal mapping for adaptive resolving of the complex singularities of Stokes wave
• Singularity formation on a fluid interface during the Kelvin-Helmholtz instability development
• Exact solutions for nonlinear development of Kelvin-Helmholtz instability for counterflow of superfluid and normal components of Helium II
• Charged-Surface Instability Development in Liquid Helium; Exact Solutions
• Dynamics of Poles in 2D Hydrodynamics with Free Surface: New Constants of Motion
• Non-Canonical Hamiltonian Structure and Poisson Bracket for 2D Hydrodynamics with Free Surface
• Exactly Integrable Dynamics of Interface between Ideal Fluid and Light Viscous Fluid
• Short branch cut approximation in $2$D Hydrodynamics with Free Surface

Cited by in corpus (1)

• Free Surface in 2D Potential Flow: Singularities, Invariants and Virtual Fluid