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 through the timedependent conformal mapping 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} and the complex velocity. We also proved the nonexistence of the timedependent rational solution of that problem for the second and the firstorder moving pole.
 Publication:

Water Waves
 Pub Date:
 April 2021
 DOI:
 10.1007/s4228602000040y
 arXiv:
 arXiv:1911.11609
 Bibcode:
 2021WatWa...3..251L
 Keywords:

 Water waves;
 Complex singularities;
 Conformal map;
 Fluid dynamics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Nonlinear Sciences  Pattern Formation and Solitons;
 Physics  Fluid Dynamics
 EPrint:
 16 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1809.09584