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 time-dependent 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 /zw 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.
- Publication:
-
Water Waves
- Pub Date:
- April 2021
- DOI:
- 10.1007/s42286-020-00040-y
- 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
- E-Print:
- 16 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1809.09584