2012/06/10 by В. Е. Захаров, V. E. Zakharov, Zakharov, V. E. +3 · 1 citation
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Aquatic and Environmental Studies #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Fluid dynamics and aerodynamics studies #nlin.SI #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1206.2046
arxiv created 2012/06/10 · openalex publication_date 2012/06/10 · arxiv updated 2012/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The potential flow of two-dimensional ideal incompressible fluid with a free surface is studied. Using the theory of conformal mappings and Hamiltonian formalism allows us to derive exact equations of surface evolution. Simple form of the equations helped to discover new integrals of motion. These integrals are connected with the analytical properties of conformal mapping and complex velocity. Simple form of the equations also makes the numerical simulations of the free surface evolution very straightforward. In the limit of almost flat surface the equations can be reduced to the Hopf equation.