1983/04/01 by Joseph B. Keller, Michael J. Miksis · 4 citations
Engineering · #Fluid Dynamics Simulations and Interactions #Fluid Dynamics and Heat Transfer #Fluid dynamics and aerodynamics studies
paper · doi:10.1137/0143018
crossref issued 1983/04/01 · crossref published 1983/04/01 · crossref published-print 1983/04/01 · openalex publication_date 1983/04/01 · crossref created 2005/02/23 · crossref deposited 2017/01/29 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/30
Time-dependent potential flows of a liquid with a free surface are considered, with surface tension the force that drives them. Two types of configuration are analyzed, in each of which the flow and the free surface are self-similar at all times. One is a model of a breaking sheet of liquid. The other is a model of the flow near the intersection of the free surface of a liquid with a solid boundary. In both flows, the velocities are found to be proportional to ( σ /ρ t )1/3 , where σ is the surface tension, ρ is the liquid density and t is the time from the start of the motion. Each free surface is determined by converting the problem to an integrodifferential system of equations for the free surface and the potential on it. This system is discretized and solved numerically. On the resulting surfaces there are waves, which are also calculated analytically.