2024/09/12 by David Meyer, Meyer, David, Christian Seis +1 · 1 citation
Engineering · #Fluid dynamics and aerodynamics studies #Fluid Dynamics and Vibration Analysis #Spacecraft and Cryogenic Technologies
paper · pdf · doi:10.48550/arxiv.2409.08220
In this work, we construct traveling wave solutions to the two-phase Euler equations, featuring a vortex sheet at the interface between the two phases. The inner phase exhibits a uniform vorticity distribution and may represent a vacuum, forming what is known as a hollow vortex. These traveling waves take the form of ring-shaped vortices with a small cross-sectional radius, referred to as thin rings. Our construction is based on the implicit function theorem, which also guarantees local uniqueness of the solutions. Additionally, we derive asymptotics for the speed of the ring, generalizing the well-known Kelvin--Hicks formula to cases that include surface tension.