Steady vortex patch with polygonal symmetry for the planar Euler equations in a disc

Publication date: February 2020Source: Nonlinear Analysis: Real World Applications, Volume 51Author(s): Daomin Cao, Jie Wan, Guodong WangAbstractIn this paper, we construct two types of vortex patch equilibria for the two-dimensional Euler equations in a disc. The first type is called the “N+1 type” equilibrium, in which a central vortex patch is surrounded by N identical patches with opposite signs, and the other type is called the “2N type” equilibrium, in which the centers of N identical positive patches and N negative patches lie evenly on a circle. The construction is performed by solving a variational problem for the vorticity in which the kinetic energy is maximized subject to some symmetry constraints, and then analyzing the asymptotic behavior as the vorticity strength goes to infinity.

Source: Nonlinear Analysis: Real World Applications - August 29, 2019 Category: Research Source Type: research