Exact solution to a Liouville equation with Stuart vortex distribution on the surface of a torus.

ABSTRACT: A steady solution of the incompressible Euler equation on a toroidal surface T R , r of major radius R and minor radius r is provided. Its streamfunction is represented by an exact solution to the modified Liouville equation, ∇ T R , r 2 ψ = c   e d ψ + ( 8 / d ) κ , where ∇ T R , r 2 and κ denote the Laplace-Beltrami operator and the Gauss curvature of the toroidal surface respectively, and c, d are real parameters with cd < 0. This is a generalization of the flows with smooth vorticity distributions owing to Stuart (Stuart 1967 J. Fluid Mech. 29, 417-440. (doi:10.1017/S0022112067000941)) in the plane and Crowdy (Crowdy 2004 J. Fluid Mech. 498, 381-402. (doi:10.1017/S0022112003007043)) on the spherical surfac

SUBMITTER: Sakajo T 

PROVIDER: S-EPMC6501666 | biostudies-literature | 2019 Apr

REPOSITORIES: biostudies-literature