Dynamics of a nonlinear dipole vortex

A localized stationary dipole solution to the Euler equations with a relationship between the vorticity and streamfunction given as omega=-psi+psi(3) is presented. By numerical integration of the Euler equations this dipole is shown to be unstable. However, the initially unstable dipole reorganizes itself into a new nonlinear dipole, which is found to be stable. This new structure has a functional relationship given as omega=alpha psi+beta psi(3)-gamma psi(5). Such dipoles are stable to head-on collisions and they are capable of creating tripolar structures when colliding off axis. The effects of increasing Newtonian viscosity on the nonlinear dipole is studied revealing that even though the nonlinearity is weakening, the dipole does not relax towards a Lamb dipole. (C) 1995 American Institute of Physics.