Abstract

Fluid of uniform vorticity is expelled from a line source against a wall. An exact analytical solution is obtained for the nonlinear problem determining the final steady state. Sufficiently close to the source, the flow is irrotational and isotropic, turning on the vortical scale $\sqrt{Q/\omega}$ (for area flux $Q$ and vorticity $\omega$) to travel along the wall to the right (for $\omega>0$). The flow is linearly stable with perturbations propagating unattenuated along the interface between vortical and irrotational fluid. Fully nonlinear numerical integrations of the time-dependent equations of motion show that flow started from rest does indeed closely approach the steady state. Superposing an opposing dipole at the origin changes the momentum flux of the flow and leads to the growth of a bulge in the flow near the origin, a phenomenon seen in many rotating outflow experiments. When density variations are allowed the governing equation is no longer Laplace's equation but solutions can be obtained through a long-wave theory.

Co-authors: Sean Jamshidi (UCL), Robb McDonald (UCL)