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In this paper we derive the equations of motion for two-layer point vortexmotion on the upper half plane. We study the invariants using symmetry,including the Hamiltonian and show that the two vortex problem is integrable.We characterize all two vortex motions for the cases where the vortex strengthsare both equal, $\Gamma_{1}=\Gamma_{2}=1$ and when they are opposite$\Gamma_{1}=-\Gamma_{2}=1$. We also prove that there are no equilibria for thetwo vortex problem when $\Gamma_{1}=-\Gamma_{2}=1$.\ We show that there is onlyone relative equilibrium configuration when $\Gamma_{1}=\Gamma_{2}=1$ and thevortices are in different layers. We also make observations concerning thefinite-time collapse of two vortices in the half plane. We then compare theregimes of motion for both cases (motion on the half plane) with the case ofthe two-layer vortex problem on the entire plane. We also study several classesof streamline topologies for two vortices in different layers. We conclude witha Hamiltonian study of integrable two-layer 3 vortex motion on the half planeby studying integrable symmetrical configurations and provide a rich class ofnew relative equilibria.

Integrable two layer point vortex motion on the half plane