Abstract
We formulate the two-layer quasigeostrophic potential vortex (QGPV) model as an infinite-dimensional Hamiltonian system and apply Noether’s theorem to derive the conservation laws for these equations. The point (singular) vortex QGPV model is also analyzed as a finite-dimensional Hamiltonian system. By virtue of its point symmetries, the invariants for the finite-dimensional system are obtained. The existence of these point symmetries is used to prove the integrability of the three-vortex QGPV problem. We analyze the relative equilibrium configurations for the three-vortex, two-layer problem and study collapsing and merging (collapse in different layers) configurations. We also study two special classes of symmetrical four-vortex QGPV problems and establish their integrability and present some simulations for one of these classes of integrable QGPV four-vortex problems.
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