Relating interfacial Rossby wave interaction in shear flows with Feynman's two-state coupled quantum system model for the Josephson junction

Super-currents, tunneling across insulators in Josephson junctions, have a one-to-one classical analog to action-at-a-distance between two interfacial Rossby waves in shear flows. Quantum avoided crossing between eigenstates, described by the Klein-Gordon equation, is obtained as well for the Rossby wave normal modes. Both the quantum and the classical dynamics are formulated as coupled two-state systems and presented on a Bloch sphere, where the Hadamard gate transforms the two normal modes into an intuitive computational basis of two single Rossby waves. Yet, lacking analogs to quantum collapse and entanglement, the Rossby wave system cannot serve as a qubit prototype, even in principle.