  Here we show how Feynman's simplified model for the Josephson junction, as a
macroscopic two-state coupled quantum system, has a one-to-one correspondence
with the stable dynamics of two interfacial Rossby waves in piecewise linear
shear flows. The conservation of electric charge and energy of the
superconducting electron gas layers become respectively equivalent to the
conservation of wave action and pseudoenergy of the Rossby waves. Quantum-like
tunneling is enabled via action-at-a-distance between the two Rossby waves.
Furthermore, the quantum-like phenomena of avoided crossing between
eigenstates, described by the Klein-Gordon equation, is obtained as well in the
classical shear flow system. In the latter, it results from the inherent
difference in pseudoenergy between the in-phase and anti-phased normal modes of
the interfacial waves. This provides an intuitive physical meaning to the role
of the wavefunction's phase in the quantum system. A partial analog to the
quantum collapse of the wavefunction is also obtained due to the existence of a
separatrix between "normal mode regions of influence" on the phase plane,
describing the system's dynamics. As for two-state quantum bits (qubits), the
two-Rossby wave system solutions can be represented on a Bloch sphere, where
the Hadamard gate transforms the two normal modes/eigenstates into an intuitive
computational basis in which only one interface is occupied by a Rossby wave.
Yet, it is a classical system which lacks exact analogs to collapse and
entanglement, thus cannot be used for quantum computation, even in principle.
