We study hydrodynamic spin coupling in a two-rotor corral using direct numerical simulation of the two-dimensional incompressible Navier-Stokes equations. An active rotor is driven at angular velocity $\mathrm{\Omega }$, and a nearby torque-free passive rotor selects an angular velocity $\omega$ through hydrodynamic torque balance. The signed gear ratio $\mathrm{\Gamma }=\omega /\mathrm{\Omega }$ distinguishes corotation from counterrotation, with Reynolds number $\mathrm{Re}=\left|\mathrm{\Omega }\right|r^2/\nu$. Motivated by a recent quasi-two-dimensional experiment [Smith et al., Phys. Rev. Lett. 136, 024001 (2026)], we use a distributed Lagrange multiplier/fictitious domain method to compute planar phase diagrams of $\mathrm{\Gamma }(G,\mathrm{Re})$ at corral sizes $C=3$, 4.5, and 6. The planar model recovers the benchmark gap route at $\mathrm{Re}=20$: An intermediate counterrotation band, a wide-gap transition to corotation, gear-ratio magnitudes of order ${10}^{-2}$, and the observed sequence of vortex attachment, detachment, and merger. It also produces a reentrant-like gap structure with a small-gap corotation region whose relation to the experimental close-range geometric state remains unresolved. The main discrepancy is the high-$\mathrm{Re}$ boundary. At the experimental midgap transect $G\approx 0.3$, the planar gear ratio approaches zero from the counterrotating side but does not cross through $\mathrm{Re}=400$; at the narrower gap $G=0.22$, by contrast, the planar terminal spin reverses near $\mathrm{Re}=44$ while a gap-facing arc of counterrotating traction persists. The computed traction-based arc exhibits less contraction and deflection than the pathline-defined experimental shear zone; because these are different observables, the comparison identifies distinct diagnostic signatures without assigning the discrepancy to a unique mechanism. The planar model captures the broad gap-route structure and supports Reynolds-driven spin reversal, but places the boundary at smaller gaps over the sampled range. Finite-depth secondary motion, end-wall stresses, and apparatus geometry are candidate contributors to the remaining mismatch.

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• Fluid-particle interactions
• Vortex dynamics
• 2-dimensional systems
• Direct numerical simulations
• Navier-Stokes equation