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We present the first magnetohydrodynamic simulation in which a circumbinarydisk around a relativistic binary black hole feeds mass to individual accretiondisks ("mini-disks") around each black hole. Mass flow through the accretionstreams linking the circumbinary disk to the mini-disks is modulatedquasi-periodically by the streams' interaction with a nonlinear $m=1$ densityfeature, or "lump", at the inner edge of the circumbinary disk: the streamsupplying each mini-disk comes into phase with the lump at a frequency $0.74$times the binary orbital frequency. Because the binary is relativistic, thetidal truncation radii of the mini-disks are not much larger than theirinnermost stable circular orbits; consequently, the mini-disks' inflow timesare shorter than the conventional estimate and are comparable to the streammodulation period. As a result, the mini-disks are always in inflowdisequilibrium, with their masses and spiral density wave structures respondingto the stream's quasi-periodic modulation. The fluctuations in each mini-disk'smass are so large that as much as $75\%$ of the total mini-disk mass can becontained within a single mini-disk. Such quasi-periodic modulation of themini-disk structure may introduce distinctive time-dependent features in thebinary's electromagnetic emission.

Quasi-Periodic Behavior of Mini-Disks in Binary Black Holes Approaching Merger