Viscous effects on the temporal behavior and spatial structure of torsional oscillation normal modes of the Earth's fluid core are examined. If the viscosity of the fluid core is equal to that inferred from theoretical and experimental studies of liquid metals, then viscous effects on torsional oscillations are unlikely to be important; however, if the viscosity is as high as allowed from observational constraints, then Ekman layers at the fluid core boundaries may play an important role in damping torsional oscillations. The observationally inferred decay time of decadal torsional oscillations leads to an upper bound on the viscosity of the fluid core at the core-mantle boundary of the order of 10⁻² m²/s. A sufficiently large viscosity would result in torsional oscillation normal modes that undergo pure decay, as opposed to damped oscillatory motion. The viscosity value at which the temporal behavior switches between these regimes depends on the period of the normal mode. Numerical geodynamo models must reach an Ekman number of the order of 10⁻⁷ for free-slip boundaries or 10⁻¹⁰ for no-slip boundaries to accurately model the temporal behavior of decadal period torsional oscillations.