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Spiral perturbations in a gravitationally unstable accretion disk regulatedisk evolution through angular-momentum transport and heating and provide anobservational signature of gravitational instability (GI). We use global 3Dsimulations to systematically characterize and understand these spiralperturbations. The spiral perturbations and the resulting transport are overallinsensitive to the cooling type, with the exception that radiative cooling,especially in the optically thick regime, reduces the amplitude of temperatureperturbations. Spiral perturbations are localized around corotation, allowingtransport to be approximated by a local $\alpha$ viscosity to zeroth order inaspect ratio ($H/R$), but only after averaging over multiple orbits in timeand/or multiple scale heights in space. Meanwhile, large-amplitudeperturbations from strong gravitoturbulence can cause $\mathcalO(\alpha^{1/2})$ deviation in the cooling rate of the disk. We developempirical prescriptions for the angular-momentum transport, heating, andcooling in a gravitoturbulent disk that capture the deviation from a viscous,unperturbed disk to first order in $H/R$ and $\alpha^{1/2}$. The spiralperturbations in saturated gravitoturbulence are clumpy, with dense clumpsforming through the nonlinear coupling between multiple modes at different $m$.Observationally, the clumpy gravitoturbulence produced by saturated GI can bemistaken with observational noise or embedded companions, especially underfinite resolution. Meanwhile, grand-design spirals with $m$-fold symmetry maybe uncommon among disks in saturated gravitoturbulence, and we speculate thatthey may instead be a signature of recently triggered or decaying GI.

Global Simulations of Gravitational Instability in Protostellar Disks  with Full Radiation Transport II. Locality of Gravitoturbulence, Clumpy  Spirals, and Implications for Observable Substructure