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We conduct a series of numerical experiments into the nature ofthree-dimensional (3D) hydrodynamics in the postbounce stalled-shock phase ofcore-collapse supernovae using 3D general-relativistic hydrodynamic simulationsof a $27$-$M_\odot$ progenitor star with a neutrino leakage/heating scheme. Wevary the strength of neutrino heating and find three cases of 3D dynamics: (1)neutrino-driven convection, (2) initially neutrino-driven convection andsubsequent development of the standing accretion shock instability (SASI), (3)SASI dominated evolution. This confirms previous 3D results of Hanke et al.2013, ApJ 770, 66 and Couch & Connor 2014, ApJ 785, 123. We carry outsimulations with resolutions differing by up to a factor of $\sim$4 anddemonstrate that low resolution is artificially favorable for explosion in the3D convection-dominated case, since it decreases the efficiency of energytransport to small scales. Low resolution results in higher radial convectivefluxes of energy and enthalpy, more fully buoyant mass, and stronger neutrinoheating. In the SASI-dominated case, lower resolution damps SASI oscillations.In the convection-dominated case, a quasi-stationary angular kinetic energyspectrum $E(\ell)$ develops in the heating layer. Like other 3D studies, wefind $E(\ell) \propto \ell^{-1}$ in the "inertial range," while theory andlocal simulations argue for $E(\ell) \propto \ell^{-5/3}$. We argue thatcurrent 3D simulations do not resolve the inertial range of turbulence and areaffected by numerical viscosity up to the energy containing scale, creating a"bottleneck" that prevents an efficient turbulent cascade.

Neutrino-driven Turbulent Convection and Standing Accretion Shock Instability in Three-Dimensional Core-Collapse Supernovae