  Neutrino-driven convection plays a crucial role in the development of
core-collapse supernova (CCSN) explosions. However, the complex mechanism that
triggers the shock revival and the subsequent explosion has remained
inscrutable for many decades. Multidimensional simulations suggest that the
growth of fluid instabilities and the development of turbulent convection will
determine the morphology of the explosion. We have performed 3D simulations
using spherical-polar coordinates covering a reduced angular extent (90 degree
computational domain), and with angular resolutions of 2 degrees, 1 degree, 1/2
degree, and 1/4 degree, to study the development of turbulence in core-collapse
supernova explosions on a time scale of order 100 ms. We have employed the
multi-physics Chimera code that includes detailed nuclear physics and spectral
neutrino transport. Coarse resolution models do not develop an inertial range,
presumably due to the bottleneck effect, such that the energy is prevented from
cascading down to small scales and tends to accumulate at large scales.
High-resolution models instead, start to recover the k^{-5/3} scaling of
Kolmogorov's theory. Stochasticity and few simulation samples limit our ability
to predict the development of explosions. Over the simulated time period, our
models show no clear trend in improving (or diminishing) conditions for
explosion as the angular resolution is increased. However, we find that
turbulence provides an effective pressure behind the shock (approx. 40 - 50 %
of the thermal pressure), which can contribute to the shock revival and be
conducive for the development of the explosion. Finally, we show that the
turbulent energy power spectrum of reduced angular extent and full 4 pi models
are consistent, thus indicating that a 90 degree computational domain is an
adequate configuration to study the character of turbulence in CCSNe.
