  We present the dynamical properties of 294 cores embedded in twelve IRDCs
observed as part of the ASHES Survey. Protostellar cores have higher gas
masses, surface densities, column densities, and volume densities than
prestellar cores, indicating core mass growth from the prestellar to the
protostellar phase. We find that ~80% of cores with virial parameter ($\alpha$)
measurements are gravitationally bound ($\alpha$< 2). We also find an
anti-correlation between the mass and the virial parameter of cores, with
massive cores having on average lower virial parameters. Protostellar cores are
more gravitationally bound than prestellar cores, with an average virial
parameter of 1.2 and 1.5, respectively. The observed non-thermal velocity
dispersion (from N$_{2}$D$^{+}$ or DCO$^{+}$) is consistent with simulations in
which turbulence is continuously injected, whereas the core-to-core velocity
dispersion is neither in agreement with driven nor decaying turbulence
simulations. We find no significant increment in the line velocity dispersion
from prestellar to protostellar cores, suggesting that dense gas within the
core traced by these deuterated molecules is not yet severely affected by
turbulence injected from outflow activity at the early evolutionary stages
traced in ASHES. The most massive cores are strongly self-gravitating and have
greater surface density, Mach number, and velocity dispersion than cores with
lower masses. Dense cores have not significant velocity shifts relative to
their low-density envelopes, suggesting that dense cores are co-moving with
their envelopes. We conclude that the observed core properties are more in line
with predictions of ``clump-fed" scenarios rather than with ``core-fed"
scenarios.
