  We investigate the generation of turbulence during the prestellar
gravitational contraction of a turbulent spherical core. We define the ratio
$g$ of the one-dimensional turbulent velocity dispersion, $\sigma_\mathrm{1D}$
to the gravitational velocity $v_g$, to then analytically estimate $g$ under
the assumptions of a) equipartition or virial equilibrium between the
gravitational ($E_g$) and turbulent kinetic ($E_\mathrm{turb}$) energies and b)
stationarity of transfer from gravitational to turbulent energy (implying
$E_\mathrm{turb}/E_g=$cst). In the equipartition and virial cases, we find
$g=\sqrt{1/3}\approx0.58$ and $g=\sqrt{1/6}\approx0.41$, respectively; in the
stationary case we find $g=\langle v_\mathrm{rad}\rangle L_d/(4\pi\sqrt{3}\eta
Rv_g)$, where $\eta$ is an efficiency factor, $L_d$ is the energy injection
scale of the turbulence, and $R$ is the core's radius. Next, we perform AMR
simulations of the prestellar collapse of an isothermal, transonic turbulent
core at two different resolutions, and a non-turbulent control simulation. We
find that the turbulent simulations collapse at the same rate as the
non-turbulent one, so that the turbulence generation does not significantly
slow down the collapse. We also find that a) the simulations approach near
balance between the rates of energy injection from the collapse and of
turbulence dissipation; b) $g\approx0.395\pm0.035$, close to the "virial" value
(turbulence is $\sim35-40\%$ of non-thermal linewidth); c) the injection scale
is $L_d\lesssim R$, and d) the "turbulent pressure" $\rho\sigma_\mathrm{1D}^2$
scales as $\sim\rho^{1.64}$, an apparently nearly-adiabatic scaling. We propose
that this scaling and the nearly virial values of the turbulent velocity
dispersion may be reconciled with the non-delayed collapse rate if the
turbulence is dissipated as soon as it is generated.
