  Supersonic turbulence in the interstellar medium (ISM) is closely linked to
the formation of stars, and hence many theories connect the stellar initial
mass function (IMF) with the turbulent properties of molecular clouds. Here we
test three turbulence-based IMF models (by Padoan & Nordlund 2002, Hennebelle &
Chabrier 2008, and Hopkins 2012), which predict the relation between the
high-mass slope ($\Gamma$) of the IMF, $\mathrm{d} N/\mathrm{d} \log M \propto
M^{\Gamma}$ and the exponent n of the velocity power spectrum of turbulence,
$E_v(k)\propto k^{-n} $, where $n\approx 2$ corresponds to typical ISM
turbulence. Using hydrodynamic simulations, we drive turbulence with an unusual
index of $n\approx 1$, measure $\Gamma$, and compare the results with $n\approx
2$. We find that reducing $n$ from 2 to 1 primarily changes the high-mass
region of the IMF (beyond the median mass), where we measure high-mass slopes
within the 95 per cent confidence interval of $-1.5<\Gamma<-1$ for $n \approx
1$ and $-3.7<\Gamma<-2.4$ for $n\approx 2$, respectively. Thus, we find that
$n=1$ results in a significantly flatter high-mass slope of the IMF, with more
massive stars formed than for $n \approx 2$. We compare these simulations with
the predictions of the three IMF theories. We find that while the Padoan &
Nordlund theory matches our simulations with fair accuracy, the other theories
either fail to reproduce the main qualitative outcome of the simulations or
require some modifications. We conclude that turbulence plays a key role in
shaping the IMF, with a shallower turbulence power spectrum producing a
shallower high-mass IMF, and hence more massive stars.
