  We investigate the relation between the turbulent Mach number (\mach) and the
escape fraction of Lyman continuum photons ($f_{\rm esc}$) in high-redshift
galaxies. Approximating the turbulence as isothermal and isotropic, we show
that the increase in the variance in column densities from $\mathcal{M}=1$ to
$\mathcal{M}=10$ causes $f_{\rm esc}$ to increase by $\approx 25$\%, and the
increase from $\mathcal{M}=1$ to $\mathcal{M}=20$ causes $f_{\rm esc}$ to
increases by $\approx 50$\% for a medium with opacity $\tau\approx1$. At a
fixed Mach number, the correction factor for escape fraction relative to a
constant column density case scales exponentially with the opacity in the cell,
which has a large impact for simulated star forming regions. Furthermore, in
simulations of isotropic turbulence with full atomic/ionic cooling and
chemistry, the fraction of HI drops by a factor of $\approx 2.5$ at
$\mathcal{M}\approx10$ even when the mean temperature is $\approx5\times10^3
K$. If turbulence is unresolved, these effects together enhance $f_{\rm esc}$
by a factor $>3$ at Mach numbers above 10. Such Mach numbers are common at
high-redshifts where vigorous turbulence is driven by supernovae, gravitational
instabilities, and merger activity, as shown both by numerical simulations and
observations. These results, if implemented in the current hydrodynamical
cosmological simulations to account for unresolved turbulence, can boost the
theoretical predictions of the Lyman Continuum photon escape fraction and
further constrain the sources of reionization.
