  Massive ($M >30\,$M$_{\odot}$) stars exhibit luminosities that are near the
Eddington-limit for electron scattering causing the increase in opacity
associated with iron at $T\approx180,000\,$K to trigger supersonic convection
in their outer envelopes. Three dimensional radiative hydrodynamics simulations
by Jiang and collaborators with the Athena++ computational tool have found
order of magnitude density and radiative flux fluctuations in these convective
regions, even at optical depths $\gg100$. We show here that radiation can
diffuse out of a parcel during the timescale of convection in these optically
thick parts of the star, motivating our use of a "pseudo" Mach number to
characterize both the fluctuation amplitudes and their correlations. In this
first paper, we derive the impact of these fluctuations on the radiative
pressure gradient needed to carry a given radiative luminosity. This
implementation leads to a remarkable improvement between 1D and 3D radiative
pressure gradients, and builds confidence in our path to an eventual 1D
implementation of these intrinsically 3D envelopes. However, simply reducing
the radiation pressure gradient is not enough to implement a new 1D model.
Rather, we must also account for the impact of two other aspects of turbulent
convection: the substantial pressure, and the ability to transport an
appreciable fraction of the luminosity, which will be addressed in upcoming
works. This turbulent convection also arises in other instances where the
stellar luminosity approaches the Eddington luminosity. Hence, our effort
should apply to other astrophysical situations where an opacity peak arises in
a near Eddington limited, radiation pressure dominated plasma.
