  The intense irradiation received by hot Jupiters suppresses convection in the
outer layers of their atmospheres and lowers their cooling rates. "Inflated"
hot Jupiters, i.e., those with anomalously large transit radii, require
additional sources of heat or suppressed cooling. We consider the effect of
forced turbulent mixing in the radiative layer, which could be driven by
atmospheric circulation or by another mechanism. Due to stable stratification
in the atmosphere, forced turbulence drives a downward flux of heat. Weak
turbulent mixing slows the cooling rate by this process, as if the planet was
irradiated more intensely. Stronger turbulent mixing buries heat into the
convective interior, provided the turbulence extends to the
radiative-convective boundary. This inflates the planet until a balance is
reached between the heat buried into and radiated from the interior. We also
include the direct injection of heat due to the dissipation of turbulence or
other effects. Such heating is already known to slow planetary cooling. We find
that dissipation also enhances heat burial from mixing by lowering the
threshold for turbulent mixing to drive heat into the interior. Strong
turbulent mixing of heavy molecular species such as TiO may be necessary to
explain stratospheric thermal inversions. We show that the amount of mixing
required to loft TiO may overinflate the planet by our mechanism. This possible
refutation of the TiO hypothesis deserves further study. Our inflation
mechanism requires a deep stratified layer that only exists when the absorbed
stellar flux greatly exceeds the intrinsic emitted flux. Thus it would be less
effective for more luminous brown dwarfs and for longer period gas giants,
including Jupiter and Saturn.
