  By generalizing the theory of convection to any type of thermal and
compositional source terms (diabatic processes), we show that thermohaline
convection in Earth oceans, fingering convection in stellar atmospheres, and
moist convection in Earth atmosphere are deriving from the same general
diabatic convective instability. We show also that "radiative convection"
triggered by CO/CH4 transition with radiative transfer in the atmospheres of
brown dwarfs is analog to moist and thermohaline convection. We derive a
generalization of the mixing length theory to include the effect of source
terms in 1D codes. We show that CO/CH4 radiative convection could significantly
reduce the temperature gradient in the atmospheres of brown dwarfs similarly to
moist convection in Earth atmosphere thus possibly explaining the reddening in
brown-dwarf spectra. By using idealized two-dimensional hydrodynamic
simulations in the Ledoux unstable regime, we show that compositional source
terms can indeed provoke a reduction of the temperature gradient. The L/T
transition could be explained by a bifurcation between the adiabatic and
diabatic convective transports and could be seen as a giant cooling crisis: an
analog of the boiling crisis in liquid/steam-water convective flows. This
mechanism with other chemical transitions could be present in many giant and
earth-like exoplanets. The study of the impact of different parameters
(effective temperature, compositional changes) on CO/CH4 radiative convection
and the analogy with Earth moist and thermohaline convection is opening the
possibility to use brown dwarfs to better understand some aspects of the
physics at play in the climate of our own planet.
