Tropical Atmospheric Circulations with Humidity Effects

The main objective of this article is to study the effect of the moisture on the planetary scale atmospheric circulation over the tropics. The modeling we adopt is the Boussinesq equations coupled with a diffusive equation of humidity and the humidity dependent heat source is modeled by a linear approximation of the humidity. The rigorous mathematical analysis is carried out using the dynamic transition theory. In particular, we obtain the same types of transitions and hence the scenario of the El Ni\~no mechanism as described in \cite{MW2,MW3}. The effect of the moisture only lowers slightly the magnitude of the critical thermal Rayleigh number.