title: Tropical atmospheric circulations with humidity effects.
abstract: The main objective of this article is to study the effect of the moisture on the planetary scale atmospheric circulation over the tropics. The modelling we adopt is the Boussinesq equations coupled with a diffusive equation of humidity, and the humidity-dependent heat source is modelled by a linear approximation of the humidity. The rigorous mathematical analysis is carried out using the dynamic transition theory. In particular, we obtain mixed transitions, also known as random transitions, as described in Ma & Wang (2010Discrete Contin. Dyn. Syst.26, 1399-1417. (doi:10.3934/dcds.2010.26.1399); 2011Adv. Atmos. Sci.28, 612-622. (doi:10.1007/s00376-010-9089-0)). The analysis also indicates the need to include turbulent friction terms in the model to obtain correct convection scales for the large-scale tropical atmospheric circulations, leading in particular to the right critical temperature gradient and the length scale for the Walker circulation. In short, the analysis shows that the effect of moisture lowers the magnitude of the critical thermal Rayleigh number and does not change the essential characteristics of dynamical behaviour of the system.
authors.affiliation: Institute of Applied Mathematical Sciences , National Taiwan University , Taipei 10617, Taiwan, Republic of China.
authors.forename: Chun-Hsiung
authors.initials: CH
authors.lastname: Hsia
authors.affiliation: Department of Mathematics , National Taiwan University , Taipei 10617, Taiwan, Republic of China.
authors.forename: Chang-Shou
authors.initials: CS
authors.lastname: Lin
authors.affiliation: Department of Mathematics , Sichuan University , Chengdu, People's Republic of China.
authors.forename: Tian
authors.initials: T
authors.lastname: Ma
authors.affiliation: Department of Mathematics , Indiana University , Bloomington, IN 47405, USA.
authors.forename: Shouhong
authors.initials: S
authors.lastname: Wang
keywords: humidity; transition; tropical atmospheric circulation