The rudiments of a self-consistent two-phase thermodynamical theory of intraseasonal and interannual variability for the tropical cloud-ocean mixed layer system are presented. In this paper we study some basic properties of low-frequency phenomena in the tropical coupled cloud-ocean mixed layer system under low mean wind speed conditions and attempt to seek a unified thermodynamical framework in which the thermodynamical oscillation can be studied and understood. In order to do so, all wves in the atmosphere and in the ocean are initially filtered out, and the coupled system is purely thermodynamic. An air-ocean coupled model designed especially for the low wind speed condition is employed to test the basic thermodynamic feedback mechanism between clouds and the ocean mixed layer. The model has four parts: (1) a shallow-water system for the large-scale atmosphere motion; (2) a cloud model, (3) a marine atmospheric boundary layer, in which the physical processes are parameterized into the bulk formulae through a geostrophic drag coefficient and corresponding heat and moisture exchange coefficients; and (4) an oceanic mixed layer model. The coupled model is solved analytically as an eigenvalue problem. Three nondimensional model parameters are found to be very important in separating growing or decaying, oscillatory or nonoscillatory modes: (1) the ocean surface stability index, &egr;; (2) the surface water budget index, &ggr;; and (3) the mean diapycnal gradient of the spiciness (&khgr;) in the entrainment zone, Δ.

The sign of &egr; divides the ocean mixed layer into shallowing (&egr;>0) and entrainment (&egr;20&egr;+11 for &ggr;=-0.1, Δ>20&egr;+11.8 for &ggr;=-0.2, and Δ>20&egr;+14.6 for &ggr;=-0.5. The model results also demonstrate that the exchanges of heat and water across the sea surface lead to both growing and decaying modes of oscillation on two different time scales, owing to the stability of the atmosphere. For an unstable atmosphere the time scale is about 20--30 days. However, the time scale is approximately 1--3 years for a stable atmosphere. This work introduces the new concept of two-phase thermodynamics for the coupled air-ocean system. Both atmosphere and ocean have two important thermodynamic variables: temperature and moisture for fractional cloudiness) for the atmosphere, and temperature and salinity for the ocean. If salinity is neglected in the ocean model, no positive feedback mechanism will be possible in the coupled air-ocean system.