Absolute instability of moisture‐coupled waves on the equatorial beta‐plane

Abstract

AbstractThe instabilities produced by a linear model of the tropical atmosphere coupled to a prognostic equation for water vapour are investigated. The basic model with no meridional wind supports unstable eastward‐propagating waves. For parameter regimes relevant to the Indo‐Pacific warm pool, the long‐time asymptotic behaviour of the unstable waves is found to be absolutely unstable, so that the amplitude of disturbances will grow in time at every point in the domain. The absolute instability of the system is realized at planetary length‐scales and intraseasonal frequencies. Other parameter choices for the system do not produce this same behaviour at these length‐ and time‐scales. It is shown that the resultant long‐time behaviour of the instability is characterized by roughly equal roles for temperature and moisture fluctuations in setting the thermodynamic tendency of the waves. With the inclusion of momentum damping, the phase speed of the absolutely unstable solution is about 7 ms. Addition of a strong background meridional moisture gradient, as in recent studies on the Madden–Julian Oscillation (MJO), appears to remove the absolute instability from the system. In a background state that varies slowly in the zonal direction, it is shown analytically that localized regions of instability may be formed, again using parameter choices relevant to the warm pool. The dynamics and thermodynamics of these local instabilities show some correspondence with the observed development of the MJO as it propagates through the warm pool.