Response of tropical convective complexes to primary circulation induced heating

Abstract

The instability due to cumulus heating in the inner region of a balanced slab-symmetric two-layer model with an underlying Ekman layer is analysed. In satisfying the water balance the heating comprises two terms: One can be associated with the wind-evaporation feedback (representing a WISHE-type parameterisation) and replaces the CISK-type heating originally employed in the classical Charney-Eliassen model. The second is associated with the mid-level vertical mass flux. The model comprises two regimes of instability depending on the scale and the dominance of either one of the heating terms: (i) Dominance of the WISHE-type heating is characterised by hyperbolic meridional eigenfunctions, which represent the spatial structure of the inner region. It requires sufficient intensity of the surface heat exchange to obtain finite growth rates within a finite scale range. Beyond a certain threshold of the heating parameter the unstable scale range extends to infinitely large values. The maximum growth rates, though relatively small, occur at the smaller scale limit, which separates both regimes. (ii) Dominance of the mid-level term requires trigonometric meridional eigenfunctions to represent the spatial structure of the inner region; the growth rates range from zero to infinity associated with a finite range of spatial scales. It joins the other regime at its large growth (and small scale) boundary. In this linear model the influence of wind induced surface heat exchange tends to enlarge the spectrum of spatial scales effected by the heating induced instability.