Walker-type mean circulations and convectively coupled tropical waves as an interacting system

Interactions between convectively coupled tropical waves and Walker-type mean circulations are examined using a two-dimensional analytic model wherein drying and cooling of the boundary layer by convective and mesoscale downdrafts are in equilibrium with the wind-induced perturbations of surface fluxes. The moist thermodynamic state directly affects the stability of the large-scale circulation by controlling the wind perturbation on surface fluxes and the strength of the convective downdrafts. Stability analyses yield two major conclusions. (i) The mean Walker circulation is linearly unstable, suggesting that it may only exist in a quasi-steady sense through the spontaneous generation of transient waves. The instability is a manifestation of positive feedback: enhanced low-level convergence increases the surface wind speed, which increases the surface flux. As a result, convective heating is increased, which further enhances the low-level convergence. The mean circulation is more unstable when its horizontal extent is small and its depth large. Hence, when the horizontal extent of the mean circulation is a few thousand kilometers, as in the authors' recent cloud-resolving simulations, the deep first-baroclinic mode circulation is too unstable to be maintained even in a quasi-steady sense, realizing a shallow double-cell structure. (ii) The convectively coupled large-scale wave differs from traditional tropical large-scale instabilities of a homogeneous mean state in an important way: the longest waves are the most unstable rather than the shortest. Linear coupling of the waves with the mean state, through wind-induced surface flux perturbations, induces monotonically growing instabilities when the ascent of the mean circulation occupies more than half of the total domain. These instabilities occur only with the odd-wavenumber modes, which have parity with the mean circulation. Otherwise, the system supports linear neutral waves that propagate slower than the dry gravity waves due to the convective coupling in the ascending region. Growing oscillatory modes occur when nonlinear advection is included, which is consistent with the observed spontaneous generation of convectively coupled waves.