New Multiscale Models and Self-Similarity in Tropical Convection

One of the unexplained striking features of tropical convection is the observed statistical self-similarity, in clusters, superclusters, and intraseasonal oscillations through complex multi-scale processes ranging from the mesoscales to the equatorial synoptic scales to the intraseasonal/planetary scales. Here new multi-spatial scale, multi-time scale, simplified asymptotic models are derived systematically from the equatorial primitive equations on the range of scales from mesoscale to equatorial synoptic to planetary/intraseasonal. New mesoscale equatorial synoptic dynamical (MESD) models and balanced MESD (BMESD) models are developed for the multi-time, multispace interaction from mesoscales to equatorial synoptic scales; new multi-time versions of the intraseasonal planetary equatorial synoptic dynamics (IPESD) models are developed for multiple spatio-temporal interactions on equatorial synoptic scales and planetary scales. All these simplified models show systematically that the main nonlinear interactions across scales are quasi-linear where eddy flux divergences of momentum and temperature from nonlinear advection from the smaller scale spatio-temporal flows as well as mean source effects accumulate in time and drive the waves on the successively larger spatio-temporal scales. Furthermore, these processes which transfer energy to the next larger, longer, spatio-temporal scales are self-similar in a suitable sense established here.