Upscale energy cascades towards equatorial waves

Abstract:

Moist equatorial waves, responsible for a large fraction of synoptic and intraseasonal tropical variability, are visible in satellite derived data such as cloud top temperature and outgoing longwave radiation, once a red background noise is removed (Kiladis et al., 2009). In the idealized studies of Gill (1980, 1982), planetary scale waves are forced by a localized steady synoptic scale heating (Gill 1980,1982). Other studies have discussed forcing by more variable forcing, e.g. an excitation by smaller scale gravity waves (Yang & Ingersoll, 2013), or by baroclinic waves from the extratropics (Wedi & Smolarkiewicz, 2010). A coherent diabatic heating of ≈1000 km zonal length, like that assumed in the Gill model, implies an aggregation of the convection into this scale. Over the last two decades, self-aggregation has been studied over a wide range of scenarios up to the atmospheric mesoscale. Here we examine the self aggregation of stochastic mesoscale forcing, as a way to excite and amplify larger scales modes. We find that the upscale energy cascade, which develops in our model with a classical -5/3 slope of the kinetic energy spectrum, leads to the formation of planetary waves with the known Matsuno-Gill dispersion relations, resulting in a wave spectrum similar to the observed, with a red background spectrum and modal equatorial waves. We find a strong dependence of the upscale cascade as well as the spectrum of excited normal modes, on the variable in which we introduce the stochastic forcing, and on the existence of moisture and the strength of latent heating. We also find that the exact shape of the mean flow may vary as in shallow water simulations of other planets by Scott and Polvani (2007), and may also depend on the character of the stochastic forcing (Suhas et al. 2017). To our knowledge, this is the first systematic study linking the explorations of moist two-dimensional turbulence with tropical meteorology and tropical waves.