Coexistence of equatorial waves & turbulence in moist shallow water simulations

Moist equatorial waves, responsible for a large fraction of synoptic and intraseasonal tropical variability, are visible in satellite observations of cloud top temperature and outgoing longwave radiation, with familiar dispersion relations appearing in space time spectra once a background red-like spectrum is removed (Kiladis et al., 2009).

Studies have suggested that the large-scale planetary waves in the equatorial region can be excited by smaller scale gravity waves (Yang & Ingersoll, 2013), baroclinic waves from the extratropics (Wedi & Smolarkiewicz, 2010), or localized synoptic scale heating (Gill 1980, 1982). In this study we examine the possibility that a continuous forcing of anomalies at the mesoscale can, through a turbulent upscale cascade, excites these waves, thus explaining both: the peaks along dispersion relations and the background red spectrum.

Our underlying assumption is that within the tropics (excluding wave forcing from the extratropics), a prerequisite to form coherent heating of ≈1000 km zonal length on an aqua planet is self-aggregation. Over the last two decades, self-aggregation has been studied over a wide range of scenarios up to the atmospheric mesoscale. In this study we examine the aggregation from the mesoscale up to the planetary scale, by applying mesoscale stochastic forcing in idealized spherical shallow water model. In particular, we examine the dependence of the large scale spectra on the field being stochastically forced, and on the existence of moisture.

We find that indeed, continuous stochastic forcing at the mesoscale can excite two-dimensional turbulence and linear tropical wave modes. When vorticity or moisture are forced in the simulations at wavenumber 100, a classical -5/3 slope of the eddy kinetic energy spectrum forms in an upscale energy cascade up to the planetary scale. Furthermore, equatorial waves emerge and Wheeler-Kiladis plots reveal a rich temporal and spatial structure of Rossby, Kelvin, Yanai, and Inertial Gravity waves. On the other hand, stochastic forcing of the divergence, or height fields only leads to a turbulent field when applied at planetary scales. Some explanations for this strong dependence on the type of forcing, and the role of moisture, will be discussed.