Turbulence and equatorial waves in moist and dry shallow-water flow, excited through mesoscale stochastic forcing

Turbulence and large-scale waves in the tropical region are studied using the spherical shallow-water equations. With mesoscale vorticity forcing, both moist and dry systems show an upscale transfer of kinetic energy which is dominated by rotational modes, scales as a power law with -5/3 exponent, requires eddy-eddy interactions and ranges from the forcing scale to the respective equatorial deformation radius. At larger planetary scales, the divergent component of the energy increases and we see a footprint of tropical waves. The dry system shows a signature of the entire family of equatorial waves, while the moist simulations show only low-frequency Rossby, Kelvin and mixed Rossby-gravity waves with an equivalent depth that matches rapid condensation estimates. Initially, runs with interactive moisture exhibit a weak inverse transfer of moisture variance as well exponential growth across a range of length-scales. This results in an equilibrium moist energy spectrum obeying a -2 power law and the formation of moisture aggregates. Once formed, aggregates propagate westward in the Tropics with speeds of the order of a few metres per second. In contrast, forcing divergence does not excite an inverse transfer, and injected energy remains trapped at the forcing scale. Height (i.e., temperature or mass) forcing results in a peak at the forcing scale, but also generates large-scale waves and projects onto rotational modes which undergo an inverse energy transfer. Similarly, forcing the moisture field by itself produces an inverse transfer of rotational energy and a well-formed large-scale equatorial wave spectrum. Notably, the height- and moisture-forced inverse transfers are different in nature. Specifically, they require the presence of ambient planetary rotation. In all, these experiments demonstrate that the vortical and divergent wind are inextricably linked with the evolving moisture field, and that large-scale equatorial waves co-exist with synoptic-scale moist turbulence.