Planetary scale balance dynamics in the tropics

A classical view of tropical dynamics is the equatorial wave theory, where the dynamics is dominated by gravity waves generated through convection, resulting in a flow that is inherently divergent. On the other hand, Charney (1963) argued that in the absence of diabatic heating, the tropics is dominated by nondivergent balanced flow. The latter view can be generalized to the case where diabatic heating is dominant, resulting in the weak temperature gradient (WTG) model of Soblet et al. (2001).

While the latter view is formally valid for mesoscale motions, it was shown that with some modifications, the WTG model can be applied to planetary scale circulations such as the Hadley cell and the classical Gill model. In addition, recent observational data also suggest that vortical modes dominate over divergent modes even at large length-scales, and therefore the balanced dynamics as proposed by Charney applies to a wider regime than assumed. However the slow dynamics in the WTG model does not admit Kelvin waves, which contribute significantly to low-frequency variability in the tropics.

In the present study, we examine the slow component of the planetary scale tropical dynamics. An asymptotic expansion is used to systematically derive a family of balance models for the shallow water equations on the equatorial beta-plane, with anisotropy (ratio of meridional to zonal scale) as the small parameter as it can be re-interpreted as a separation in timescale. We demonstrate that as the Froude number approaches unity, the slow timescale is effectively an advective timescale, and the resulting balance dynamics has small divergence and is dominated by vortical motions. This is consistent with the view of Charney, and implies that the nonlinear balance model is the planetary scale analogue of the Charney balance model. On the other hand, if we linearize the nonlinear balance model, the traditional equatorial linear longwave model emerges, where only the slow Rossby and Kelvin waves are retained. This suggests that the equatorial linear wave theory is fully consistent with the balanced view of equatorial dynamics.

In addition to the adiabatic models, we also consider the case where a diabatic heat source is present, with the aim of further clarifying the role of diabatic heating in large scale balanced dynamics in the tropics. In particular, we consider a forcing that varies in time, and determine to what degree the response is balanced.