be dominated by divergent flows associated with moist convection. No

balance condition exists in the large-scale tropical atmosphere, but

they are reduced to a set of linear equatorial waves in dry limit to

a good approximation. Various large-scale convective coherencies,

among them, the best known example would be the so-called

Madden-Julian oscillation, are considered as under a consequence of

coupling between wave dynamics and deep moist convection.

However, a systematic scale analysis indicates there is an alternative

possibility: a system dictated by a vorticity conservation law with

nondivergence to a leading-order approximation. Such an alternative

regime is identified at a scale smaller than the regime for the

convectively-coupled linear equatorial waves only by factor of three:

the latter is identified at the horizontal scale of 3000km, where as

the former at 1000km. The result reflects a fundamental subtlety in

the tropical scale analysis due to a strong sensitivity of a

nondimensional beta parameter on the horizontal scale.

Probably, the most surprising aspect of this alternative regime is

asymptotic nondivergence: i.e., the tropical large-scale dynamics is

dominated more by the vorticity than the divergence. This tendency is

systematically analyzed by using the TOGA-COARE LSA gridded data set.

It is found that the ratio of the root-mean square divergence for the

transient component to that of the vorticity is the smallest for the

scales of 20-80 days and 1500 km, indicating that the Madden-Julian

oscillation is more dominated by vorticity than divergence. The RMS

ratio goes down close to 0.2 at the Madden-Julian scale. At the

synoptic scale of a day and 1000 km, the RMS ratio is larger with a

value closer to 0.3.

This relatively weak divergence poses, however, an irony when the same

analysis is theoretically repeated both for free and forced linear

equatorial waves with varying wavenumbers and frequencies. Rather

surprisingly, the corresponding RMS ratio between the divergence and

the vorticity is much smaller, and less than 0.1 everywhere, for free

Rossby waves and also for free Kelvin waves in planetary scale limits.

The same conclusion is obtained for the forced waves except for narrow

ranges where a "resonance" of inertial-gravity waves with forcing

occurs. Thus, the observed RMS ratio is not consistent with the linear

wave theories.

The second important aspect of the alternative regime is that the

system can be described by the conservation of the absolute vorticity

in a self-contained manner to the leading order without effects of

divergence. In order to verify this point, a systematic vorticity

budget analysis is performed with use of the global NCEP analysis

data. The analysis overall confirm the scale analysis, but it also

demonstrates a non-negligible contribution of transient eddies in the

budget.

The asymptotic nature of this dynamical regime must be emphasized. It

is argued that the divergencd is negligible to the leading-order, but

it does not at all mean that the divergence is totally negligible. On

the contrary, the catalytic effect of a weak divergence is indeed

taken into account as a higher-order effect. More precisely, by

introducing a two time-scale description under an asymptotic

expansion, a weak convective feedback to the vorticity dynamics is

taken into account as a slow process.

References:

Delayen, K., and J. I. Yano, 2009:

Is Asymptotic Nondivergence of

The Large--Scale Tropical Atmosphere Consistent with

Equatorial Wave Theories?

Submitted to Tellus.

Yano, J. I., and M. Bonazzola, 2009:

Scale analysis for large-scale tropical atmospheric dynamics.

J. Atmos. Sci., 66, 159--172.

Yano, J. I., and S. Mulet, and M. Bonazzola, 2009:

Tropical Large-Scale Circulations: Asymptotically Nondivergent?

accepted to Tellus.