A Theory of Large-Scale Equatorial Waves Generated by Condensation Heat and Accelerating

Abstract

For the purpose of extending the theoretical interpretation of the large-scale equatorial waves discovered by Yanai and Maruyama (1966), a three-dimensional linearized primitive equation model of unstable waves is constructed on an equatorial beta plane.It is assumed that the release of latent heat due to moist convection in the troposphere is disturbed in proportion to the horizontal convergence in the subcloud layer responding to large-scale equatorial waves.It is found that Mode HB in the theory of unstable low latitude disturbances by Yamasaki (1969) is characterized by complex equivalent depth which simulates many aspects of YanaiMaruyama waves. This mode is further classified into various meridional modes, following Matsuno (1966). When the heat in the upper troposphere exceeds a critical value, unstable waves of free internal mode come into existence. Their growth rate increases with increasing heat in the upper troposphere.With the exception of inertio-gravity waves and Kelvin waves, mixed Rossby-gravity waves are the most unstable. The period corresponding to the observed wavelength of 10,000 km coincides with the observed period of about 4 days. The e-folding time is of the order of 10 days which, however, decreases with increasing wavelength.The energy and momentum budgets are also examined in detail. It is shown that a nonlinear forcing by Rossby type waves results in easterly acceleration of the mean zonal wind in the lower stratosphere, while Kelvin waves accelerate a westerly flow.

A Simple Diagnostic Model for the 30-50 Day Oscillation in the Tropics

“…Therefore, if the forcing is of a single dominant mode, the shallow water equations for this mode can describe the response fairly well within the layer of forcing. Above this layer, however, many vertical modes must be superposed as discussed by Hayashi (1976). The vertical distribution of the forcing used in several studies (Stevens et al, 1977 ;Geisler,1981;Geisler and Stevens, 1982) is a reasonable fit to the first baroclinic mode with the equivalent depth of 400m.…”

“…It is of importance to study the 30-50 day oscillation by the use of a general circulation model, since it gives valuable information on thermal forcing and will clarify whether or not atmosphere-ocean coupling is crucial for this periodicity, as suggested by an atmosphere-ocean model of Webster and Chou (1980) for the low frequency variability of the monsoon (see also Philander et al, 1984). In order to explain the periodicity theoretically, the convective heating must be somehow parameterized in terms of the large scale field as in the wave-CISK (Hayashi, 1970;Lindzen, 1974), since there is no predominant response at 30-50 day periods of tropical waves to random thermal forcing (Hayashi, 1976).…”

Kelvin Wave-CISK Controlled by Surface Friction

“…Although they did not remark on the importance of this mode at that time, its counterpart in the threedimensional model was re-evaluated afterwards, and the importance of surface friction was suggested in destabilization of Rossby waves and mixed Rossbygravity waves (Yamasaki, 1969(Yamasaki, , 1971, which might explain fundamental features of observed easterly waves and equatorial waves. Likewise, the mechanisms of Kelvin wave as well as mixed Rossby-gravity wave were discussed in other studies (Hayashi, 1970(Hayashi, , 1971. However, significance of surface friction in relation to the observational counterparts was not emphasized.…”

“…In the earlier linear theories for wave-CISK, several essential features of easterly waves and mixed-Rossby gravity waves were pursued (Yamasaki, 1969(Yamasaki, , 1971Hayashi, 1970Hayashi, , 1971. However, no one had remarked on Kelvin wave-CISK, except Hayashi (1970), until the beginning of the heated discussion on SCC (Hayashi and Sumi, 1986). When the discussion broke, lack of appropriate knowledge of cumulus parameterization led to confusion.…”

Super-and Sub-Harmonic Responses of Tropical Kelvin Waves to the Heating with a Seasonal Modulation

“…As is well known, cumulus heating is considered to be responsible for this energy supply. In order to include it, Yamasaki (1969), Hayashi (1970) and Lindzen (1974) have introduced the mechanism of so-called 'wave-CISK' in the studies of tropical waves. A basic assumption of this theory is that cumulus heating can be parametrized to be proportional to the vertical wind at the top of boundary layer of large-scale motion induced by the waves.…”