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 Yanai-Maruyama 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 non-linear 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.