Abstract
We consider the problem of the linear response of a stratified, equatorial, β-plane model atmosphere to specified transient sources of heat and momentum. The method of solution involves transforms in all three spatial coordinates. A finite Stürm-Liouville transform is used in z, a Fourier transform in x, and a generalized Hermite transform in y. The resulting spectral equations can then be solved analytically for a specified forcing. Of particular interest is the case of a Gaussian-shaped heat source centered at latitude yo and with e-folding radius a. The heat source is transient and has time scale 1/α. Using the Parceval relation we compute how the forced energy is partitioned between Kelvin, mixed Rossby-gravity, Rossby and gravity modes as a function of a, yo, α. Model results using a heat source centered at 11°S with an e-folding radius of 750 km and a time scale of about a day indicate that many aspects of the summertime upper tropospheric circulation over South America can be explained by the dispersive properties of Rossby and mixed Rossby-gravity waves. These results also show that the transient heat source excites Kelvin waves which propagate rapidly eastward as a nondispersive wave group. The existence of the Kelvin waves has implications for the initialization of tropical forecast models. By applying a nonlinear normal mode initialization procedure in the middle of a model simulation we investigate how the initialization distorts the subsequent evolution. Much of the distortion is associated with the Kelvin wave response.
