On the generation and dispersion of Yanai waves with a spectral Chebyshev-collocation reduced-gravity ocean model

A spectral Chebyshev-collocation method is devised for the 1-1/2 layer non-linear reduced-gravity equations. Following a general description of spectral methods with their application to meteorological and oceanographic problems the implementation of the numerical technique is described. A bicharacteristic scheme is applied to solve the equations at the boundaries incorporating the boundary conditions. This treatment enables stable time integrations (spectral methods in general are very sensitive to boundary errors). A simple transfinite grid generation method is used to construct grids over irregular (non-rectangular) simply-connected domains.;The model is used in a study of the dynamics of Yanai (or mixed Rossby-gravity) wave packets. These are of interest because of the observations of equatorial instability waves (which have the characteristics of Yanai waves) and their role in the momentum and heat budgets in the tropics. A series of experiments is performed to investigate the generation of the waves by simple cross-equatorial wind stress forcings in various configurations and the influence of a western boundary on them. They may be generated in the interior ocean as well as from a western boundary. The observations from all the oceans indicate that the waves have a preferential period and wavelength of around 26 days and 1000 km respectively. This is seen in the model results too and a plausible explanation is provided as being due to the dispersive properties of Yanai waves.