A truncated oceanic spectral model for equatorial thermodynamic studies

Abstract

Abstract A β-plane model for equatorial circulation is transformed in terms of Hermite functions into a form where the meridional dependence is expressed in terms of spectral components. Linear analysis reveals a wave-dispersion relation similar in character to the regular model but with anti-Kelvin and anti-Yanai modes present. Depending upon the length scale used for the expansion, the evanescent frequency zone between the planetary and inertia-gravity modes, and between the two Yanai modes, may be changed. The truncated model offers an alternative view of the place of the primary wave modes in the overall scheme of equatorial planetary and gravity waves. The anti-Kelvin and anti-Yanai modes play an important role in returning the balance of the equatorial energy flux to the west at the eastern boundary. Transformation of the primitive equations into spectral form with low-order meridional wave number truncation yields a tractable, economical set of equations which have applications in the study of thermodynamic processes, parameterizations and for economical testing of numerical techniques. Second-order models are derived and they clearly expose the many couplings due to non-linear effects, diffusion, viscosity, pressure terms and the β effect.