Analysis of nontraditional Coriolis terms on linear equatorial shallow water model and boundary layers

Abstract

The equatorial region is treated as a boundary layer in this study and analysed in numerical and analytical perspectives. A simple numerical equatorial dynamic model based on Zebiak and Cane’s model (ZC model) is developed in this study. Though the model contains ocean-atmosphere coupled processes, it is found that the surface layer requires a more detailed description as a singularity occurs at the equator. Dimensional analysis suggests that nontraditional Coriolis force terms and meridional diffusion terms are not negligible in the equatorial region. In consequence boundary layers occur both in meridional direction near the equator and in vertical direction, near the surface. Using matched asymptotic expansion, we conclude that the outer solutions of the problem follows parabolic characteristics. An attempt to find the inner solutions in both boundary layers (excluding overlapping region) is also presented in this study. Through the discussion of these solutions, we show that the outer solutions originate from the surface boundary layer forced by surface wind stress in both hemispheres, develop in the form of parabolic characteristics, and converge at the equator through meridionally-oriented equatorial boundary layer. The equatorial boundary layer is a transition zone that connects both hemispheres, and the vertical structure within the equatorial boundary layer is related directly with the wind stress and the meridional pressure gradient at the surface in off-equator region.