This study aims to understand the ocean's circulation, which is characterized by the presence of multiple alternating zonal jets and transient mesoscale eddies, by systematic analysis of the underlying linear dynamics of this system. For this purpose, properties of the linear normal modes such as growth rates, dispersion, spatial structure, and nonlinear self-interactions are explored for a hierarchy of idealized, vertically, and horizontally sheared flows with increasing complexity. The authors find that large-scale background vertical shear, alternating multiple zonal jets, bottom friction, and the Reynolds number have important effects on these modes. This study hypothesizes that when these effects are taken into account, the linear results can be used to predict many properties of nonlinear mesoscale eddies. This hypothesis is confirmed in Part II of this paper.
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