Hybrid Coastal and Interior Modes for Two-Dimensional Homogeneous Flow in a Cylindrical Ocean

Abstract

Flows on coastal shelves and in the deep interior ocean are often considered separately, but transport of fluid between these two regions can have important biologial or environmental consequences. This paper considers a linear coupled coastal and deep interior-ocean model in the idealized context of a homogeneous two-dimensional cylindrical ocean with a rigid lid and axisymmetric step shelf topography. Both a semianalytical mode-matching approach and brute-force finite-element numerics have been used to analyze the linear dynamics. It is shown that hybrid planetary ?-plane Rossby and topographic shelf modes emerge. The structure of these inviscid modes is clarified by considering their frequency dependence on shelf break radius, by contrasting the evolution of hybrid modes to the evolution of pure shelf and pure ?-plane Rossby modes (considering streamfunction fields and particle paths), and by showing solutions of the initial value problem. Both ?ocean? and ?laboratory? parameter values are considered. Hybrid modes exchange information between the deep ocean and coastal shelves, especially at the intermediate frequencies where the separate planetary Rossby mode and topographic shelf mode dispersion curves overlap. The role of these modes is particularly clear in an initial value problem wherein a localized initial condition on the southern shelf later leads to large-scale interior ocean circulation. Forced?dissipative calculations reveal the sensitivity of resonantly generated hybrid Rossby?shelf modes to the strength of Ekman damping. For typical oceanic and laboratory parameter values hybrid modes are altered by increasing Ekman damping but do not disappear.