A Multiwavenumber Theory for Eddy Diffusivities and Its Application to the Southeast Pacific (DIMES) Region

A multiwavenumber theory is formulated to represent eddy diffusivities. It expands on earlier single-wavenumber theories and includes the wide range of wavenumbers encompassed in eddy motions. In the limiting case in which ocean eddies are only composed of a single wavenumber, the multiwavenumber theory is equivalent to the single-wavenumber theory and both show mixing suppression by the eddy propagation relative to the mean flow. The multiwavenumber theory was tested in a region of the Southern Ocean (70 degrees-45 degrees S, 110 degrees-20 degrees W) that covers the Drake Passage and includes the tracer/float release locations during the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES). Cross-stream eddy diffusivities and mixing lengths were estimated in this region from the single-wavenumber theory, from the multiwavenumber theory, and from floats deployed in a global 1/10 degrees Parallel Ocean Program (POP) simulation. Compared to the single-wavenumber theory, the horizontal structures of cross-stream mixing lengths from the multiwavenumber theory agree better with the simulated float-based estimates at almost all depth levels. The multiwavenumber theory better represents the vertical structure of cross-stream mixing lengths both inside and outside the Antarctica Circumpolar Current (ACC). Both the single-wavenumber and multiwavenumber theories represent the horizontal structures of cross-stream diffusivities, which resemble the eddy kinetic energy patterns.