A multi-wavenumber theory for eddy diffusivities and its application to the southeast Pacific (DIMES) region

A multi-wavenumber theory is formulated to predict eddy diffusivities. It expands on earlier singlewavenumber 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 multi-wavenumber theory is equivalent to the single wavenumber theory, and both show mixing suppression by the mean flow. The multiwavenumber theory was tested in a region of the Southern Ocean (70oS−45oS, 110oW−20oW) 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 multi-wavenumber theory, and from floats deployed in a global 1/10o Parallel Ocean Program (POP) simulation. Compared to the single-wavenumber theory, the horizontal structures of cross-stream mixing lengths from the multi-wavenumber theory agree better with the simulated float-based estimates at almost all depth levels. The multi-wavenumber 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 multi-wavenumber theories predict the horizontal structures of cross-stream diffusivities, which resemble the eddy kinetic energy patterns.