## Abstract

Quasigeostrophic turbulence theory and numerical simulation are used to study the mechanisms determining the scale, structure, and equilibration of mesoscale ocean eddies. The present work concentrates on using freely decaying geostrophic turbulence to understand and explain the vertical and horizontal flow of energy through a stratified, horizontally homogeneous geostrophic fluid. It is found that the stratification profile, in particular the presence of a pycnocline, has significant, qualitative effects on the efficiency and spectral pathways of energy flow. Specifically, with uniform stratification, energy in high baroclinic modes transfers directly, quickly (within a few eddy turnaround times), and almost completely to the barotropic mode. By contrast, in the presence of oceanlike stratification, kinetic energy in high baroclinic modes transfers intermediately to the first baroclinic mode, whence it transfers inefficiently (and incompletely) to the barotropic mode. The efficiency of transfer to the barotropic mode is reduced as the pycnocline is made increasingly thin. The *β* effect, on the other hand, improves the efficiency of barotropization, but for oceanically realistic parameters this effect is relatively unimportant compared to the effects of nonuniform stratification. Finally, the nature of turbulent cascade dynamics is such as to lead to a concentration of first baroclinic mode kinetic energy near the first radius of deformation, which, in the case of a nonuniform and oceanically realistic stratification, has a significant projection at the surface. This may in part explain recent observations of surface eddy scales by TOPEX/Poseidon satellite altimetry, which indicate a correlation of surface-height variance with the scale of the first deformation radius.

*Corresponding author address:* Dr. K. Shafer Smith, Geophysical Fluid Dynamics Laboratory, Princeton University, P.O. Box 308, Princeton, NJ 08542.

Email: kss@gfdl.gov