Revisiting the Frictional Control of the Antarctic Circumpolar Current From the Energy Diagram

TL;DR

This study investigates how eddy energy and baroclinicity in the Antarctic Circumpolar Current respond to frictional changes, revealing the importance of eddy dissipation and extending the frictional control framework.

Contribution

It extends the frictional control theory by incorporating eddy energy dissipation effects and demonstrates their significance through numerical experiments.

Findings

Eddy energy varies significantly with friction in simulations.

Baroclinic energy conversion dominates at high drag, barotropic at low drag.

A generalized scaling law relates eddy dissipation to baroclinicity.

Abstract

The transport of the Antarctic Circumpolar Current (ACC) has been shown to increase with friction. Previous studies explained this counter-intuitive relationship called frictional control based on the eddy geometric parametrizations. They focused on the eddy momentum transfer and eddy energetics. To maintain the balance between wind stress and eddy interfacial form stress, eddy energy must remain unchanged as friction increases; this requires enhanced baroclinicity to compensate for stronger eddy energy dissipation. However, the independence of eddy energy has not been fully verified, and this interpretation assumes negligible barotropic energy conversion. To address this gap, we conduct sensitivity experiments in an idealized stratified reentrant channel with varying linear bottom drag. Numerical simulations show that eddy energy changes substantially with friction. Furthermore, in the high-drag regime, baroclinic energy conversion dominates eddy energy generation, whereas in the low-drag regime barotropic energy conversion contributes substantially. Despite these differences, baroclinicity increases with eddy energy dissipation across all regimes, although the relationship is somewhat weak in the low-drag regime owing to barotropic energy conversion. To explain this phenomenon, we extend the frictional control framework based on the Lorenz energy cycle. A simple scaling argument leads to a generalized frictional control, s~D(E)/{\tau}_w, where s is baroclinicity, D(E) is eddy energy dissipation, and {\tau}_w is wind stress. This framework provides a natural extension of the existing framework and successfully explains the numerical results. These results indicate that eddy dissipation controls the baroclinicity; therefore, properly parameterizing the eddy dissipation rate is essential for representing ACC dynamics in ocean models.