Eddy-mixing Entropy as a Measure of Mesoscale Turbulent Disorder in the Southern Ocean.

A novel study of Southern Ocean mesoscale turbulence is presented from a statistical mechanics perspective. An eddy-mixing entropy, a measure of turbulent disorder, is calculated for potential vorticity in coordinates of neutral density and time-mean Montgomery streamfunction. Combined with results from idealized channel models, this analysis provides a natural way of empirically investigating the geostrophic turbulence of the Southern Ocean from Bayesian statistics, or information theoretic, perspective. By considering the way the energy and enstrophy dynamics constrain the statistically steady state value of eddy-mixing entropy, progress is made towards a statistical mechanics description of a forced-dissipative channel flow. The response of eddy-mixing entropy to forcing and dissipation is investigated, examining the dependence of eddy-mixing entropy on time, longitude and neutral density in the Southern Ocean State Estimate. The concept of eddy-mixing entropy, and diagnosing its behavior in numerical ocean models, may prove valuable for developing improved stochastic parameterizations of ocean mesoscale turbulence.