TY - JOUR

T1 - Eddy-mixing entropy and its maximization in forced-dissipative geostrophic turbulence

AU - David, Tomos W.

AU - Zanna, Laure

AU - Marshall, David P.

N1 - Funding Information:
This work is funded by the UK Natural Environment Research Council award reference: 1361095. We would like to thank Antoine Venaille for insightful and helpful discussion of our work, as well as Chris O’Reilly for his assistance with the significance testing.

PY - 2018/7/27

Y1 - 2018/7/27

N2 - An equilibrium, or maximum entropy, statistical mechanics theory can be derived for ideal, unforced and inviscid, geophysical flows. However, for all geophysical flows which occur in nature, forcing and dissipation play a major role. Here, a study of eddy-mixing entropy in a forced-dissipative barotropic ocean model is presented. We heuristically investigate the temporal evolution of eddy-mixing entropy, as defined for the equilibrium theory, in a strongly forced and dissipative system. It is shown that the eddy-mixing entropy provides a descriptive tool for understanding three stages of the turbulence life cycle: growth of instability; formation of large scale structures; and steady state fluctuations. The fact that the eddy-mixing entropy behaves in a dynamically balanced way is not a priori clear and provides a novel means of quantifying turbulent disorder in geophysical flows. Further, by determining the relationship between the time evolution of entropy and the maximum entropy principle, evidence is found for the action of this principle in a forced-dissipative flow. The maximum entropy potential vorticity statistics are calculated for the flow and are compared with numerical simulations. Deficiencies of the maximum entropy statistics are discussed in the context of the mean-field approximation for energy. This study highlights the importance of entropy and statistical mechanics in the study of geostrophic turbulence.

AB - An equilibrium, or maximum entropy, statistical mechanics theory can be derived for ideal, unforced and inviscid, geophysical flows. However, for all geophysical flows which occur in nature, forcing and dissipation play a major role. Here, a study of eddy-mixing entropy in a forced-dissipative barotropic ocean model is presented. We heuristically investigate the temporal evolution of eddy-mixing entropy, as defined for the equilibrium theory, in a strongly forced and dissipative system. It is shown that the eddy-mixing entropy provides a descriptive tool for understanding three stages of the turbulence life cycle: growth of instability; formation of large scale structures; and steady state fluctuations. The fact that the eddy-mixing entropy behaves in a dynamically balanced way is not a priori clear and provides a novel means of quantifying turbulent disorder in geophysical flows. Further, by determining the relationship between the time evolution of entropy and the maximum entropy principle, evidence is found for the action of this principle in a forced-dissipative flow. The maximum entropy potential vorticity statistics are calculated for the flow and are compared with numerical simulations. Deficiencies of the maximum entropy statistics are discussed in the context of the mean-field approximation for energy. This study highlights the importance of entropy and statistical mechanics in the study of geostrophic turbulence.

KW - Fluctuating hydrodynamics

KW - nonlinear dynamics

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U2 - 10.1088/1742-5468/aad19a

DO - 10.1088/1742-5468/aad19a

M3 - Article

AN - SCOPUS:85051510455

VL - 2018

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 7

M1 - 073206

ER -