The abyssal stratification and circulation deduced from the principle of maximal entropy production

Mahdi Ben Jelloul; Rui Xin Huang

doi:10.1111/j.1600-0870.2006.00177.x

The abyssal stratification and circulation deduced from the principle of maximal entropy production

Tellus

Volume 58 (2006): Issue 3

By: Mahdi Ben Jelloul and Rui Xin Huang

Open Access

|Jan 2006

Abstract

A theory for the abyssal stratification and circulation is derived from the principle of maximal production of information entropy used in non-equilibrium statistical dynamics. For an abyssal ocean of simple geometry and simple, though plausible, parameterization of the vertical diffusivity, stratification profiles together with their associated circulation are obtained. These profiles are characterized by an abyssal thermocline thickness scaling as √κ_vH/w_s0, where w_s0 is the upwelling velocity at the top of an abyssal ocean of depth H, and κ_v is its vertical diffusivity. Remarkably, the associated circulation is barotropic and coincides with the classical theory of the abyssal circulation by Stommel and Arons.

References

Dewar , R. 2003. Information theory explanation of the fluctuation the-orem, maximum entropy production and self-organized criticality in non-equilibrium stationary states. J. Phys. A 36 , 631 .
Search in Google Scholar Back to article
Edwards , C. A. and Pedlosky , J. 1995 . The influence of distributed sources and upwelling on the baroclinic structure . J. Phys. Oceanogr . 25 , 2259 – 2284 .
Search in Google Scholar Back to article
Gargett , A. E. 1984 . Vertical eddy diffusivity in the ocean interior. ./ . Mar. Res . 42 , 359 – 393 .
Search in Google Scholar Back to article
Huang , R. X. 1993 . A two-level model for the wind- and buoyancy-forced circulation . J. Phys. Oceanogr . 23 , 104 – 115 .
Search in Google Scholar Back to article
Huang , R. X. 1999 . Mixing and energetics of the thermohaline circulation . J. Phys. Oceanogr . 29 , 727 – 746 .
Search in Google Scholar Back to article
Huang , R. X. 2004. Ocean, energy flow. In: Encyclopedia of Energy Volume 4 (ed. C. J. Cleveland ). Elsevier, Oxford , 497 – 509 .
Search in Google Scholar Back to article
Huang , R. X. and Wang , W. 2003 . Gravitational potential energy sinks in the oceans. In: Near-Boundary Processes and Their Parameterization, Proceedings, Hawaii winter workshop , 239 – 247 .
Search in Google Scholar Back to article
Jaynes , E. T. 1979 . Where do we stand on maximum entropy? In: The Maximum Entropy Formalism (eds. R. D. Levine and M. Tribus ). MIT Press , Cambridge, MA , p. 15 .
Search in Google Scholar Back to article
Ledwell , J. R. , Watson , A. J. and Law , C. S. 1993 . Evidence for slow mixing across the pycnocline fron an open-ocean tracer-release experiment . Nature 364 , 701 – 703 .
Search in Google Scholar Back to article
Munk , W. H. 1966 . Abyssal recipes . Deep-Sea Res . 13 , 707 – 730 .
Search in Google Scholar Back to article
Munk , W. H. and Wunsch , C. 1998 . The Moon and mixing: abyssal recipes II. Deep-Sea Res . 145 , 1977 – 2010 .
Search in Google Scholar Back to article
Pedlosky , J. 1992 . The baroclinic structure of the abyssal circulation . J. Phys. Oceanogr . 22 , 652 – 659 .
Search in Google Scholar Back to article
Pedlosky , J. 1996 . Ocean Circulation Theory . Springer-Verlag , Berlin , 460 .
Search in Google Scholar Back to article
Polzin , K. L. , Toole , J. M. , Ledwell , J. R. and Scmitt , R. W. 1997 . Spatial variability of turbulent mixing in the abyssal ocean . Science 276 , 93 – 96 .
Search in Google Scholar Back to article
Sandström , J. W. 1908 . Dynamicsche Versuche mit Meerwasser . Annalen der Hydrographie und Maritimen Meteorologie 36 , 6 – 23 .
Search in Google Scholar Back to article
Samelson , R. M. 1999 . Internal boundary layer scaling in “Two Layer” solutions of the thermocline equations . J. Phys. Oceanogr . 29 , 2099 – 2102 .
Search in Google Scholar Back to article
Stigebrandt , A. 1979 . Observational evidence for vertical diffusion driven by internal waves of tidal origin in the Olsofjord . J. Phys. Oceanogr . 9 , 435 – 441 .
Search in Google Scholar Back to article
Stigebrandt , A. and Aure , J. 1989 . On vertical mixing in the basin waters of fjords . J. Phys. Oceanogr . 19 , 917 – 926 .
Search in Google Scholar Back to article
Stommel , H. and Arons , A. B. 1960a. On the abyssal circulation of the world ocean-I. Stationary planetary flow patterns on a sphere. Deep-Sea Res . 6 , 140 – 154 .
Search in Google Scholar Back to article
Stommel , H. and Arons , A. B. 1960b. On the abyssal circulation of the world ocean-II. An idealized model of the circulation pattern and amplitude in oceanic basins. Deep-Sea Res . 6 , 217 – 233 .
Search in Google Scholar Back to article
Winters , K. B. , Lombard , P. N. , Riley , J. J. and D’Asaro , E. A. 1995 . Available potential energy and mixing in density-stratified fluids. J. Fluid Mech . 289 , 115 – 128 .
Search in Google Scholar Back to article
Wunsch , C. and Ferrari , R. 2004 . Vertical mixing, energy, and the general circulation of the oceans . Ann. Rev. Fluid Mech . 36 , 281 – 314 .
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1111/j.1600-0870.2006.00177.x | Journal eISSN: 3035-9554

Journal RSS Feed

Language: English

Page range: 392 - 403

Submitted on: Dec 30, 2004

Accepted on: Nov 21, 2005

Published on: Jan 1, 2006

Published by: Stockholm University Press

In partnership with: Paradigm Publishing Services

© 2006 Mahdi Ben Jelloul, Rui Xin Huang, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 58 (2006): Issue 3