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Quantifying the nonconservative production of conservative temperature, potential temperature, and entropy

Citation

Graham, FS and Mcdougall, TJ, Quantifying the nonconservative production of conservative temperature, potential temperature, and entropy, Journal of Physical Oceanography, 43, (5) pp. 838-862. ISSN 0022-3670 (2013) [Refereed Article]


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Copyright Statement

Copyright 2013 American Meteorological Society

DOI: doi:10.1175/JPO-D-11-0188.1

Abstract

The evolution equation of potential temperature has to date been treated as an approximation to the oceanic version of the first law of thermodynamics. That is, oceanographers have regarded the advection and diffusion of potential temperature as the advection and diffusion of "heat." However, the nonconservative source terms that arise in the evolution equation for potential temperature are estimated to be two orders of magnitude larger than the corresponding source terms for Conservative Temperature. In this paper the nonconservative source terms of potential temperature, Conservative Temperature, and entropy are derived for a stratified turbulent fluid, then quantified using the output of a coarse-resolution ocean model and compared to the rate of dissipation of mechanical energy, epsilon. It is shown that the error incurred in ocean models by assuming that Conservative Temperature is 100% conservative is approximately 120 times smaller than the corresponding error for potential temperature and at least 1200 times smaller than the corresponding error for entropy. Furthermore, the error in assuming that Conservative Temperature is 100% conservative is approximately 6 times smaller than the error in ignoring epsilon. Hence Conservative Temperature can be quite accurately regarded as a conservative variable and can be treated as being proportional to the "heat content" per unit mass of seawater, and therefore it should now be used in place of potential temperature in physical oceanography, including as the prognostic temperature variable in ocean models.

Item Details

Item Type:Refereed Article
Keywords:conservative temperature, entropy, potential temperature, First Law of Thermodynamics
Research Division:Earth Sciences
Research Group:Oceanography
Research Field:Oceanography not elsewhere classified
Objective Division:Environment
Objective Group:Physical and Chemical Conditions of Water
Objective Field:Physical and Chemical Conditions of Water in Fresh, Ground and Surface Water Environments (excl. Urban and Industrial Use)
UTAS Author:Graham, FS (Dr Felicity McCormack)
ID Code:89566
Year Published:2013
Web of Science® Times Cited:21
Deposited By:IMAS Research and Education Centre
Deposited On:2014-03-07
Last Modified:2017-11-01
Downloads:300 View Download Statistics

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