University Of Tasmania
F Graham_JournaL of Physical Oceanography_2013.pdf (5.43 MB)
Download file

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

Download (5.43 MB)
journal contribution
posted on 2023-05-17, 22:59 authored by Felicity McCormack, Mcdougall, TJ
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.


Publication title

Journal of Physical Oceanography










Institute for Marine and Antarctic Studies


Amer Meteorological Soc

Place of publication

45 Beacon St, Boston, USA, Ma, 02108-3693

Rights statement

Copyright 2013 American Meteorological Society

Repository Status

  • Open

Socio-economic Objectives

Measurement and assessment of freshwater quality (incl. physical and chemical conditions of water)

Usage metrics

    University Of Tasmania