Ocean Science www.ocean-sci.net 1812-0784 1812-0792 5 3 2009 10.5194/os-5-271-2009 http://www.ocean-sci.net/5/271/2009/ http://www.ocean-sci.net/5/271/2009/os-5-271-2009.html http://www.ocean-sci.net/5/271/2009/os-5-271-2009.pdf 271 283 2009-07-20 Understanding mixing efficiency in the oceans: do the nonlinearities of the equation of state for seawater matter? R. Tailleux r.g.j.tailleux@reading.ac.uk Department of Meteorology, University of Reading, UK There exist two central measures of turbulent mixing in turbulent stratified fluids that are both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy APE; 2) the turbulent rate of change Wr, turbulent of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPEr, owing to the well known exact equality D(APE)=Wr, turbulent for a Boussinesq fluid with a linear equation of state. Recently, however, Tailleux (2009) pointed out that the above equality no longer holds for a thermally-stratified compressible, with the ratio ξ=Wr, turbulent/D(APE) being generally lower than unity and sometimes even negative for water or seawater, and argued that D(APE) and Wr, turbulent actually represent two distinct types of energy conversion, respectively the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE0, and the conversion between GPEr and a different subcomponent of internal energy called "exergy" IEexergy. 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