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Understanding Mixing Efficiency in the Oceans: Do the Nonlinearities of the Equation of State for Seawater Matter? : Volume 5, Issue 3 (20/07/2009)

By Tailleux, R.

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Book Id: WPLBN0004020385
Format Type: PDF Article :
File Size: Pages 13
Reproduction Date: 2015

Title: Understanding Mixing Efficiency in the Oceans: Do the Nonlinearities of the Equation of State for Seawater Matter? : Volume 5, Issue 3 (20/07/2009)  
Author: Tailleux, R.
Volume: Vol. 5, Issue 3
Language: English
Subject: Science, Ocean, Science
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Tailleux, R. (2009). Understanding Mixing Efficiency in the Oceans: Do the Nonlinearities of the Equation of State for Seawater Matter? : Volume 5, Issue 3 (20/07/2009). Retrieved from

Description: 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. In this paper, the behaviour of the ratio ξ is examined for different stratifications having all the same buoyancy frequency N vertical profile, but different vertical profiles of the parameter Υ=Α P/(ΡCp), where α is the thermal expansion coefficient, P the hydrostatic pressure, Ρ the density, and Cp the specific heat capacity at constant pressure, the equation of state being that for seawater for different particular constant values of salinity. It is found that ξ and Wr, turbulent depend critically on the sign and magnitude of dΥ/dz, in contrast with D(APE), which appears largely unaffected by the latter. These results have important consequences for how the mixing efficiency should be defined and measured in practice, which are discussed.

Understanding mixing efficiency in the oceans: do the nonlinearities of the equation of state for seawater matter?

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