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www.ocean-sci-discuss.net/6/371/2009/
doi:10.5194/osd-6-371-2009
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Understanding mixing efficiency in the oceans: do the nonlinearities of the equation of state for seawater matter?
Department of Meteorology, University of Reading, UK
Abstract. There exist two central measures of turbulent diffusive mixing in turbulent stratified fluids, which are both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy APE; 2) the rate of change Wr,mixing of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as representing the same kind of energy conversion, i.e., the irreversible conversion of APE into GPEr, owing to the well known result that D(APE)≈Wr,mixing in a Boussinesq fluid with a linear equation of state. Here, this idea is challenged by showing that while D(APE) remains largely unaffected by a nonlinear equation of state, Wr,mixing is in contrast strongly affected by the latter. This result is rationalized by using the recent results of Tailleux (2008), which argues that D(APE) represents the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE0, whereas Wr,mixing represents the conversion between a different subcomponent of internal energy – called the "exergy" IEexergy – and GPEr. It follows that the concept of mixing efficiency, which represents the fraction of the stirring mechanical energy ultimately dissipated by molecular diffusion is related to D(APE), not Wr,mixing, which ensures that it should be largely unaffected by the nonlinear character of the equation of state, and therefore correctly described in the context of a Boussinesq fluid with a linear equation of state. The variations of GPEr, on the other hand, are sensitive to the linear or nonlinear character of the equation of state.
Discussion Paper (PDF, 839 KB) Interactive Discussion (Closed, 7 Comments) Final Revised Paper (OS)
Citation: Tailleux, R.: Understanding mixing efficiency in the oceans: do the nonlinearities of the equation of state for seawater matter?, Ocean Sci. Discuss., 6, 371-387, doi:10.5194/osd-6-371-2009, 2009. Bibtex EndNote Reference Manager XML
