World Library  

Add to Book Shelf
Flag as Inappropriate
Email this Book

Understanding Mixing Efficiency in the Oceans: Do the Nonlinearities of the Equation of State for Seawater Matter? : Volume 6, Issue 1 (24/02/2009)

By Tailleux, R.

Click here to view

Book Id: WPLBN0003973071
Format Type: PDF Article :
File Size: Pages 17
Reproduction Date: 2015

Title: Understanding Mixing Efficiency in the Oceans: Do the Nonlinearities of the Equation of State for Seawater Matter? : Volume 6, Issue 1 (24/02/2009)  
Author: Tailleux, R.
Volume: Vol. 6, Issue 1
Language: English
Subject: Science, Ocean, Science
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


APA MLA Chicago

Tailleux, R. (2009). Understanding Mixing Efficiency in the Oceans: Do the Nonlinearities of the Equation of State for Seawater Matter? : Volume 6, Issue 1 (24/02/2009). Retrieved from

Description: Department of Meteorology, University of Reading, UK. 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.

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

%REFERENCE 1 %; %REFERENCE 2 %; %Andrews, D. G. 1981 %A note on potential energy density in a stratified compressible fluid. %J. Fluid Mech. 107, 227–236. %; % Ansumali, S., Karlin, I.V., and Öttinger, H.C. % Thermodynamic theory of incompressible hydrodynamics. % Phys. Rev. Lett. 94, 080602. %; % Bannon, P. R. 1995 % Hydrostatic adjustment: Lamb's problem. % J. Atm. Sci. 52, 1753–1752. %; % Bannon, P. R. 2004 % Lagrangian available enrgetics and parcel instabilities. % J. Atm. Sci. 61, 1754–1767. %; % Batchelor, G.K. 1967 % An introduction to Fluid Dynamics. Cambridge University Press. 615 pp. %; % Bejan, A. 1997 % Advanced Engineering Thermodynamics. John Wiley and Sons, Inc., % 850 pp. %; % Bejan, A. 2000 % Shape and Structure, from Engineering to Nature. % Cambridge University Press, 324 pp. %; % Boussinesq, J. 1903 % Théorie analytique de la chaleur. Vol 2. Gauthier-Villars, Paris. %; % Bryden, H.L., Longworth, H.R., and Cunningham, S.A. 2005 % Slowing of the Atlantic meridional overturning circulation at % 25 degrees N. Nature, 438, 655-657. %; % Bugnion, V., Hill, C., and Stone, P.H. 2006 % An adjoint analysis of meridional overturning circulation in an % ocean model. J. Climate, 19, 3732–3750. %; % Bugnion, V., Hill, C., and Stone, P.H. 2006 % An adjoint analysis of meridional overturning circulation in a % hybrid coupled model. J. Climate, 19, % 3751–3767.; Caulfield, C. P. and Peltier, W. R.: The anatomy of the mixing transition in homogeneous and stratified free shear layers, J. Fluid Mech., 413, 1–47, 2000.; % Codoban, S. and Shepherd, T. G. 2003 % Energetics of a symmetric circulation including momentum constraints. % J. Atmos. Sci. 60, 2019–2028. %; % Colin de Verdière, A. C. 1988 % Buoyancy driven planetary flows. % J. Mar. Res. 46, 215–265. %; % Colin de Verdière, A. C. 1993 % On the oceanic thermohaline circulation. % in Modelling oceanic climate interactions, % Willebrand and D.Anderson, Nato-Asi series I, Vol II, % 151–183. %; % Coman, M. A., Griffiths, R. W., and Hughes, G. O. 2006 % Sandström's experiments revisited. % J. Mar. Res. 64, 783–796. %; %Dalziel, S. B., Patterson, M. D., Caulfield, C. P., and % Coomaraswamy, I. A. 2008 % Mixing efficiency in high-aspect-ratio Rayleigh-Taylor experiments. % Phys. Fluids, 20, 065106. %; % Defant, A. 1961 % Physical Oceanography, vol. 1. Pergamon. %; % de Groot, S.R. and Mazur, P. 1962 % Non-equilibrium thermodynamics. North Holland Publishers. %; % de Szoeke, R. A. and Samelson, R. M. 2002 % The duality between the Boussinesq and non-Boussinesq hydrostatic % equations of motion. % J. Phys. Oceanogr. 32, 2194–2203. %; % Dutton, J. 1986 % The ceaseless wind: An introduction to the theory of atmospheric % motion. Dover. 617 pp. %; % Eckart, C. 1948 % An analysis of the stirring and mixing processes in incompressible % fluids. J. Mar. Res., 7, 265–275. %; % Eden, C. and Greatbatch, R. J. 2008 % Toward a mesoscale eddy closure. % Ocean Modelling, 20, 223–229.; Feistel, R.: A new extended Gibbs thermodynamic potential of seawater, Prog. Oceanogr., 58, 43–114, 2003.; Fofonoff, N. P.: Physical properties of seawater, edited by: Hill, M. N., The Sea, Vol. 1, Wiley-Interscience, 3–30, 1962.; Fofonoff, N. P.: Nonlinear limits to ocean thermal structure, J. Mar. Res., 56, 793–811, 1998.; Fofonoff, N. P.: Thermal stability of the world ocean thermoclines, J. Phys. Oceanogr., 31, 2169–2177, 2001.; % Gade, H. G. and Gustafsson, K. E. 2004 % Application of classical thermodynamic principles to the study % of oceanic overturning circulation. % Tellus 56A, 371–386. %; % Gent, P. and McWilliams, J. C. 1990 % Isopycnal mixing in ocean circulation models. % J. Phys. Oceanogr. 20, 150–155. %; % Gibbs, W. 1878 % On the equilibrium of heterogenous substances. % Trans. Conn. Acad. III, 343–524. %; % Gnanadesikan, A. 1999 % A simple predictive model for the structure of the pycnocline. % Science 283, 2077-2079. %; % Gnanadesikan, A., Slater, R.D., Swath


Click To View

Additional Books

  • About Uncertainties in Practical Salinit... (by )
  • Exploring the Isopycnal Mixing and Heliu... (by )
  • Modeling of the Circulation in the North... (by )
  • Chaotic Variability of the Meridional O... (by )
  • Global Representation of Tropical Cyclon... (by )
  • Transient Residence and Exposure Times :... (by )
  • Dynamically Constrained Ensemble Perturb... (by )
  • Interannual Coherent Variability of Ssta... (by )
  • First Air–sea Gas Exchange Laboratory St... (by )
  • Retroflection from a Double-slanted Coas... (by )
  • Adjustment of the Basin-scale Circulatio... (by )
  • Comparison of Seawifs and Modis Time Ser... (by )
Scroll Left
Scroll Right


Copyright © World Library Foundation. All rights reserved. eBooks from World Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.