On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy

Journal of Fluid Mechanics

Volumn 638, Issue , 2009, Pages 339-382

  Tailleux, Rémi ^a  

^a UNIVERSITY OF READING   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BUOYANCY; CONTROL NONLINEARITIES; DIFFUSION IN SOLIDS; ENERGY CONVERSION; ENTROPY; EQUATIONS OF STATE; HEAT ENGINES; KINETIC ENERGY; KINETICS; MIXING; MOLECULAR PHYSICS; OCEANOGRAPHY; POTENTIAL ENERGY; VISCOUS FLOW;

COMPRESSIBLE NAVIER-STOKES EQUATIONS; ENTROPY PRODUCTION RATES; FLUX RICHARDSON NUMBER; GRAVITATIONAL POTENTIAL ENERGY; IRREVERSIBLE THERMODYNAMICS; NON-LINEARITY PARAMETER; STRATIFIED TURBULENT MIXING; SURFACE BUOYANCY FLUX;

DIFFUSION IN LIQUIDS;

BOUSSINESQ EQUATION; BUOYANCY; KINETIC ENERGY; NAVIER-STOKES EQUATIONS; POTENTIAL ENERGY; RICHARDSON NUMBER; STRATIFIED FLUID; THERMODYNAMICS; TURBULENT MIXING;

EID: 76249100440     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S002211200999111X     Document Type: Article

References (72)

1. Balmforth, N. J. & Young, W. R. 2003 Diffusion-limited scalar cascades. J. Fluid Mech. 482, 91-100.
2. Bannon, P. R. 2004 Lagrangian available energetics and parcel instabilities. J. Atmos. Sci. 61, 1754-1767.
3. Barry, M. E., Ivey, G. N., Winters, K. B. & Imberger, J. 2001 Measurements of diapycnal diffusivities in stratified fluids. J. Fluid Mech. 442, 267-291.
4. Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
5. Bejan, A. 1997 Advanced Engineering Thermodynamics. John Wiley.
6. Bouruet-Aubertot, P., Sommeria, J. & Staquet, C. 1996 Stratified turbulence produced by internal wave breaking: two-dimensional numerical experiments. Dyn. Atm. Oceans 23, 357-369.
7. Caulfield, C. P. & Peltier, W. R. 2000 The anatomy of the mixing transition in homogeneous and stratified free shear layers. J. Fluid Mech. 413, 1-47.
8. Colin de Verdière, A. 1993 On the oceanic thermohaline circulation. In Modelling Oceanic Climate Interactions (ed. J. Willebrand & D. L. T. Anderson), vol.2, pp. 151-183.
9. Nato-Asi Series I., Dalziel, S. B., Patterson, M. D., Caulfield, C. P. & Coomaraswamy, I. A. 2008 Mixing efficiency in high-aspect-ratio Rayleigh-Taylor experiments. Phys. Fluids 20, 065106.
10. de Groot, S. R. & Mazur, P. 1962 Non-Equilibrium Thermodynamics. North Holland.
11. de Szoeke, R. A. & Samelson, R. M. 2002 The duality between the Boussinesq and non-Boussinesq hydrostatic equations of motion. J. Phys. Oceanogr. 32, 2194-2203.
12. Eckart, C. 1948 An analysis of the stirring and mixing processes in incompressible fluids. J. Mar. Res. 7, 265-275.
13. Feistel, R. 2003 A new extended Gibbs thermodynamic potential of seawater. Prog. Oceanogr. 58, 43-114.
14. Fofonoff, N. P. 1962 Physical properties of seawater In The Sea (ed. M. N. Hill), vol.1, pp. 3-30. Wiley-Interscience.
15. Fofonoff, N. P. 1998 Nonlinear limits to ocean thermal structure. J. Mar. Res. 56, 793-811.
16. Fofonoff, N. P. 2001 Thermal stability of the world ocean thermoclines. J. Phys. Oceanogr. 31, 2169-2177.
17. Gibbs, W. 1878 On the equilibrium of heterogeneous substances. Trans. Conn. Acad. 3, 343-524.
18. Gnanadesikan, A., Slater, R. D., Swathi, P. S. & Vallis, G. K. 2005 The energetics of the ocean heat transport. J. Climate 18, 2604-2616.
19. Gregg, M. C. 1987 Diapycnal mixing in the thermocline: a review. J. Geophys. Res. 92 (C5), 5249-5286.
20. Griffies, S. M. 2004 Fundamentals of Ocean Climate Models. Princeton University Press.
21. Haltiner, G. J. & Williams, R. T. 1980 Numerical Prediction and Dynamic Meteorology. John Wiley.
22. Holliday, D. & McIntyre, M. E. 1981 On potential energy density in an incompressible stratified fluid. J. Fluid Mech. 107, 221-225.
23. Holloway, G. 1986 Considerations on the theory of temperature spectra in stably stratified turbulence. J. Phys. Oceanogr. 16, 2179-2183.
24. Huang, R. X. 1998 Mixing and available potential energy in a Boussinesq ocean. J. Phys. Oceanogr. 28, 669-678.
25. Huang, R. X. 2004 Ocean, energy flows in. Encycl. Energy 4, 497-509.
26. Huang, R. X. 2005 Available potential energy in the world's oceans. J. Mar. Res. 63, 141-158.
27. Hughes, G. O. & Griffiths, R. W. 2006 A simple convective model of the global overturning circulation, including effects of entrainment into sinking regions. Ocean Modelling 12, 46-79.
28. Hughes, G. O. & Griffiths, R. W. 2008 Horizontal convection. Annu. Rev. Fluid Mech. 40, 185-208.
29. Hughes, G. O., Hogg, A. McC. & Griffiths, R. W. 2009 Available potential energy and irreversible mixing in the meridional overturning circulation. J. Phys. Oceanogr. (in press).
30. Jeffreys, H. 1925 On fluid motions produced by differences of temperature and humidity. Q. J. Roy. Met. Soc. 51, 347-356.
31. Kondepudi, D. & Prigogine, I. 1998 Modern Thermodynamics. From Heat Engines to Dissipative structures. John Wiley & Sons.
32. Kuhlbrodt, T. 2008 On Sandström's inferences from his tank experiments: a hundred years later. Tellus 60, 819-836.
33. Kuhlbrodt, T., Griesel, A., Levermann, A., Hofmann, M. & Rahmstorf, S. 2007 On the driving processes of the Atlantic meridional overturning circulation. Rev. Geophys. 45, doi:10.1029/2004RG00166.
34. Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics. Pergamon Press.
35. Lindborg, E. 2006 The energy cascade in a strongly stratified fluid. J. Fluid Mech. 550, 207-242.
36. Linden, P. F. 1979 Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn. 13, 3-23.
37. Linden, P. F. & Redondo, J. M. 1991 Molecular mixing in Rayleigh-Taylor instability. Part 1: global mixing. Phys. Fluids A 3, 1269-1277.
38. Lorenz, E. N. 1955 Available potential energy and the maintenance of the general circulation. Tellus 7, 157-167.
39. Margules, M. 1903 Uber die Energie der Stürme. Jahrb. Zentralanst. Meteorol. Wien 40, 1-26.
40. Marquet, P. 1991 On the concept of exergy and available enthalpy: application to atmospheric energetics. Q. J. Roy. Met. Soc. 117, 449-475.
41. McDougall, T. J., Church, J. A. & Jackett, D. R. 2003 Does the nonlinearity of the equation of state impose an upper bound on the buoyancy frequency? J. Mar. Res. 61, 745-764.
42. McEwan, A. D. 1983a The kinematics of stratified mixing through internal wavebreaking. J. Fluid Mech. 128 47-57.
43. McEwan, A. D. 1983b Internal mixing in stratified fluids. J. Fluid Mech. 128, 59-80.
44. Molemaker, M. J. & McWilliams, J. C. 2009 A complete energy budget using a local available potential energy density. J. Fluid Mech. (in press).
45. Mullarney, J. C., Griffiths, R. W. & Hughes, G. O. 2004 Convection driven by differential heating at a horizontal boundary. J. Fluid Mech. 516, 181-209.
46. Munk, W. & Wunsch, C. 1998 Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res. 45, 1977-2010.
47. Nakamura, N. 1996 Two-dimensional mixing, edge formation, and permeability diagnosed in area coordinates. J. Atmos. Sci. 53, 1524-1537.
48. Nycander, J., Nilsson, J., Döös & Broström, G. 2007 Thermodynamic analysis of the ocean circulation. J. Phys. Oceanogr. 37, 2038-2052.
49. Oakey, N. S. 1982 Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements. J. Phys. Oceanogr. 22, 256-271.
50. Oort, A. H., Anderson, L. A. & Peixoto, J. P. 1994 Estimates of the energy cycle of the oceans. J. Geophys. Res. 99 (C4), 7665-7688.
51. Osborn, T. R. & Cox, C. S. 1972 Oceanic fine structure. Geophys. Astr. Fluid Dyn. 3, 321-345.
52. Osborn, T. R. 1980 Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10, 83-89.
53. Ottinger, H. C. 2005 Beyond equilibrium thermodynamics. Wiley Intersciences.
54. Paparella, F. & Young, W. R. 2002 Horizontal convection is non turbulent. J. Fluid Mech. 466, 205-214.
55. Pauluis, O. 2007 Sources and sinks of available potential energy in a moist atmosphere. J. Atmos. Sci. 64, 2627-2641.
56. Peltier, W. R. & Caulfield, C. P. 2003 Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 35, 135-167.
57. Roullet, G. & Klein, P. 2009 Available potential energy diagnosis in a direct numerical simulation of rotating stratified turbulence. J. Fluid Mech. 624, 45-55.
58. Sandström, J. W. 1908 Dynamische versuche mit meerwasser. Ann. Hydrodynam. Marine Meteorol. 36, 6-23.
59. Siggers, J. H., Kerswell, R. R. & Balmforth, N. J. 2004 Bounds on horizontal convection. J. Fluid Mech. 517, 55-70.
60. Staquet, C. 2000 Mixing in a stably stratified shear layer: two-and three-dimensional numerical experiments. Fluid Dyn. Res. 27, 367-404.
61. Tailleux, R. 2009 Understanding mixing efficiency in the oceans: Do the nonlinearities of the equation of state matter? Ocean Sciences 5, 271-283.
62. Tailleux, R. & Grandpeix, J. Y. 2004 On the seemingly incompatible parcel and globally integrated views of the energetics of triggered atmospheric deep convection over land. Q. J. Roy. Met. Soc. 130, 3223-3243.
63. Tailleux, R. & Rouleau, L. 2009 The effect of mechanical stirring on horizontal convection. Tellus A (in press).
64. Thorpe, S. A. 2005 The Turbulent Ocean. Cambridge University Press.
65. Tseng, Y.-H. & Ferziger, J. 2001 Mixing and available potential energy in stratified flows. Phys. Fluids 13, 1281-1293.
66. Wang, W. & Huang, R. X. 2005 An experimental study on thermal circulation driven by horizontal differential heating. J. Fluid Mech. 540, 49-73.
67. Winters, K. B. & d'Asaro, E. A. 1996 Diascalar flux and the rate of fluid mixing. J. Fluid Mech. 317, 179-193.
68. Winters, K. B., Lombard, P. N. Riley, J. J. & d'Asaro, E. A. 1995 Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289, 115-228.
69. Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36, 281-314.
70. Zeldovich, Y. B. 1937 The asymptotic law of heat transfer at small velocities in the finite domain problem. Zh. Eskp. Teoret. Fiz. 7, 12, 1466-1468.
71. Reprinted in English in the Selected Works of Yakov Borisovich Zeldovich, vol. 1: Chemical Physics and Hydrodynamics (ed. J. P. Ostriker, G. I. Barrenblatt & R. A. Sunyaev). Princeton University Press, 1992.
72. Zilitinkevich, S. S., Elperin, T., Kleeorin, N., Rogachevskii, I., Esau, I., Mauritsen, T. & Miles, M. W. 2008 Turbulence energetics in stably stratified flows: strong and weak mixing regimes. Q. J. Roy. Met. Soc. 134, 793-799.