Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T14:57:59.551Z Has data issue: false hasContentIssue false
  • English
  • Français

On the validity of single-parcel energetics to assess the importance of internal energy and compressibility effects in stratified fluids

Published online by Cambridge University Press:  13 February 2015

Rémi Tailleux
Rémi Tailleux*
Affiliation:
Department of Meteorology, University of Reading, Earley Gate, PO Box 243, Reading RG6 6BB, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

It is often assumed on the basis of single-parcel energetics that compressible effects and conversions with internal energy are negligible whenever typical displacements of fluid parcels are small relative to the scale height of the fluid (defined as the ratio of the squared speed of sound to the gravitational acceleration). This paper shows that the above approach is flawed, however, and that a correct assessment of compressible effects and internal energy conversions requires the consideration of the energetics of at least two parcels or, more generally, of mass-conserving parcel rearrangements. As a consequence, it is shown that it is the adiabatic lapse rate and its derivative with respect to pressure, rather than the scale height, that controls the relative importance of compressible effects and internal energy conversions when considering the global energy budget of a stratified fluid. Only when mass conservation is properly accounted for is it possible to explain why the available internal energy can account for up to 40 % of the total available potential energy in the oceans. This is considerably larger than the prediction of single-parcel energetics, according to which this number should be no more than approximately 2 %.

JFM classification

Turbulent Flows: Compressible turbulence Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Stratified flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 767 , 25 March 2015 , R2
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics, p. 615. Cambridge University Press.Google Scholar
Eden, C., Czeschel, L. & Olbers, D. 2014 Toward energetically consistent ocean models. J. Phys. Oceanogr. 44, 3160–3184.CrossRefGoogle Scholar
Gade, H. G. & Gustafsson, K. E. 2004 Application of classical thermodynamic principles to the study of oceanic overturning circulation. Tellus A 56, 371–386.CrossRefGoogle Scholar
Huang, R. X. 2005 Available potential energy in the world’s oceans. J. Mar. Res. 63, 141–158.CrossRefGoogle Scholar
IOC, SCOR & IAPSO2010 The international thermodynamic equation of seawater – 2010: calculations and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No 56, UNESCO (English), 196 pp.Google Scholar
Kuhlbrodt, T., Griesel, A., Montoya, M., Levermann, A., Hofmann, M. & Rahmstorf, S. 2007 On the driving processes of the Atlantic meridional overturning circulation. Rev. Geophys. 45, RG2001.CrossRefGoogle Scholar
McDougall, T. J. 1987 Neutral surfaces. J. Phys. Oceanogr. 17, 1950–1964.2.0.CO;2>CrossRefGoogle Scholar
McDougall, T. J. & Barker, P. M.2011 Getting started with TEOS-10 and the Gibbs Seawater (GSW) Oceaongraphic Toolbox. 28 pp. SCOR/IAPSO WG127, ISBN 978-0-646-55621-5.Google Scholar
McDougall, T. J. & Feistel, R. 2003 What causes the adiabatic lapse rate? Deep-Sea Res. I 50, 1523–1535.CrossRefGoogle Scholar
Oliver, K. I. & Tailleux, R. 2013 Thermobaric control of gravitational potential energy generation by diapycnal mixing in the deep ocean. Geophys. Res. Lett. 40, 327–331.CrossRefGoogle Scholar
Oort, A. H., Ascher, S. C., Levitus, S. & Peixoto, J. P. 1989 New estimates of the available potential energy in the ocean. J. Geophys. Res. 94, 3187–3200.CrossRefGoogle Scholar
Reid, R. O., Elliott, B. A. & Olson, D. B. 1981 Available potential energy: a clarification. J. Phys. Oceanogr. 11, 15–29.2.0.CO;2>CrossRefGoogle Scholar
de Szoeke, R. A. & Samelson, R. M. 2002 The duality between Boussinesq and non-Boussinesq hydrostatic equations of motion. J. Phys. Oceanogr. 30, 2194–2203.2.0.CO;2>CrossRefGoogle Scholar
Tailleux, R. 2009 On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models, and the ocean heat engine controversy. J. Fluid Mech. 638, 339–382.CrossRefGoogle Scholar
Tailleux, R. 2010 Entropy versus APE production: on the buoyancy power input in the oceans energy cycle. Geophys. Res. Lett. 37, L22603.CrossRefGoogle Scholar
Tailleux, R. 2012 Thermodynamics/dynamics coupling in weakly compressible turbulent stratified fluids. ISRN Thermodyn. 2012, 609701.CrossRefGoogle Scholar
Tailleux, R. 2013 Irreversible compressible work and available potential energy dissipation in turbulent stratified fluids. Phys. Scr. T 155, 014033.Google Scholar
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. R. Meteorol. Soc. 130, 3223–3243.CrossRefGoogle Scholar
Thorpe, A. J., Hoskins, B. J. & Innocentini, V. 1989 The parcel method in baroclinic atmosphere. J. Atmos. Sci. 46, 1274–1284.2.0.CO;2>CrossRefGoogle Scholar
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36, 281–314.CrossRefGoogle Scholar
Young, W. R. 2010 Dynamic enthalpy, conservative temperature, and the seawater Boussinesq approximation. J. Phys. Oceanogr. 40, 394–400.CrossRefGoogle Scholar