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Local available energetics of multicomponent compressible stratified fluids

Published online by Cambridge University Press:  12 March 2018

Rémi Tailleux Open the ORCID record for Rémi Tailleux [Opens in a new window]
Rémi Tailleux*
Affiliation:
Department of Meteorology, University of Reading, Earley Gate, PO Box 243, Reading RG6 6BB, UK
*
†Email address for correspondence: [email protected]
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Abstract

We extend the local theory of available potential energy (APE) to a general multicomponent compressible stratified fluid, accounting for the effects of diabatic sinks and sources. As for simple compressible fluids, the total potential energy density of a fluid parcel is the sum of its available elastic energy and APE density. These respectively represent the adiabatic compression/expansion work needed to bring it from its reference pressure to its actual pressure and the work against buoyancy forces required to move it from its reference state position to its actual position. Our expression for the APE density is new and is derived using only elementary manipulations of the equations of motion; it is significantly simpler than existing published expressions, while also being more transparently linked to the relevant form of APE density for the Boussinesq and hydrostatic primitive equations. Our new framework is used to clarify the links between some aspects of the energetics of Boussinesq and real fluids, as well as to shed light on the physical basis underlying the choice of reference state(s) in local APE theory.

JFM classification

Geophysical and Geological Flows: Stratified flows Mixing: Turbulent mixing
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 842 , 10 May 2018 , R1
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Copyright
© 2018 Cambridge University Press 

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References

Andrews, D. G. 1981 A note on potential energy density in a stratified compressible fluid. J. Fluid Mech. 107, 227–236.Google Scholar
Andrews, D. G. 2006 On the available energy density for axisymmetric motions of a compressible stratified fluid. J. Fluid Mech. 569, 481–492.Google Scholar
Bannon, P. R. 2003 Hamiltonian description of idealized binary geophysical fluids. J. Atmos. Sci. 60, 2809–2819.Google Scholar
Codoban, S. & Shepherd, T. G. 2003 Energetics of a symmetric circulation including momentum constraints. J. Atmos. Sci. 60, 2019–2028.Google Scholar
Harris, B. L. & Tailleux, R. 2018 Assessment of algorithms for computing moist available potential energy. Q. J. R. Meteorol. Soc. (accepted), arXiv:1712.02112.Google Scholar
Holliday, D. & McIntyre, M. E. 1981 On potential energy density in an incompressible, stratified fluid. J. Fluid Mech. 107, 221–225.CrossRefGoogle Scholar
Kucharski, F. 1997 On the concept of exergy and available potential energy. Q. J. R. Meteorol. Soc. 123, 2141–2156.Google Scholar
Kucharski, F. & Thorpe, A. J. 2000 Local energetics of an idealized baroclinic wave using extended exergy. J. Atmos. Sci. 57, 3272–3284.Google Scholar
Lorenz, E. N. 1955 Available potential energy and the maintenance of the general circulation. Tellus 7, 138–157.Google Scholar
MacCready, P. & Giddings, S. N. 2016 The mechanical energy budget of a regional ocean model. J. Phys. Oceanogr. 46, 2719–2733.CrossRefGoogle Scholar
Margules, M. 1903 Über die Energie der Stürme. Jarhb. Zentralanst. Meteorol. Wien 40, 1–26.Google Scholar
Molemaker, M. J. & McWilliams, J. C. 2010 Local balance and cross-scale flux of available potential energy. J. Fluid Mech. 645, 295–314.Google Scholar
Novak, L. & Tailleux, R.2018 On the local view of atmospheric available potential energy. J. Atmos. Sci. (accepted), arXiv:1711.08660.Google Scholar
Peixoto, J. P. & Oort, A. H. 1992 Physics of Climate. AIP.Google Scholar
Peng, J., Zhang, L. & Zhang, Y. 2015 On the local available energetics in a moist compressible atmosphere. J. Atmos. Sci. 72, 1551–1561.Google Scholar
Roullet, G., Capet, X. & Maze, G. 2014 Global interior eddy available potential energy diagnosed from argo floats. Geophys. Res. Lett. 41, 1651–1656.Google Scholar
Roullet, G. & Klein, P. 2009 Available potential energy diagnosis in a direct numerical simulation of rotating stratified turbulence. J. Fluid Mech. 624, 45–55.Google Scholar
Saenz, J. A., Tailleux, R., Butler, E. D., Hughes, G. O. & Oliver, K. I. C. 2015 Estimating Lorenz’s reference state in an ocean with a nonlinear equation of state for seawater. J. Phys. Oceanogr. 45, 1242–1257.Google Scholar
Scotti, A., Beardsley, R. & Butman, B. 2006 On the interpretation of energy and energy fluxes of nonlinear waves: an example from Massachusetts Bay. J. Fluid Mech. 561, 103–112.Google Scholar
Scotti, A. & White, B. 2014 Diagnosing mixing in stratified turbulent flows with a locally defined available potential energy. J. Fluid Mech. 740, 114–135.Google Scholar
Shepherd, T. G. 1993 A unified theory of available potential energy. Atmos.-Ocean 31, 1–26.Google Scholar
Tailleux, R. 2010 Entropy versus APE production: on the buoyancy power input in the oceans energy cycle. Geophys. Res. Lett. 37, L22603.Google Scholar
Tailleux, R. 2013a Available potential energy and exergy in stratified fluids. Annu. Rev. Fluid Mech. 45, 35–58.Google Scholar
Tailleux, R. 2013b Available potential energy density for a multicomponent Boussinesq fluid with a nonlinear equation of state. J. Fluid Mech. 735, 499–518.Google Scholar
Tailleux, R. 2013c Irreversible compressible work and available potential energy dissipation. Phys. Scr. T155, 014033.CrossRefGoogle Scholar
Tailleux, R., Lazar, A. & Reason, C. J. C. 2005 Physics and dynamics of density-compensated temperature and salinity anomalies. Part I. Theory. J. Phys. Oceanogr. 35, 849–864.Google Scholar
Winters, K. B. & Barkan, R. 2013 Available potential energy density for Boussinesq fluid flow. J. Fluid Mech. 714, 476–488.Google Scholar
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, 115–128.Google Scholar
Wong, K. C., Tailleux, R. & Gray, S. L. 2016 The computation of reference state and APE production by diabatic processes in an idealized tropical cyclone. Q. J. R. Meteorol. Soc. 142, 2646–2657.Google Scholar
Zemskova, V. E., White, B. L. & Scotti, A. 2015 Available potential energy and the general circulation: partitioning wind, buoyancy forcing, and diapycnal mixing. J. Phys. Oceanogr. 45, 1510–1531.Google Scholar