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On the calculation of the available potential energy of an isolated perturbation in a density-stratified fluid

  • KEVIN G. LAMB (a1)

Abstract

Two methods for calculating the available potential energy (APE) of an isolated feature in a density-stratified fluid, such as an internal solitary wave or an eddy, are compared. The first formulation calculates the APE by integrating the perturbation potential energy density Ew. The second uses an available potential energy density Ea. Both formulations are based on the reference density obtained by adiabatically rearranging the density field to a state of minimum energy. It is shown, under more general conditions than used previously, that (i) the integrals of Ew and Ea over a finite domain are identical; and (ii) that for an isolated feature in an unbounded domain, the far-field density can be used as the reference density if Ea is used to find the APE. This is not the case when Ew is used, hence use of the available potential energy density formulation is simpler in this situation.

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Andrews, D. G. 1981 A note on potential energy density in a stratified compressible fluid. J. Fluid Mech. 107, 227236.
Arneborg, L. 2002 Mixing efficiences in patchy turbulence. J. Phys. Oceanogr. 32, 14961506.
Benzohra, M. & Millot, C. 1995 Hydrodynamics of an open sea algerian eddy. Deep-Sea Res. I 42, 18311847.
Bogucki, D. & Garrett, C. 1993 A simple model for the shear-induced decay of an internal solitary wave. J. Phys. Oceanogr. 23, 17671776.
Hebert, D. 1988 The available potential energy of an isolated feature. J. Geophys. Res. 93, 556564.
Henning, C. C. & Vallis, G. K. 2004 The effects of mesoscale eddies on the main subtropical thermocline. J. Phys. Oceanogr. 34, 24282443.
Holliday, D. & McIntyre, M. E. 1981 On potential energy density in an incompressible stratified fluid. J. Fluid Mech. 107, 221225.
Huang, R. X. 2005 Available potential energy in the world's oceans. J. Marine Res. 63, 141158.
Klymak, J. M. & Moum, J. N. 2003 Internal solitary waves of elevation advancing on a shoaling shelf. Geophys. Res. Lett. 30 (20), 2045, doi:10.1029/2006GL025932.
Klymak, J. M., Pinkel, R., Liu, C.-T., Liu, A. K. & David, L. 2006 Prototypical solitons in the south china sea. Geophys. Res. Lett. 33, L11607, doi:10.1029/2006GL025932.
Lamb, K. G. 2007 Energy and pseudoenergy flux in the internal wave field generated by tidal flow over topography. Cont. Shelf Res. 27, 12081232.
Legg, S. & McWilliams, J. C. 2001 Convective modifications of a geostrophic eddy field. J. Phys. Oceanogr. 31, 874891.
Lorenz, E. N. 1955 Available potential energy and the maintenance of the general circulation. Tellus 7, 157167.
Moum, J. N., Klymak, J. M., Nash, J. D., Perlin, A. & Smyth, W. D. 2007 Energy transport by nonlinear internal waves. J. Phys. Oceanogr. 37, 19681988.
Prater, M. D. & Sanford, T. B. 1994 A meddy off cape st. vincent. part i: Description. J. Phys. Oceanogr. 24, 15721586.
Reid, R. O., Elliot, B. E. & Olson, D. B. 1981 Available potential energy: a clarification. J. Phys. Oceanogr. 10, 90104.
Scotti, A., Beardsley, R. & Butman, B. 2006 On the interpretation of energy and energy fluxes of nonlinear internal waves: an example from massachusetts bay. J. Fluid Mech. 561, 103112.
Shepherd, T. 1993 A unified theory of available potential energy. Atmos. Oceans 31, 126.
Venayagamoorthy, S. K. & Fringer, O. B. 2005 Nonhydrostatic and nonlinear contributions to the energy flux budget in nonlinear internal waves. Geophys. Res. Lett. 32, L15603, doi:10.1029/2005GL023432.
Winters, K. B., Lombard, P. N., Riley, J. J. & D'Asaro, E. A. 1995 Available potential energy and mixing in stratified fluids. J. Fluid Mech. 289, 115128.
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On the calculation of the available potential energy of an isolated perturbation in a density-stratified fluid

  • KEVIN G. LAMB (a1)

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