An exact thickness-weighted average formulation of the boussinesq equations

Journal of Physical Oceanography

Volumn 42, Issue 5, 2012, Pages 692-707

  Young, William R ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AVERAGE VELOCITY; BOUSSINESQ EQUATIONS; BUOYANCY FREQUENCY; CARTESIAN COORDINATE; EDDY FLUXES; EDDY FORCING; FULLY NONLINEAR; MOMENTUM EQUATION; POTENTIAL VORTICITY; ROTATING FLOW; SECOND ORDERS;

BUOYANCY; STATISTICAL METHODS; THREE DIMENSIONAL; VORTEX FLOW;

EQUATIONS OF MOTION;

BOUSSINESQ EQUATION; BUOYANCY; EDDY; ROSSBY WAVE; ROTATING FLOW; STRATIFIED FLOW; THREE-DIMENSIONAL MODELING; TURBULENT FLOW; VORTICITY;

EID: 84861473167     PISSN: 00223670     EISSN: 15200485     Source Type: Journal    
DOI: 10.1175/JPO-D-11-0102.1     Document Type: Article

References (43)

1. Aiki, H., and T. Yamagata, 2006: Energetics of the layer-thickness form drag based on an integral identity. Ocean Sci., 2, 161-171.
2. Aiki, H., T. Jacobson, and T. Yamagata, 2004: Parameterizing ocean eddy transports from surface to bottom. J. Geophys. Res., 31, L19302, doi:10.1029/2004GL020703.
3. Andrews, D. G., 1983: A finite-amplitude Eliassen-Palm theorem in isentropic coordinates. J. Atmos. Sci., 40, 1877-1883.
4. Andrews, D. G., and M. E. McIntyre, 1976: Planetary waves in vertical and horizontal shear: The generalized Eliassen-Palm relation and the mean zonal acceleration. J. Atmos. Sci., 33, 2031-2048.
5. Boyd, J. P., 1976: The noninteraction of waves with the zonally averaged flow on a spherical Earth and the interrelationships of eddy fluxes of energy, heat and momentum. J. Atmos. Sci., 33, 2285-2291.
6. Bretherton, F. P., 1966: Critical layer instability in baroclinic flows. Quart. J. Roy. Meteor. Soc., 92, 325-334.
7. Cessi, P., 2008: An energy-constrained parametrization of eddy buoyancy flux. J. Phys. Oceanogr., 38, 1807-1819.
8. Charney, J. G., and P. G. Drazin, 1961: Propagation of planetary scale disturbances from the lower into the upper atmosphere. J. Geophys. Res., 66, 83-109.
9. Davis, R. E., 1994: Diapycnal mixing in the ocean: Equations for large-scale budgets. J. Phys. Oceanogr., 24, 777-800.
10. de Szoeke, R. A., and A. F. Bennett, 1993: Microstructure fluxes across density surfaces. J. Phys. Oceanogr., 23, 2254-2264.
11. Dritschel, D. G., and M. E. McIntyre, 2008: Multiple jets as PV staircases: The Phillips effect and the resilience of eddytransport barriers. J. Atmos. Sci., 65, 855-874.
12. Ferrari, R., S. M. Griffies, G. Nurser, and G. K. Vallis, 2010: A boundary value problem for the parameterized mesoscale eddy transport. Ocean Modell., 32, 143-156.
13. Ferreira, D., and J. Marshall, 2006: Formulation and implementation of a "residual mean" ocean circulation model. Ocean Modell., 13, 86-107.
14. Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150-155.
15. Gent, P. R., and J. C. McWilliams, 1996: Eliassen-Palm fluxes and the momentum equation in a non-eddy-resolving ocean circulation model. J. Phys. Oceanogr., 26, 2539-2546.
16. Gent, P. R., J. Willebrand, T. J. McDougall, and J. C. McWilliams, 1995: Parameterizing eddy-induced tracer transports in ocean circulation models. J. Phys. Oceanogr., 25, 463-474.
17. Greatbatch, R. J., 1998: Exploring the relationship between eddyinduced transport velocity, vertical momentum transfer, and the isopycnal flux of potential vorticity. J. Phys. Oceanogr., 28, 422-432.
18. Greatbatch, R. J., and K. G. Lamb, 1990: On parameterizing vertical mixing of momentum in non-eddy resolving ocean models. J. Phys. Oceanogr., 20, 1634-1637.
19. Greatbatch, R. J., and T. J. McDougall, 2003: The non-Boussinesq temporal residual mean. J. Phys. Oceanogr., 33, 1231-1239.
20. Griffies, S. M., 1998: The Gent-McWilliams skew flux. J. Phys. Oceanogr., 28, 831-841.
21. Griffies, S. M., 2004: Fundamentals of Ocean Climate Models. Princeton University Press, 518 pp.
22. Haynes, P. H., and M. E. McIntyre, 1987: On the evolution of vorticity and potential vorticity in the presence of diabatic heating and frictional or other forces. J. Atmos. Sci., 44, 828- 841.
23. Haynes, P. H., and M. E. McIntyre, 1990: On conservation and impermeability theorems for potential vorticity. J. Atmos. Sci., 47, 2021-2031.
24. Jacobson, T., and H. Aiki, 2006: An exact energy for TRM theory. J. Phys. Oceanogr., 36, 558-564.
25. Killworth, P. D., 1997: On the parameterization of eddy transfer: Part I. Theory. J. Mar. Res., 55, 1171-1197.
26. Killworth, P. D., 2001: Boundary conditions on quasi-Stokes velocities in parameterizations. J. Phys. Oceanogr., 31, 1132-1155.
27. Lee, M.-M., and H. Leach, 1996: Eliassen-Palm flux and eddy potential vorticity flux for a nonquasigeostrophic time-mean flow. J. Phys. Oceanogr., 26, 1304-1319.
28. McDougall, T. J., and P. C. McIntosh, 1996: The temporal-residualmean velocity. Part I: Derivation and the scalar conservation equations. J. Phys. Oceanogr., 26, 2653-2665.
29. McDougall, T. J., and P. C. McIntosh, 2001: The temporal-residual-mean velocity. Part II: Isopycnal interpretation and the tracer and momentum equations. J. Phys. Oceanogr., 31, 1222-1246.
30. Morse, P. M., and H. Feshbach, 1953: Methods of Theoretical Physics, Part I. McGraw-Hill, 997 pp.
31. Plumb, A. R., 1986: Three-dimensional propagation of transient quasi-geostrophic eddies and its relatonship with eddy forcing of the time-mean flow. J. Atmos. Sci., 43, 1657-1678.
32. Plumb, A. R., and R. Ferrari, 2005: Transformed Eulerian-mean theory. Part I: Nonquasigeostrophic theory for eddies on a zonalmean flow. J. Phys. Oceanogr., 35, 165-174.
33. Rhines, P. B., 1982: Basic dynamics of the large-scale geostrophic circulation. Summer Study Program in Geophysical Fluid Dynamics, Woods Hole Oceanographic Institution Tech. Rep., 1-47.
34. Rhines, P. B., and W. R. Holland, 1979: A theoretical discussion of eddydriven mean flows. Dyn. Atmos. Oceans, 3, 289-325.
35. Rhines, P. B., and W. R. Young, 1982: Homogenization of potential vorticity in planetary gyres. J. Fluid Mech., 122, 347-367.
36. Simmonds, J. G., 1982: A Brief on Tensor Analysis. Springer-Verlag, 92 pp.
37. Smith, R. D., 1999: The primitive equations in the stochastic theory of adiabatic stratified turbulence. J. Phys. Oceanogr., 29, 1865- 1880.
38. Starr, V. P., 1945: A quasi-Lagrangian system of hydrodynamical equations. J. Meteor., 2, 227-237.
39. Taylor, G. I., 1915: Eddy motion in the atmosphere. Philos. Trans. Roy. Soc. London, 215A, 1-23.
40. Treguier, A. M., I. M. Held, and V. D. Larichev, 1997: On the parameterization of quasigeostrophic eddies in primitive equation ocean models. J. Phys. Oceanogr., 27, 567-580.
41. Visbeck, M., J. Marshall, T. Haine, and M. A. Spall, 1997: Specification of eddy transfer coefficients in coarse-resolution ocean circulation models. J. Phys. Oceanogr., 27, 381-402.
42. Winters, K. B., and E. A. D'Asaro, 1996: Diascalar flux and the rate of fluid mixing. J. Fluid Mech., 317, 179-193.
43. Young, W. R., and P. B. Rhines, 1980: Rossby wave action, energy, and enstrophy in forced mean flows. Geophys. Astrophys. Fluid Dyn., 15, 39-52.