Canonical transfer and multiscale energetics for primitive and quasigeostrophic atmospheres

Journal of the Atmospheric Sciences

Volumn 73, Issue 11, 2016, Pages 4439-4468

  Liang, X San ^a  

^a NANJING UNIVERSITY OF INFORMATION SCIENCE AND TECHNOLOGY   (China)

Author keywords

Diagnostics; Dynamics; Energy transport; Instability; Madden Julian oscillation

Indexed keywords

ASTROPHYSICS; BUOYANCY; CLIMATOLOGY; DYNAMICS; ENERGY TRANSFER; KINETIC ENERGY; KINETICS; PLASMA DIAGNOSTICS; PLASMA STABILITY; POTENTIAL ENERGY;

ENERGY TRANSPORT; ENGINEERING FLUIDS; GEOPHYSICAL FLUID DYNAMICS; HAMILTONIAN MECHANICS; MADDEN-JULIAN OSCILLATION; MULTISCALE WINDOW TRANSFORMS; PRIMITIVE EQUATIONS; QUASI-GEOSTROPHIC MODEL;

TRANSPORT PROPERTIES;

EID: 84994166949     PISSN: 00224928     EISSN: 15200469     Source Type: Journal    
DOI: 10.1175/JAS-D-16-0131.1     Document Type: Article

References (74)

1. Andrews, D., and M. McIntyre, 1976: Planetary waves in horizontal and vertical shear: The generalized Eliassen-Palm relation and the mean zonal acceleration. J. Atmos. Sci., 33, 2031-2048, doi:10.1175/1520-0469(1976)033<2031:PWIHAV>2.0.CO;2
2. Berloff, P. S., 2005: On dynamically consistent eddy fluxes. Dyn. Atmos. Oceans, 38, 123-146, doi:10.1016/j.dynatmoce.2004.11.003
3. Boyd, J., 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, doi:10.1175/1520-0469(1976)033<2285:TNOWWT>2.0.CO;2
4. Bühler, O., 2009: Waves and Mean Flows. Cambridge University Press, 370 pp
5. Cai, M., and M. Mak, 1990: On the basic dynamics of regional cyclogenesis. J. Atmos. Sci., 47, 1417-1442, doi:10.1175/1520-0469(1990)047<1417:OTBDOR>2.0.CO;2
6. Cai, M., S. Yang, H. M. van den Dool, and V. E. Kousky, 2007: Dynamical implications of the orientation of atmospheric eddies: A local energetics perspective. Tellus, 59A, 127-140, doi:10.1111/j.1600-0870.2006.00213.x
7. Chapman, C. C., A. E. Kiss, and S. R. Rintoul, 2015: The dynamics of Southern Ocean storm tracks. J. Phys. Oceanogr., 45, 884-903, doi:10.1175/JPO-D-14-0075.1
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, doi:10.1029/JZ066i001p00083
9. Chen, R., G. R. Flier, and C. Wunsch, 2014: A description of local and nonlocal eddy-mean flow interaction in a globally eddy-permitting state estimate. J. Phys. Oceanogr., 44, 2336-2352, doi:10.1175/JPO-D-14-0009.1
10. Chorin, A. J., 1994: Vorticity and Turbulence. Springer-Verlag, 173 pp
11. Dewar, W. K., and J. M. Bane, 1989: Gulf Stream dynamics. Part II. Eddy energetics at 73°W. J. Phys. Oceanogr., 19, 1574-1587, doi:10.1175/1520-0485(1989)019<1574:GSDPIE>2.0.CO;2
12. Dickinson, R. E., 1969: Theory of planetary wave-zonal flow interaction. J. Atmos. Sci., 26, 73-81, doi:10.1175/1520-0469(1969)026<0073:TOPWZF>2.0.CO;2
13. Eliassen, A., and E. Palm, 1961: On the transfer of energy in stationary mountain waves. Geofys. Publ., 22 (3), 1-23
14. Fels, S. B., and R. S. Lindzen, 1974: The interaction of thermally excited gravity waves with mean flows. Geophys. Fluid Dyn., 6, 149-191, doi:10.1080/03091927409365793
15. Fournier, A., 2002: Atmospheric energetics in the wavelet domain. Part I: Governing equations and interpretation for idealized flows. J. Atmos. Sci., 59, 1182-1197, doi:10.1175/1520-0469(2002)059<1182:AEITWD>2.0.CO;2
16. Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150-160, doi:10.1175/1520-0485(1990)020<0150:IMIOCM>2.0.CO;2
17. Greatbatch, R. J., 1998: Exploring the relationship between eddy-induced transport velocity, vertical momentum transfer, and the isopycnal flux of potential vorticity. J. Phys. Oceanogr., 28, 422-432, doi:10.1175/1520-0485(1998)028<0422:ETRBEI>2.0.CO;2
18. Haidvogel, D., J. C. McWilliams, and P. Gent, 1992: Boundary current separation in a quasigeostrophic, eddy-resolving ocean circulation model. J. Phys. Oceanogr., 22, 882-902, doi:10.1175/1520-0485(1992)022<0882:BCSIAQ>2.0.CO;2
19. Harrison, D. E., and A. R. Robinson, 1978: Energy analysis of open regions of turbulent flows-Mean eddy energetics of a numerical ocean circulation experiment. Dyn. Atmos. Oceans, 2, 185-211, doi:10.1016/0377-0265(78)90009-X
20. Haynes, P. H., 1988: Forced, dissipative generalizations of finite-amplitude wave-activity conservation relations for zonal and nonzonal basic flows. J. Atmos. Sci., 45, 2352-2362, doi:10.1175/1520-0469(1988)045<2352:FDGOFA>2.0.CO;2
21. Holland, W. R., 1978: The role of mesoscale eddies in the general circulation of the ocean-numerical experiments using a wind-driven quasi-geostrophic model. J. Phys. Oceanogr., 8, 363-392, doi:10.1175/1520-0485(1978)008<0363:TROMEI>2.0.CO;2
22. Holliday, D., and M. E. McIntyre, 1981: On potential energy density in an incompressible, stratified fluid. J. Fluid Mech., 107, 221-225, doi:10.1017/S0022112081001742
23. Holopainen, E. O., 1978: A diagnostic study on the kinetic energy balance of the long-term mean flow and the associated transient fluctuations in the atmosphere. Geophysica, 15, 125-145
24. Hoskins, B. J., J. Brian, I. N. James, and G. H. White, 1983: The shape, propagation and mean-flow interaction of large-scale weather systems. J. Atmos. Sci., 40, 1595-1612, doi:10.1175/1520-0469(1983)040<1595:TSPAMF>2.0.CO;2
25. Hsu, P.-C., T. Li, and C.-H. Tsou, 2011: Interactions between boreal summer intraseasonal oscillations and synoptic-scale disturbances over the western North Pacific. Part I: Energetics diagnosis. J. Climate, 24, 927-941, doi:10.1175/2010JCLI3833.1
26. Huang, N. E., Z. Shen, and S. R. Long, 1999: A new view of nonlinear water waves: The Hilbert spectrum. Annu. Rev. Fluid Mech., 31, 417-457, doi:10.1146/annurev.fluid.31.1.417
27. Iima, M., and S. Toh, 1995: Wavelet analysis of the energy transfer caused by convective terms: Application to the Burgers shock. Phys. Rev., 52E, 6189-6201
28. Ingersoll, A. P., 2005: Boussinesq and anelastic approximations revisited: Potential energy release during thermobaric instability. J. Phys. Oceanogr., 35, 1359-1369, doi:10.1175/JPO2756.1
29. Jin, F. F., 2010: Eddy-induced instability for low-frequency variability. J. Atmos. Sci., 67, 1947-1964, doi:10.1175/2009JAS3185.1
30. Kao, S. K., 1968: Governing equations and spectra for atmospheric motion and transports in frequency, wave-number space. J. Atmos. Sci., 25, 32-38, doi:10.1175/1520-0469(1968)025<0032:GEASFA>2.0.CO;2
31. Liang, X. S., and A. R. Robinson, 2004: A study of the Iceland-Faeroe frontal variability using the multiscale energy and vorticity analysis. J. Phys. Oceanogr., 34, 2571-2591, doi:10.1175/JPO2661.1
32. Liang, X. S., and M. Wang, 2004: A study of turbulent wakes using a novel localized stability analysis. Proc. Summer Program 2004, Stanford, CA, Stanford Center for Turbulence Research and NASA Ames Research Center, 211-222. [Available online at https://web.stanford.edu/group/ctr/ctrsp04/liang.pdf.]
33. Liang, X. S., and A. R. Robinson, 2005: Localized multiscale energy and vorticity analysis: I. Fundamentals. Dyn. Atmos. Oceans, 38, 195-230, doi:10.1016/j.dynatmoce.2004.12.004
34. Liang, X. S., and D. G. M. Anderson, 2007: Multiscale window transform. SIAM J. Multiscale Model. Simul., 6, 437-467, doi:10.1137/06066895X
35. Liang, X. S., and A. R. Robinson, 2007: Localized multi-scale energy and vorticity analysis: II. Finite-amplitude instability theory and validation. Dyn. Atmos. Oceans, 44, 51-76, doi:10.1016/j.dynatmoce.2007.04.001
36. Liang, X. S., and A. R. Robinson, 2009: Multiscale processes and nonlinear dynamics of the circulation and upwelling events off Monterey Bay. J. Phys. Oceanogr., 39, 290-313, doi:10.1175/2008JPO3950.1
37. Lindzen, R. S., and B. Farrell, 1987: Atmospheric dynamics: U.S. national report to International Union of Geodesy and Geophysics 1983-1986. Rev. Geophys., 25, 323-328, doi:10.1029/RG025i003p00323
38. Lorenz, E. N., 1955: Available potential energy and the maintenance of the general circulation. Tellus, 7, 157-167, doi:10.1111/j.2153-3490.1955.tb01148.x
39. Luo, D., J. Cha, L. Zhong, and A. Dai, 2014: A nonlinear multiscale interaction model for atmospheric blocking: The eddy-blocking matching mechanism. Quart. J. Roy. Meteor. Soc., 140, 1785-1808, doi:10.1002/qj.2337
40. Madden, R. A., and P. R. Julian, 1971: Detection of a 40-50 day oscillation in the zonal wind in the tropical Pacific. J. Atmos. Sci., 28, 702-708, doi:10.1175/1520-0469(1971)028<0702:DOADOI>2.0.CO;2
41. Madden, R. A., and P. R. Julian, 2005: Historical perspective. Intraseasonal Variability in the Atmosphere-Ocean Climate System, W. K.-M. Lau and D. Waliser, Eds., Springer, 1-18
42. Majda, A. J., and J. A. Biello, 2004: A multiscale model for tropical intraseasonal oscillations. Proc. Natl. Acad. Sci. USA, 101, 4736-4741, doi:10.1073/pnas.0401034101
43. Majda, A. J., and Q. Yang, 2016: A multiscale model for the intraseasonal impact of the diurnal cycle over the maritime continent on the Madden-Julian oscillation. J. Atmos. Sci., 73, 579-604, doi:10.1175/JAS-D-15-0158.1
44. Marshall, D. P., and A. J. Adcroft, 2010: Parameterization of ocean eddies: Potential vorticity mixing, energetics and Arnold's first stability theorem. Ocean Modell., 32, 188-204, doi:10.1016/j.ocemod.2010.02.001
45. Marshall, J. C., 1984: Eddy-mean-flow interaction in a barotropic ocean model. Quart. J. Roy. Meteor. Soc., 110, 573-590, doi:10.1002/qj.49711046502
46. Matsuno, T., 1971: A dynamical model of the stratospheric sudden warming. J. Atmos. Sci., 28, 1479-1494, doi:10.1175/1520-0469(1971)028<1479:ADMOTS>2.0.CO;2
47. McIntyre, M. E., 1980: An introduction to the generalized Lagrangian-mean description of wave, mean-flow interaction. Pure Appl. Geophys., 118, 152-176, doi:10.1007/BF01586449
48. McWilliams, J. C., 2006: Fundamentals of Geophysical Fluid Dynamics. Cambridge University Press, 249 pp
49. McWilliams, J. C., and J. M. Restrepo, 1999: The wave-driven ocean circulation. J. Phys. Oceanogr., 29, 2523-2540, doi:10.1175/1520-0485(1999)029<2523:TWDOC>2.0.CO;2
50. Moncrieff, M. W., 2004: Analytic representation of the large-scale organization of tropical convection. J. Atmos. Sci., 61, 1521-1538, doi:10.1175/1520-0469(2004)061<1521:AROTLO>2.0.CO;2
51. Murakami, S., 2011: Atmospheric local energetics and energy interactions between mean and eddy fields. Part I: Theory. J. Atmos. Sci., 68, 760-768, doi:10.1175/2010JAS3664.1
52. Nakamura, N., and A. Solomon, 2010: Finite-amplitude wave activity and mean flow adjustments in the atmospheric general circulation. Part I: Quasigeostrophic theory and analysis. J. Atmos. Sci., 67, 3967-3983, doi:10.1175/2010JAS3503.1
53. Pedlosky, J., 1987: Geophysical Fluid Dynamics. Springer-Verlag, 710 pp
54. Pinardi, N., and A. R. Robinson, 1986: Quasigeostrophic energetics of open ocean regions. Dyn. Atmos. Oceans, 10, 185-219, doi:10.1016/0377-0265(86)90013-8
55. Plumb, R. A., 1983: A new look at the energy cycle. J. Atmos. Sci., 40, 1669-1688, doi:10.1175/1520-0469(1983)040<1669:ANLATE>2.0.CO;2
56. Plumb, R. A., 1986: Three-dimensional propagation of transient quasi-geostrophic eddies and its relationship with the eddy forcing of the time-mean flow. J. Atmos. Sci., 43, 1657-1678, doi:10.1175/1520-0469(1986)043<1657:TDPOTQ>2.0.CO;2
57. Plumb, R. A., and R. Ferrari, 2005: Transformed Eulerian-mean theory. Part I: Nonquasigeostrophic theory for eddies on a zonal-mean flow. J. Phys. Oceanogr., 35, 165-174, doi:10.1175/JPO-2669.1
58. Pope, S. B., 2004: Turbulent Flows. Cambridge University Press, 771 pp
59. Rhines, P. B., and W. R. Holland, 1979: A theoretical discussion of eddy-driven mean flows. Dyn. Atmos. Oceans, 3, 289-325, doi:10.1016/0377-0265(79)90015-0
60. Salby, M. L., 1996: Fundamentals of Atmospheric Physics. Academic Press, 627 pp
61. Saltzman, B., 1957: Equations governing the energetics of the larger scales of atmospheric turbulence in the domain of wave number. J. Meteor., 14, 513-523, doi:10.1175/1520-0469(1957)014<0513:EGTEOT>2.0.CO;2
62. Saltzman, B., 1970: Large-scale atmospheric energetics in the wave-number domain. Rev. Geophys. Space Phys., 8, 289-302, doi:10.1029/RG008i002p00289
63. Sheng, J., and Y. Hayashi, 1990: Estimation of atmospheric energetics in the frequency domain during the FGGE year. J. Atmos. Sci., 47, 1255-1268, doi:10.1175/1520-0469(1990)047<1255:EOAEIT>2.0.CO;2
64. Strang, G., and T. Nguyen, 1997: Wavelets and Filter Banks. 2nd ed. Wellesley-Cambridge Press, 520 pp
65. Su, Z., A. Ingersoll, A. Steward, and A. Thompson, 2016: Ocean convective available potential energy. Part II: Energetics of thermobaric convection and thermobaric cabbeling. J. Phys. Oceanogr., 46, 1097-1115, doi:10.1175/JPO-D-14-0156.1
66. Tailleux, R., 2013: Available potential energy and energy in stratified fluids. Annu. Rev. Fluid Mech., 45, 35-58, doi:10.1146/annurev-fluid-011212-140620
67. Takaya, K., 2001: A formulation of a phase-independent wave-activity flux for stationary and migratory quasigeostrophic eddies on a zonally varying basic flow. J. Atmos. Sci., 58, 608-627, doi:10.1175/1520-0469(2001)058<0608:AFOAPI>2.0.CO;2
68. Trenberth, K. E., 1986: An assessment of the impact of transient eddies on the zonal flow during a blocking episode using localized Eliassen-Palm flux diagnostics. J. Atmos. Sci., 43, 2070-2087, doi:10.1175/1520-0469(1986)043<2070:AAOTIO>2.0.CO;2
69. Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, 745 pp
70. Visbeck, M., J. Marshall, T. Haine, and M. Spall, 1997: Specification of eddy transfer coefficients in coarse-resolution ocean circulation models. J. Phys. Oceanogr., 27, 381-402, doi:10.1175/1520-0485(1997)027<0381:SOETCI>2.0.CO;2
71. Waterman, S., and S. R. Jayne, 2011: Eddy-mean flow interactions in the along-stream development of a western boundary current jet: An idealized model study. J. Phys. Oceanogr., 41, 682-707, doi:10.1175/2010JPO4477.1
72. Wheeler, M. C., and H. H. Hendon, 2004: An all-season real-time multivariate MJO index: Development of an index for monitoring and prediction. Mon. Wea. Rev., 132, 1917-1932, doi:10.1175/1520-0493(2004)132<1917:AARMMI>2.0.CO;2
73. Winters, K., and R. Barkan, 2013: Available potential energy density for Boussinesq fluid flow. J. Fluid Mech., 714, 476-488, doi:10.1017/jfm.2012.493
74. Winters, K., P. Lombard, J. Riley, and E. D'Asaro, 1995: Available potential energy and mixing in density-stratified fluids. J. Fluid Mech., 289, 115-128, doi:10.1017/S002211209500125X