A closer look at chaotic advection in the stratosphere. part i: geometric structure

Journal of the Atmospheric Sciences

Volumn 56, Issue 24, 1999, Pages 4134-4152

  Ngan, Keith ^a,b   Shepherd, Theodore G ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CORRELATION METHODS; MATHEMATICAL MODELS; UPPER ATMOSPHERE;

CHAOTIC ADVECTION; EULERIAN AUTOCORRELATION; LAGRANGIAN AUTOCORRELATION; ROSSBY WAVE CRITICAL LAYERS;

ATMOSPHERIC MOVEMENTS;

ADVECTION; GEOMETRY; MIXING; STRATOSPHERE;

EID: 0033573468     PISSN: 00224928     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0469(1999)056<4134:ACLACA>2.0.CO;2     Document Type: Article

References (56)

1. Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics. Academic Press, 489 pp.
2. Antonsen, T. M., Z. Fan, E. Ott, and E. Garcia-Lopez, 1996: The role of chaotic orbits in the determination of power spectra of passive scalars. Phys. Fluids, 8, 3094-3104.
3. Badii, R., K. Heinzelmann, P. F. Meier, and A. Politi, 1988: Correlation functions and generalized Lyapunov exponents. Phys. Rev. A, 37, 1323-1328.
4. Batchelor, G. K., 1952: The effect of homogeneous turbulence on material lines and surfaces. Proc. Roy. Soc. London A, 213,349366.
5. _, 1959: Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1, General discussion and the case of small conductivity. J. Fluid Mech., S, 113-133.
6. Beagley, S. R., J. de Grandpré, J. N. Koshyk, N. A. McFarlane, and T. G. Shepherd, 1997: Radiative-dynamical climatology of the first-generation Canadian Middle Atmosphere Model. Almos.Ocean, 35,293-331.
7. Beigie, D., A. Leonard, and S. Wiggins, 1994: Invariant manifold templates for chaotic advection. Chaos Applied to Fluid Mixing, H. Aref and M. S. El Naschie, Eds., Pergamon Press, 5-124.
8. Bowman, K. P., 1993a: Large-scale isentropic mixing properties of the Antarctic polar vortex from analyzed winds. J. Geophys. Res., 98,23013-23027.
9. _, 1993b: Barotropic simulation of large-scale mixing in the Antarctic polar vortex. J. Atmos. Sei., 50, 2902-2914.
10. _, 1996: Rossby wave phase speeds and mixing barriers in the stratosphere. Part I: Observations. J. Atmos. Sei., 53, 905-916.
11. Chertkov, M., G. Falkovich, I. Kolokolov, and I. Lebedev, 1995: Statistics of a passive scalar advected by a large-scale two-dimensional velocity field: Analytic solution. Phys. Rev. E, 51, 5609-5627.
12. Côté, J., M. Roch, A. Staniforth, and L. Pillion, 1993: A variableresolution semi-Lagrangian finite-element global model of the shallow-water equations. Mon. Wea. Rev., 121, 231-243.
13. Crisanti, A., and A. Vulpiani, 1993: On the effects of noise and drift on diffusion in fluids. J. Stat. Phys., 70, 197-211.
14. Dresselhaus, E., and M. Tabor, 1989: The persistence of strain in dynamical systems. J. Phys. A, 22, 971-984.
15. Dritschel, D. G., P. H. Haynes, M. N. Juckes, and T. G. Shepherd, 1991: The stability of a two-dimensional vorticity filament under uniform strain. J. Fluid Mech., 230, 647-665.
16. Haller, G., and A. C. Poje, 1998: Finite time transport in aperiodic flows. Physica D, 119, 352-380.
17. Haynes, P. H., 1987: On the instability of sheared disturbances. J. Fluid Mech., 175, 463-478.
18. _, 1989: The effect of barotropic instability on the nonlinear evolution of a Rossby-wave critical layer. J. Fluid Mech., 207, 231266.
19. _, and M. E. Mclntyre, 1987: On the representation of Rossbywave critical layers and wave breaking in zonally truncated models. J. Atmos. Sei., 44, 2359-2382.
20. _, and J. Anglade, 1997: The vertical-scale cascade in atmospheric tracers due to large-scale differential advection. J. Atmos. Sei., 54, 1121-1136.
21. Held, I. M., and P. J. Phillips, 1987: Linear and nonlinear barotropic decay on the sphere. J. Atmos. Sei., 44, 200-207.
22. Ishioka, K., and S. Yoden, 1995: Non-linear aspects of a barotropically unstable polar vortex in a forced-dissipative system: Flow regimes and tracer transport. J. Meteor. Soc. Japan, 73, 201212.
23. Jana, S. C., G. Metcalfe, and J. M. Ottino, 1994: Experimental and computational study of mixing in complex Stokes flow: The vortex mixing flow and multicellular cavity flows. J. Fluid Mech., 269, 199-246.
24. Juckes, M. N., 1989: A shallow water model of the winter stratosphere. J. Atmos. Sei., 46, 2934-2955.
25. _, and M. E. Mclntyre, 1987: A high-resolution one-layer model of breaking planetary waves in the stratosphere. Nature, 328, 590-596.
26. Killworth, P. D., and M. E. Mclntyre, 1985: Do Rossby-wave critical layers absorb, reflect or over-reflect? J. Fluid Mech., 161, 449492.
27. Kraichnan, R. H., 1974: Convection of a passive scalar by a quasiuniform random straining field. J. Fluid Mech., 64, 737-762.
28. Malhotra, N., and S. Wiggins, 1998: Geometric structures, lobe dynamics, and Lagrangian transport in flows with aperiodic timedependence, with applications to Rossby wave flow. J. Nonlinear Sei., S, 401-456.
29. McCalpin, J. D., 1988: A quantitative analysis of the dissipation inherent in semi-Lagrangian advection. Mon. Wea. Rev., 116, 2330-2336.
30. Methven, J., and B. Hoskins, 1999: The advection of high-resolution tracers by low-resolution winds. J. Atmos. Sei., 56, 3262-3285.
31. Miller, P. D., C. K. R. T. Jones, A. M. Rogerson, and L. J. Pratt, 1997: Quantifying transport in numerically generated velocity fields. Physica D, 110, 105-122.
32. Ngan, K., 1997: Chaotic advection in the stratosphere. Ph.D. thesis, University of Toronto, 179 pp.
33. _, and T. G. Shepherd, 1997: Chaotic mixing and transport in Rossby-wave critical layers. J. Fluid Mech., 334, 315-351.
34. _, and _, 1999: A closer look at chaotic advection in the stratosphere. Part II: Statistical diagnostics. J. Atmos. Sei., 56, 4153-4166.
35. Norton, \V. A., 1994: Breaking Rossby waves in a model stratosphere diagnosed by a vortex-following coordinate system and a technique for advecting material contours. J. Atmos. Sei., 51, 654673.
36. Ottino, J. M., 1989: The Kinematics of Mixing: Stretching, Chaos and Transport. Cambridge University Press, 364 pp.
37. Pierce, R. B., and T. D. A. Fairlie, 1993: Chaotic advection in the . stratosphere: Implications for the dispersal of chemically perturbed air from the polar vortex. J. Geophys. Res., 98, 18 589-18595.
38. _, _, W. L. Grase, R. Swinbank, and A. O'Neill, 1994: Mixing processes within the polar night jet. J. Atmos. Sei., 51, 29572972.
39. Pierrehumbert, R. T., 1994: Tracer microstructure in the large-eddy dominated regime. Chaos Applied to Fluid Mixing, H. Aref and M. S. El Naschie, Eds., Pergamon Press, 347-366.
40. Poje, A. C., and G. Haller, 1999: Geometry of cross-stream mixing in a double-gyre ocean model. J. Phys. Oceanogr., 29, 16491665.
41. Polvani, L. M., D. W. Waugh, and R. A. Plumb, 1995: On the subtropical edge of the stratospheric surf zone. J. Atmos. Sei., 52, 1288-1309.
42. Randel, W. J., and I. M. Held, 1991: Phase speed spectra of transient eddy fluxes and critical layer absorption. J. Atmos. Sei., 48,688697.
43. Rogerson, A. M., P. D. Miller, L. J. Pratt, and C. K. R. T. Jones, 1999: Lagrangian motion and fluid exchange in a barotropic meandering jet. J. Phys. Oceanogr., 29, 2635-2655.
44. Salby, M. L., 1992: The influence of planetary-wave transience on horizontal air motions in the stratosphere. J. Atmos. Sei., 49, 405-421.
45. _, and R. R. Garcia, 1987: Vacillations induced by interference of stationary and traveling planetary waves. J. Atmos. Sei., 44, 2679-2711.
46. _, _, D. O'Sullivan, and J. Tribbia, 1990a: Global transport calculations with an equivalent barotropic system. J. Atmos. Sei., 47, 188-214.
47. _, D. O'Sullivan, R. R. Garcia, and P. Callaghan, 199Ub: Air motions accompanying the development of a planetary wave critical layer. J. Annas. Sei.. 47, 1179-1204.
48. Schoeberl, M. R., and P. A. Newman, 1995: A multiple-level trajectory analysis of vortex filaments. J. Geophys. Res., 100, 25 80125815.
49. Scinocca, J. E, and P. H. Haynes, 1998: Dynamical forcing of planetary waves by tropospheric baroclinic eddies. J. Atmos. Sei., 55, 2361-2392.
50. Sutton, R. T., H. Maclean, R. Swinbank, A. O'Neill, and F. W. Taylor, 1994: High-resolution stratospheric tracer fields estimated from satellite observations using Lagrangian trajectory calculations. J. Atmos. Sei., 51, 2995-3005.
51. Swanson, K. L., and R. T. Pierrehumbert, 1997: Lower-tropospheric heat transport in the Pacific storm track. J. Atmos. Sei., 54,15331543.
52. Tuck, A. E, and Coauthors, 1997: The Brewer-Dobson circulation in the light of high-altitude in-situ aircraft observations. Quart. J. Roy. Meteor. Soc., 123, 1-69.
53. Waugh, D. \V., and D. G. Dritschel, 1991: The stability of filamentary vorticity in two-dimensional geophysical vortex-dynamics models. J. Fluid Alech., 231, 575-598.
54. _, and R. A. Plumb, 1994: Contour advection with surgery: A technique for investigating fine-scale structure in tracer transport. J. Atmos. Sei., 51, 530-540.
55. Wiggins, S., 1990: Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer, 672 pp.
56. _, 1992: Chaotic Transport in Dynamical Systems. Springer, 301 pp.