Abstract
In this paper, in an equivalent barotropic framework a new forced nonlinear Schroedinger equation is proposed to examine the interaction between the planetary-scale waves and the localized synoptic-scale eddies upstream. With the help of the perturbed inverse scattering transform method, nonlinear parameter equations can be derived to describe the evolution of the dipole soliton amplitude, frequency, group velocity and phase under the forcing of localized synoptic-scale eddies. The numerical solutions of these equations predict that in the interaction between the weak dipole soliton (weak incipient dipole anomaly) and the synoptic-scale eddies, only when the high-frequency eddies themselves have a moderate parameter match they can near resonantly enhance a quasi-stationary large-amplitude split flow. The instantaneous total streamfunction field (the sum of background westerly wind, envelope Rossby soliton and synoptic-scale waves) is found to be very similar to the observed Berggren-type blocking on the weather map(Berggren et al. 1949). The role of synoptic-scale eddies is to increase the amplitude of large-scale dipole anomaly flow, and to decrease its group velocity, phase velocity and zonal wavenumber so that the dipole anomaly system can be amplified and transferred from dispersive system to very weak dispersive one. This may explain why and how the synoptic-scale eddies can reinforce and maintain vortex pair block. Furthermore, it is clearly found that during the prevalence of the vortex pair block the synoptic-scale eddies are split into two branches around the vortex pair block due to the feedback of amplified dipole block.
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References
Benney, D. J., 1979: Large-amplilude Rossby waves. Stud. App. Math., 60, 1–10.
Berggren, R.. B. Bolin, and C. G. Rossby, 1949: An Aero logical Study of zonal motion, its perturbations and break-down. Tellus, 2, 14–37.
Butchart. N., K. Haines, and J. C. Marshall. 1989: A theoretical and diagnostic study of solitary waves and atmos- pheric blocking. J. Almos. Sci.. 2063-2078.
Cai, M.. and M. Mak, 1990: Symbiotic relation between planetary and synoptic-scale waves. J. Atmos. Sci., 47, 2953–2968.
Colucci, S. J., Loesch A. Z. L. F. Bosart, 1981: Spectral evolution of a blocking episode and comparison with wave interaction theory. J. Atmos. Sci., 38, 2092–2111.
Colucci, S. J., 1985: Explosive cyclogenesis and large-scale circulation changes: Implications for atmospheric block- ing. J. Atmos. Sci.,42, 2701–2717.
Colucci, S. J., 1987: Comparative diagnosis of blocking versus nonblocking planetary-scale circulation changes dur- ing synoptic-scale cyclogenesis. J. Atmos: Sci.,44, 124–139.
Crum, F. X., and D. E. Stevens, 1988: A case study atmospheric blocking using isentropic analysis. Mon. Wea. Rev., 116, 223–241.
Dole, R. M., 1986: Persistent anomalies of the extratropical Northern Hemisphere winter time circulation: structure. Mon. Wea. Rev., 114, 178–207.
Frisius, T., Lunkeit, F., Fraedrich, K., James, 1. N., 1998: Storm-trackorganization and variability in a simplified atmospheric global circulation model. Q. J. R. Meteor. Soc., 124, 1021–1043.
Green, J. S. A., 1977: The weather during July 1977: Some dynamical consideration of the drought. Weather, 32, 120–126.
Hansen, A., and T. C. Chen, 1982: A spectral energetics analysis of atmospheric blocking. Mon. Wea. Rev., 110, 1146–1159.
Haines, K.., and J. C. Marshall, 1987: Eddy-forced coherent structures as a prototype of atmospheric blocking. Quart. J. Roy. Meteor. Soc, 113,681–704.
Hasegawa, A., and Y. Kodama, 1995: Solitons in optical communications. Clarendon Press, 320pp.
Holopainen, E., and C. Fortelius, 1987: High-frequency transient eddies and blocking. J. Atmos. Sci., 44, 1632–1645.
Illari, L., and J. C. Marshall, 1983: On the interpretation of eddy fluxes during a blocking episode. J. Atmos. Sci., 40, 2232–2242.
Harri, L., 1984: A diagnostic study of the potential vorticity in a warm blocking anticyclone. J. Atmos. Sci., 41, 3518–3526.
Jeffrey, A., Kawahara, T., 1982: Asymptotic Methods in Nonlinear Wave Theory. Pitman Press, 273pp.
Lejen S, H., and H, Kland, 1983: Characteristics of Northern Hemisphere blocking as determined from a long series of observational data. Tellus, 35A, 350–362.
Lupo, A., R., and P. J. Smith, 1995: Planetary and synoptic-scale interactions during the life cycle of a mid-latitude anticyclone over the North Atlantic. Tellus. 47A, 575–596.
Luo Dehai, 1999a: Near-resonant topographically forced envelope Rossby solitons in a barotropic flow. Geophys. Astrophys. Fluid Dyn., 90, 161–188.
Luo Dehai, 1999b: Envelope Rossby solitons in the large-scale atmosphere and blocking circulations, China Meteoro- logical Press, 113pp. (in Chinese)
Luo Dehai, 2000: Planetary-scale baroclinic envelope Rossby solitons in a two-layer model and their interaction with synoptic-scale eddies. Dyn. Atmos. Oceans, 32, 27–74.
Malanotte-Rizzoli, P., and P. Malguzzi, 1987: Coherent structures in a baroclinic atmosphere. Part III: Block for-mation and eddy forcing.J. Atmos. Sci., 44, 2493–2505.
Malguzzi, P.. 1993: An analytical study on the feedback between large- and small-scale eddies. ,/. Atmos. Sci., 50, 1429–1436.
McWilliams, J. C, 1980: An application of equivalent modons to atmospheric blocking. Dyn. Atmos. Oceans, 5, 219–238.
Mu Mu, Wu Yonghui, Tang Mozhi, and Liu Haiyan. 1999: Nonlinear stability analysis of the zonal flows at middle and high latitudes. Adv. Atmos. Sci.. 16, 569–580.
Mullen, S. L., 1987: Transient eddy forcing of blocking flows. J. Atmos. Sci., 44, 3–22.
Nakamura, H., and J. M. Wallace, 1990: Observed changes in baroclinic wave activity during the life cycles of low-frequency circulation anomalies. J. Atmos. Sci.. 47. 1100–1116.
Nakamura, H., and J. M. Wallace, 1993: Synoptic behaviour of baroclinic eddies during the blocking onset. Mon. Wea. Rev., 121, 1892–1903.
Nakamura, H., Nakamura, M., and J. L. Anderson, 1997: The role of high- and low-frequency dynamics in block- ing formation. Mon. Wea. Rev.. 125. 2074–2093.
Neilley, P. P., 1990, Interaction between synoptic-scale eddies and the large-scale flow during the life cycles of per- sistent flow anomalies. Ph. D. dissertation, MIT, 272pp.
Pierrehumbert, R. T., and P. Malguzzi, 1984: Forced coherent structures and local equilibria in a barotropic atmos-phere. J. Atmos. Sci., 41, 246–257.
Rex, D. F., 1950: Blocking action in the middle troposphere and its effet uponregional climate. I: An aerological study of blocking action. Tellus, 2, 196–301.
Robinson, W. A., 1991: The dynamics of low-frequency variability in a simple model of the global atmosphere. J. Atmos. Sci., 48, 429–441.
Shutts, G. J., 1983: The propagation of eddies in diffluent jetstreams: eddy vorticity forcing of blocking flow fields. Quart. J. R. Meteor. Soc. 109, 737–761.
Taniuti.T., and K. Nishihara, 1983: Nonlinear waves. Pitman Publishing Limited, 258.
Tsou, C. S., and P. J., Smith, 1990: The role of synoptic/ planetary-scale interaction during the development of a blocking anticyclone. Tellus. 42A, 174–193.
Tung, K. K., and A. S. Lindzen, 1979: A theory of stationary long waves. Part I: A simple theory of blocking. Mon. Wea. Rev., 107, 714–734.
Vautard, R., B. Legras and M. Deque, 1988a: On the source of midlatitude low-frequency variability. Part I: A sta- tistical approach to persistence. J. Atmos. Sci., 45, 2811–2843.
Vautard, R., and B. Legras, 1988b: On the source of midlatitude low-frequency variability. Part II: Nonlinear equilibration of weather regimes. J. Atmos. Sci., 45, 2845–2867.
Yamagata, T., 1980: The stability, modulation and long wave resonance of a planetary wave in a rotating, two-layer fluid on a channel beta-plane. J. Meteor. Soc. Japan, 58, 160–171.
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This research was supported jointly by the Foundation for University Key Teacher by the Ministry of Education and by the National Natural Science Foundation of China (49775266, 49905007)), the Knowledge Innovation Key Project of Chinese Academy of Sciences in the Resource Environment Field (Grant No. KZCX 2-203) and the National Key Foundation Research Project (G1998040900, Part I).
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Dehai, L., Jianping, L. Barotropic interaction between planetary- and synoptic-scale waves during the life cycles of blockings. Adv. Atmos. Sci. 17, 649–670 (2000). https://doi.org/10.1007/s00376-000-0026-5
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DOI: https://doi.org/10.1007/s00376-000-0026-5