Charney's Model—the Renowned Prototype of Baroclinic Instability—Is Barotropically Unstable As Well
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摘要
The Charney model is reexamined using a new mathematical tool, the multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis developed by Liang and Robinson to deal with realistic geophysical fluid flow processes. Traditionally, though this model has been taken as a prototype of baroclinic instability, it actually undergoes a mixed one. While baroclinic instability explains the bottom-trapped feature of the perturbation, the second extreme center in the perturbation field can only be explained by a new barotropic instability when the Charney–Green number γ 1, which takes place throughout the fluid column, and is maximized at a height where its baroclinic counterpart stops functioning.The giving way of the baroclinic instability to a barotropic one at this height corresponds well to the rectification of the tilting found on the maps of perturbation velocity and pressure. Also established in this study is the relative importance of barotropic instability to baroclinic instability in terms of γ. When γ 1, barotropic instability is negligible and hence the system can be viewed as purely baroclinic; when γ 1, however, barotropic and baroclinic instabilities are of the same order;in fact, barotropic instability can be even stronger. The implication of these results has been discussed in linking them to real atmospheric processes.
The Charney model is reexamined using a new mathematical tool, the multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis developed by Liang and Robinson to deal with realistic geophysical fluid flow processes. Traditionally, though this model has been taken as a prototype of baroclinic instability, it actually undergoes a mixed one. While baroclinic instability explains the bottom-trapped feature of the perturbation, the second extreme center in the perturbation field can only be explained by a new barotropic instability when the Charney–Green number γ 1, which takes place throughout the fluid column, and is maximized at a height where its baroclinic counterpart stops functioning.The giving way of the baroclinic instability to a barotropic one at this height corresponds well to the rectification of the tilting found on the maps of perturbation velocity and pressure. Also established in this study is the relative importance of barotropic instability to baroclinic instability in terms of γ. When γ 1, barotropic instability is negligible and hence the system can be viewed as purely baroclinic; when γ 1, however, barotropic and baroclinic instabilities are of the same order;in fact, barotropic instability can be even stronger. The implication of these results has been discussed in linking them to real atmospheric processes.
The Charney model is reexamined using a new mathematical tool, the multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis developed by Liang and Robinson to deal with realistic geophysical fluid flow processes. Traditionally, though this model has been taken as a prototype of baroclinic instability, it actually undergoes a mixed one. While baroclinic instability explains the bottom-trapped feature of the perturbation, the second extreme center in the perturbation field can only be explained by a new barotropic instability when the Charney–Green number γ 1, which takes place throughout the fluid column, and is maximized at a height where its baroclinic counterpart stops functioning.The giving way of the baroclinic instability to a barotropic one at this height corresponds well to the rectification of the tilting found on the maps of perturbation velocity and pressure. Also established in this study is the relative importance of barotropic instability to baroclinic instability in terms of γ. When γ 1, barotropic instability is negligible and hence the system can be viewed as purely baroclinic; when γ 1, however, barotropic and baroclinic instabilities are of the same order;in fact, barotropic instability can be even stronger. The implication of these results has been discussed in linking them to real atmospheric processes.
引文
Badin,G.,2014:On the role of non-uniform stratification and short-wave instabilities in three-layer quasi-geostrophic turbulence.Physics of Fluids,26,096603,https://doi.org/10.1063/1.4895590.
Badin,G.,and F.Crisciani,2018:Variational Formulation of Fluid and Geophysical Fluid Dynamics:Mechanics,Symmetries and Conservation Laws.Advances in Geophysical and Environmental Mechanics and Mathematics,Springer,182 pp,https://doi.org/10.1007/978-3-319-59695-2.
Blackmon,M.L.,J.M.Wallace,N.-C.Lau,and S.L.Mullen,1977:An observational study of the northern hemisphere wintertime circulation.J.Atmos.Sci.,34,1040-1053,https://doi.org/10.1175/1520-0469(1977)034<1040:AOSOTN>2.0.CO;2.
Boyd,J.P.,1976:The noninteraction of waves with the zonally averaged flow on a spherical earth and the interrelationships on eddy fluxes of energy,heat and momentum.J.Atmos.Sci.,33,2285-2291,https://doi.org/10.1175/1520-0469(1976)033<2285:TNOWWT>2.0.CO;2.
Branscome,L.E.,1983:The Charney Baroclinic stability problem:Approximate solutions and modal structures.J.Atmos.Sci.,40,1393-1409,https://doi.org/10.1175/1520-0469(1983)040<1393:TCBSPA>2.0.CO;2.
Bretherton,F.P.,1966:Critical layer instability in baroclinic flows.Quart.J.Roy.Meteor.Soc.,92,325-334,https://doi.org/10.1002/qj.49709239302.
Brown,Jr.J.A.,1969:A numerical investigation of hydrodynamic instability and energy conversions in the quasi-geostrophic atmosphere:Part I.J.Atmos.Sci.,26,352-365,https://doi.org/10.1175/1520-0469(1969)026<0352:ANIOHI>2.0.CO;2.
Burger,A.P.,1962:On the non-existence of critical wavelengths in a continuous baroclinic stability problem.J.Atmos.Sci.,19,31-38,https://doi.org/10.1175/1520-0469(1962)019<0031:OTNEOC>2.0.CO;2.
Cai,M.,and M.Mak,1990:On the basic dynamics of regional cyclogenesis.J.Atmos.Sci.,47,1417-1442,https://doi.org/10.1175/1520-0469(1990)047<1417:OTBDOR>2.0.CO;2.
Chai,J.Y.,and G.K.Vallis,2014:The role of criticality on the horizontal and vertical scales of extratropical eddies in a dry GCM.J.Atmos.Sci.,71,2300-2318,https://doi.org/10.1175/JAS-D-13-0351.1.
Chang,E.K.M.,1993:Downstream development of baroclinic waves as inferred from regression analysis.J.Atmos.Sci.,50,2038-2053,https://doi.org/10.1175/1520-0469(1993)050<2038:DDOBWA>2.0.CO;2.
Chang,E.K.M.,and I.Orlanski,1993:On the dynamics of a storm track.J.Atmos.Sci.,50,999-1015,https://doi.org/10.1175/1520-0469(1993)050<0999:OTDOAS>2.0.CO;2.
Chapman,C.C.,A.M.Hogg,A.E.Kiss,and S.R.Rintoul,2015:The dynamics of southern ocean storm tracks.J.Phys.Oceanogr.,45,884-903,https://doi.org/10.1175/JPO-D-14-0075.1.
Charney,J.G.,1947:The dynamics of long waves in a baroclinic westerly current.J.Meteor.,4,136-162,https://doi.org/10.1175/1520-0469(1947)004<0136:TDOLWI>2.0.CO;2.
Charney,J.G.,and P.G.Drazin,1961:Propagation of planetaryscale disturbances from the lower into the upper atmosphere.J.Geophys.Res.,66,83-109,https://doi.org/10.1029/JZ066i001p00083.
Deng,Y.,and M.Mak,2006:Nature of the differences in the intraseasonal variability of the pacific and Atlantic storm tracks:A diagnostic study.J.Atmos.Sci.,63,2602-2615,https://doi.org/10.1175/JAS3749.1.
Dickinson,R.E.,1969:Theory of planetary wave-zonal flow interaction.J.Atmos.Sci.,26,73-81,https://doi.org/10.1175/1520-0469(1969)026<0073:TOPWZF>2.0.CO;2.
Edmon,H.J.,Jr.,B.J.Hoskins,and M.E.McIntyre,1980:Eliassen-palm cross sections for the troposphere.J.Atmos.Sci.,37,2600-2616,https://doi.org/10.1175/1520-0469(1980)037<2600:EPCSFT>2.0.CO;2.
Farrell,B.F.,1982:Pulse asymptotics of the Charney Baroclinic instability problem.J.Atmos.Sci.,39,507-517,https://doi.org/10.1175/1520-0469(1982)039<0507:PAOTCB>2.0.CO;2.
Fels,S.B.,and R.S.Lindzen,1973:The interaction of thermally excited gravity waves with mean flows.Geophys.Fluid Dyn.,5,211-212.https://doi.org/10.1080/03091927308236117.
Fournier,A.,2002:Atmospheric energetics in the wavelet domain.Part I:Governing equations and interpretation for idealized flows.J.Atmos.Sci.,59,1182-1197,https://doi.org/10.1175/1520-0469(2002)059<1182:AEITWD>2.0.CO;2.
Fullmer,J.W.A.,1982:The baroclinic instability of highly structured one-dimensional basic states.J.Atmos.Sci.,39,2371-2387,https://doi.org/10.1175/1520-0469(1982)039<2371:TBIOHS>2.0.CO;2.
Gall,R.,1976a:Structural changes of growing baroclinic waves.J.Atmos.Sci.,33,374-390,https://doi.org/10.1175/1520-0469(1976)033<0374:SCOGBW>2.0.CO;2.
Gall,R.,1976b:A comparison of linear baroclinic instability theory with the eddy statistics of a general circulation model.J.Atmos.Sci.,33,349-373,https://doi.org/10.1175/1520-0469(1976)033<0349:ACOLBI>2.0.CO;2.
Geisler,J.E.,and R.R.Garcia,1977:Baroclinic instability at long wavelengths on aβ-plane.J.Atmos.Sci.,34,311-321,https://doi.org/10.1175/1520-0469(1977)034<0311:BIALWO>2.0.CO;2.
Gill,A.E.,1982:Atmosphere-Ocean Dynamics.Academic Press,662 pp.
Green,J.S.A.,1960:A problem in baroclinic stability.Quart.J.Roy.Meteor.Soc.,86,237-251,https://doi.org/10.1002/qj.49708636813.
Green,J.S.A.,1970:Transfer properties of the large-scale eddies and the general circulation of the atmosphere.Quart.J.Roy.Meteor.Soc.,96,157-185,https://doi.org/10.1002/qj.49709640802.
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,https://doi.org/10.1016/0377-0265(78)90009-X.
Held,I.M.,1978:The vertical scale of an unstable baroclinic wave and its importance for eddy heat flux parameterizations.J.Atmos.Sci.,35,572-576,https://doi.org/10.1175/1520-0469(1978)035<0572:TVSOAU>2.0.CO;2.
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.
Hoskins,B.J.,and P.J.Valdes,1990:On the existence of stormtracks.J.Atmos.Sci.,47,1854-1864,https://doi.org/10.1175/1520-0469(1990)047<1854:OTEOST>2.0.CO;2.
Hoskins,B.J.,M.E.McIntyre,and A.W.Robertson,1985:On the use and significance of isentropic potential vorticity maps.Quart.J.Roy.Meteor.Soc.,111,877-946,https://doi.org/10.1002/qj.49711147002.
Kao,S.-K.,and V.R.Taylor,1964:Mean kinetic energies of eddy and mean currents in the atmosphere.J.Geophys.Res.,69,1037-1049,https://doi.org/10.1029/JZ069i006p01037.
Kuo,H.-L.,1949:Dynamic instability of two-dimensional nondivergent flow in a barotropic atmosphere.J.Meteor.,6,105-122,https://doi.org/10.1175/1520-0469(1949)006<0105:DIOTDN>2.0.CO;2.
Kuo,H.-L.,1952:Three-dimensional disturbances in a baroclinic zonal current.J.Meteor.,9,260-278,https://doi.org/10.1175/1520-0469(1952)009<0260:TDDIAB>2.0.CO;2.
Kuo,H.-L.,1979:Baroclinic instabilities of linear and jet profiles in the atmosphere.J.Atmos.Sci.,36,2360-2378,https://doi.org/10.1175/1520-0469(1979)036<2360:BIOLAJ>2.0.CO;2.
Lapeyre,G.,and P.Klein,2006:Dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory.J.Phys.Oceanogr.,36,165-176,https://doi.org/10.1175/JPO2840.1.
Liang,X.S.,2016:Canonical transfer and multiscale energetics for primitive and quasigeostrophic atmospheres.J.Atmos.Sci.,73,4439-4468,https://doi.org/10.1175/JAS-D-16-0131.1.
Liang,X.S.,and A.R.Robinson,2005:Localized multiscale energy and vorticity analysis:I.Fundamentals.Dyn.Atmos.Oceans,38,195-230,https://doi.org/10.1016/j.dynatmoce.2004.12.004.
Liang,X.S.,and D.G.M.Anderson,2007:Multiscale window transform.Multiscale Model.Simul.,6,437-467.
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,https://doi.org/10.1016/j.dynatmoce.2007.04.001.
Liang,X.S.,and L.Wang,2018:The cyclogenesis and decay of typhoon damrey.Coastal Environment,Disaster,and Infrastructure,X.S.Liang and Y.Z.Zhang,Eds.,IntechOpen,https://doi.org/10.5772/intechopen.80018.
Lindzen,R.S.,and B.Farrell,1980:A simple approximate result for the maximum growth rate of baroclinic instabilities.J.Atmos.Sci.,37,1648-1654,https://doi.org/10.1175/1520-0469(1980)037<1648:ASARFT>2.0.CO;2.
Lorenz,E.N.,1955:Available potential energy and the maintenance of the general circulation.Tellus,7,157-167,https://doi.org/10.1111/j.2153-3490.1955.tb01148.x.
Lorenz,E.N.,1967:The Nature and Theory of the General Circulation of the Atmosphere.World Meteorological Organization,161 pp.
McWilliams,J.C.,and J.M.Restrepo,1999:The wave-driven ocean circulation.J.Phys.Oceanogr.,29,2523-2540,https://doi.org/10.1175/1520-0485(1999)029<2523:TWDOC>2.0.CO;2.
Miles,J.W.,1964:A note on Charney’s model of zonal-wind instability.J.Atmos.Sci.,21,451-452,https://doi.org/10.1175/1520-0469(1964)021<0451:ANOCMO>2.0.CO;2.
Nakamura,H.,1992:Midwinter suppression of baroclinic wave activity in the pacific.J.Atmos.Sci.,49,1629-1642,https://doi.org/10.1175/1520-0469(1992)049<1629:MSOBWA>2.0.CO;2.
Orlanski,I.,and J.Katzfey,1991:The life cycle of a cyclone wave in the southern hemisphere.Part I:Eddy energy budget.J.Atmos.Sci.,48,1972-1998,https://doi.org/10.1175/1520-0469(1991)048<1972:TLCOAC>2.0.CO;2.
Pedlosky,J.,1987:Geophysical Fluid Dynamics.2nd ed.,Springer-Verlag,710 pp.
Pierrehumbert,R.T.,and K.L.Swanson,1995:Baroclinic instability.Annual Review of Fluid Mechanics,27,419-467,https://doi.org/10.1146/annurev.fl.27.010195.002223.
Plumb,R.A.,1983:A new look at the energy cycle.J.Atmos.Sci.,40,1669-1688,https://doi.org/10.1175/1520-0469(1983)040<1669:ANLATE>2.0.CO;2.
Pope,S.B.,2000:Turbulent flows.Cambridge University Press,806 pp.
Ragone,F.,and G.Badin,2016:A study of surface semigeostrophic turbulence:Freely decaying dynamics.J.Fluid Mech.,792,740-774,https://doi.org/10.1017/jfm.2016.116.
Simmons,A.J.,and B.J.Hoskins,1978:The life cycles of some nonlinear baroclinic waves.J.Atmos.Sci.,35,414-432,https://doi.org/10.1175/1520-0469(1978)035<0414:TLCOSN>2.0.CO;2.
Simons,T.J.,1972:The nonlinear dynamics of cyclone waves.J.Atmos.Sci.,29,38-52,https://doi.org/10.1175/1520-0469(1972)029<0038:TNDOCW>2.0.CO;2.
Song,R.T.,1971:A numerical study of the three-dimensional structure and energetics of unstable disturbances in zonal currents:Part II.J.Atmos.Sci.,28,565-586,https://doi.org/10.1175/1520-0469(1971)028<0565:ANSOTT>2.0.CO;2.
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,https://doi.org/10.1175/1520-0469(1986)043<2070:AAOTIO>2.0.CO;2.
Vallis,G.K.,2006:Atmospheric and Oceanic Fluid Dynamics:Fundamentals and Large-Scale Circulation.Cambridge University Press,770 pp.
Yin,J.H.,2002:The peculiar behavior of baroclinic waves during the midwinter suppression of the pacific storm track.PhDdissertation,University of Washington,137 pp.
Zhao,Y.-B.,and X.S.Liang,2018:On the inverse relationship between the boreal wintertime Pacific jet strength and stormtrack intensity.J.Climate,31,9545-9564,https://doi.org/10.1175/JCLI-D-18-0043.1.
Zhao,Y.-B.,X.S.Liang,and J.P.Gan,2016:Nonlinear multiscale interactions and internal dynamics underlying a typical eddyshedding event at Luzon Strait.J.Geophys.Res.Oceans,121,8208-8229,https://doi.org/10.1002/2016JC012483.
Zhao,Y.-B.,X.S.Liang,and W.J.Zhu,2018:Differences in storm structure and internal dynamics of the two storm source regions over East Asia.Acta Meteorologica Sinica,76(5),663-679,http://dx.doi.org/10.11676/qxxb2018.033.(in Chinese)
a Note that the time tendency in Eqs.(8)and(9)in Charney’s model is meaningless since the basic flow has been assumed to be steady. Nevertheless, it has nothing to do with the other terms in the energy equation, in which we are interested most.
Badin,G.,and F.Crisciani,2018:Variational Formulation of Fluid and Geophysical Fluid Dynamics:Mechanics,Symmetries and Conservation Laws.Advances in Geophysical and Environmental Mechanics and Mathematics,Springer,182 pp,https://doi.org/10.1007/978-3-319-59695-2.
Blackmon,M.L.,J.M.Wallace,N.-C.Lau,and S.L.Mullen,1977:An observational study of the northern hemisphere wintertime circulation.J.Atmos.Sci.,34,1040-1053,https://doi.org/10.1175/1520-0469(1977)034<1040:AOSOTN>2.0.CO;2.
Boyd,J.P.,1976:The noninteraction of waves with the zonally averaged flow on a spherical earth and the interrelationships on eddy fluxes of energy,heat and momentum.J.Atmos.Sci.,33,2285-2291,https://doi.org/10.1175/1520-0469(1976)033<2285:TNOWWT>2.0.CO;2.
Branscome,L.E.,1983:The Charney Baroclinic stability problem:Approximate solutions and modal structures.J.Atmos.Sci.,40,1393-1409,https://doi.org/10.1175/1520-0469(1983)040<1393:TCBSPA>2.0.CO;2.
Bretherton,F.P.,1966:Critical layer instability in baroclinic flows.Quart.J.Roy.Meteor.Soc.,92,325-334,https://doi.org/10.1002/qj.49709239302.
Brown,Jr.J.A.,1969:A numerical investigation of hydrodynamic instability and energy conversions in the quasi-geostrophic atmosphere:Part I.J.Atmos.Sci.,26,352-365,https://doi.org/10.1175/1520-0469(1969)026<0352:ANIOHI>2.0.CO;2.
Burger,A.P.,1962:On the non-existence of critical wavelengths in a continuous baroclinic stability problem.J.Atmos.Sci.,19,31-38,https://doi.org/10.1175/1520-0469(1962)019<0031:OTNEOC>2.0.CO;2.
Cai,M.,and M.Mak,1990:On the basic dynamics of regional cyclogenesis.J.Atmos.Sci.,47,1417-1442,https://doi.org/10.1175/1520-0469(1990)047<1417:OTBDOR>2.0.CO;2.
Chai,J.Y.,and G.K.Vallis,2014:The role of criticality on the horizontal and vertical scales of extratropical eddies in a dry GCM.J.Atmos.Sci.,71,2300-2318,https://doi.org/10.1175/JAS-D-13-0351.1.
Chang,E.K.M.,1993:Downstream development of baroclinic waves as inferred from regression analysis.J.Atmos.Sci.,50,2038-2053,https://doi.org/10.1175/1520-0469(1993)050<2038:DDOBWA>2.0.CO;2.
Chang,E.K.M.,and I.Orlanski,1993:On the dynamics of a storm track.J.Atmos.Sci.,50,999-1015,https://doi.org/10.1175/1520-0469(1993)050<0999:OTDOAS>2.0.CO;2.
Chapman,C.C.,A.M.Hogg,A.E.Kiss,and S.R.Rintoul,2015:The dynamics of southern ocean storm tracks.J.Phys.Oceanogr.,45,884-903,https://doi.org/10.1175/JPO-D-14-0075.1.
Charney,J.G.,1947:The dynamics of long waves in a baroclinic westerly current.J.Meteor.,4,136-162,https://doi.org/10.1175/1520-0469(1947)004<0136:TDOLWI>2.0.CO;2.
Charney,J.G.,and P.G.Drazin,1961:Propagation of planetaryscale disturbances from the lower into the upper atmosphere.J.Geophys.Res.,66,83-109,https://doi.org/10.1029/JZ066i001p00083.
Deng,Y.,and M.Mak,2006:Nature of the differences in the intraseasonal variability of the pacific and Atlantic storm tracks:A diagnostic study.J.Atmos.Sci.,63,2602-2615,https://doi.org/10.1175/JAS3749.1.
Dickinson,R.E.,1969:Theory of planetary wave-zonal flow interaction.J.Atmos.Sci.,26,73-81,https://doi.org/10.1175/1520-0469(1969)026<0073:TOPWZF>2.0.CO;2.
Edmon,H.J.,Jr.,B.J.Hoskins,and M.E.McIntyre,1980:Eliassen-palm cross sections for the troposphere.J.Atmos.Sci.,37,2600-2616,https://doi.org/10.1175/1520-0469(1980)037<2600:EPCSFT>2.0.CO;2.
Farrell,B.F.,1982:Pulse asymptotics of the Charney Baroclinic instability problem.J.Atmos.Sci.,39,507-517,https://doi.org/10.1175/1520-0469(1982)039<0507:PAOTCB>2.0.CO;2.
Fels,S.B.,and R.S.Lindzen,1973:The interaction of thermally excited gravity waves with mean flows.Geophys.Fluid Dyn.,5,211-212.https://doi.org/10.1080/03091927308236117.
Fournier,A.,2002:Atmospheric energetics in the wavelet domain.Part I:Governing equations and interpretation for idealized flows.J.Atmos.Sci.,59,1182-1197,https://doi.org/10.1175/1520-0469(2002)059<1182:AEITWD>2.0.CO;2.
Fullmer,J.W.A.,1982:The baroclinic instability of highly structured one-dimensional basic states.J.Atmos.Sci.,39,2371-2387,https://doi.org/10.1175/1520-0469(1982)039<2371:TBIOHS>2.0.CO;2.
Gall,R.,1976a:Structural changes of growing baroclinic waves.J.Atmos.Sci.,33,374-390,https://doi.org/10.1175/1520-0469(1976)033<0374:SCOGBW>2.0.CO;2.
Gall,R.,1976b:A comparison of linear baroclinic instability theory with the eddy statistics of a general circulation model.J.Atmos.Sci.,33,349-373,https://doi.org/10.1175/1520-0469(1976)033<0349:ACOLBI>2.0.CO;2.
Geisler,J.E.,and R.R.Garcia,1977:Baroclinic instability at long wavelengths on aβ-plane.J.Atmos.Sci.,34,311-321,https://doi.org/10.1175/1520-0469(1977)034<0311:BIALWO>2.0.CO;2.
Gill,A.E.,1982:Atmosphere-Ocean Dynamics.Academic Press,662 pp.
Green,J.S.A.,1960:A problem in baroclinic stability.Quart.J.Roy.Meteor.Soc.,86,237-251,https://doi.org/10.1002/qj.49708636813.
Green,J.S.A.,1970:Transfer properties of the large-scale eddies and the general circulation of the atmosphere.Quart.J.Roy.Meteor.Soc.,96,157-185,https://doi.org/10.1002/qj.49709640802.
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,https://doi.org/10.1016/0377-0265(78)90009-X.
Held,I.M.,1978:The vertical scale of an unstable baroclinic wave and its importance for eddy heat flux parameterizations.J.Atmos.Sci.,35,572-576,https://doi.org/10.1175/1520-0469(1978)035<0572:TVSOAU>2.0.CO;2.
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.
Hoskins,B.J.,and P.J.Valdes,1990:On the existence of stormtracks.J.Atmos.Sci.,47,1854-1864,https://doi.org/10.1175/1520-0469(1990)047<1854:OTEOST>2.0.CO;2.
Hoskins,B.J.,M.E.McIntyre,and A.W.Robertson,1985:On the use and significance of isentropic potential vorticity maps.Quart.J.Roy.Meteor.Soc.,111,877-946,https://doi.org/10.1002/qj.49711147002.
Kao,S.-K.,and V.R.Taylor,1964:Mean kinetic energies of eddy and mean currents in the atmosphere.J.Geophys.Res.,69,1037-1049,https://doi.org/10.1029/JZ069i006p01037.
Kuo,H.-L.,1949:Dynamic instability of two-dimensional nondivergent flow in a barotropic atmosphere.J.Meteor.,6,105-122,https://doi.org/10.1175/1520-0469(1949)006<0105:DIOTDN>2.0.CO;2.
Kuo,H.-L.,1952:Three-dimensional disturbances in a baroclinic zonal current.J.Meteor.,9,260-278,https://doi.org/10.1175/1520-0469(1952)009<0260:TDDIAB>2.0.CO;2.
Kuo,H.-L.,1979:Baroclinic instabilities of linear and jet profiles in the atmosphere.J.Atmos.Sci.,36,2360-2378,https://doi.org/10.1175/1520-0469(1979)036<2360:BIOLAJ>2.0.CO;2.
Lapeyre,G.,and P.Klein,2006:Dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory.J.Phys.Oceanogr.,36,165-176,https://doi.org/10.1175/JPO2840.1.
Liang,X.S.,2016:Canonical transfer and multiscale energetics for primitive and quasigeostrophic atmospheres.J.Atmos.Sci.,73,4439-4468,https://doi.org/10.1175/JAS-D-16-0131.1.
Liang,X.S.,and A.R.Robinson,2005:Localized multiscale energy and vorticity analysis:I.Fundamentals.Dyn.Atmos.Oceans,38,195-230,https://doi.org/10.1016/j.dynatmoce.2004.12.004.
Liang,X.S.,and D.G.M.Anderson,2007:Multiscale window transform.Multiscale Model.Simul.,6,437-467.
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,https://doi.org/10.1016/j.dynatmoce.2007.04.001.
Liang,X.S.,and L.Wang,2018:The cyclogenesis and decay of typhoon damrey.Coastal Environment,Disaster,and Infrastructure,X.S.Liang and Y.Z.Zhang,Eds.,IntechOpen,https://doi.org/10.5772/intechopen.80018.
Lindzen,R.S.,and B.Farrell,1980:A simple approximate result for the maximum growth rate of baroclinic instabilities.J.Atmos.Sci.,37,1648-1654,https://doi.org/10.1175/1520-0469(1980)037<1648:ASARFT>2.0.CO;2.
Lorenz,E.N.,1955:Available potential energy and the maintenance of the general circulation.Tellus,7,157-167,https://doi.org/10.1111/j.2153-3490.1955.tb01148.x.
Lorenz,E.N.,1967:The Nature and Theory of the General Circulation of the Atmosphere.World Meteorological Organization,161 pp.
McWilliams,J.C.,and J.M.Restrepo,1999:The wave-driven ocean circulation.J.Phys.Oceanogr.,29,2523-2540,https://doi.org/10.1175/1520-0485(1999)029<2523:TWDOC>2.0.CO;2.
Miles,J.W.,1964:A note on Charney’s model of zonal-wind instability.J.Atmos.Sci.,21,451-452,https://doi.org/10.1175/1520-0469(1964)021<0451:ANOCMO>2.0.CO;2.
Nakamura,H.,1992:Midwinter suppression of baroclinic wave activity in the pacific.J.Atmos.Sci.,49,1629-1642,https://doi.org/10.1175/1520-0469(1992)049<1629:MSOBWA>2.0.CO;2.
Orlanski,I.,and J.Katzfey,1991:The life cycle of a cyclone wave in the southern hemisphere.Part I:Eddy energy budget.J.Atmos.Sci.,48,1972-1998,https://doi.org/10.1175/1520-0469(1991)048<1972:TLCOAC>2.0.CO;2.
Pedlosky,J.,1987:Geophysical Fluid Dynamics.2nd ed.,Springer-Verlag,710 pp.
Pierrehumbert,R.T.,and K.L.Swanson,1995:Baroclinic instability.Annual Review of Fluid Mechanics,27,419-467,https://doi.org/10.1146/annurev.fl.27.010195.002223.
Plumb,R.A.,1983:A new look at the energy cycle.J.Atmos.Sci.,40,1669-1688,https://doi.org/10.1175/1520-0469(1983)040<1669:ANLATE>2.0.CO;2.
Pope,S.B.,2000:Turbulent flows.Cambridge University Press,806 pp.
Ragone,F.,and G.Badin,2016:A study of surface semigeostrophic turbulence:Freely decaying dynamics.J.Fluid Mech.,792,740-774,https://doi.org/10.1017/jfm.2016.116.
Simmons,A.J.,and B.J.Hoskins,1978:The life cycles of some nonlinear baroclinic waves.J.Atmos.Sci.,35,414-432,https://doi.org/10.1175/1520-0469(1978)035<0414:TLCOSN>2.0.CO;2.
Simons,T.J.,1972:The nonlinear dynamics of cyclone waves.J.Atmos.Sci.,29,38-52,https://doi.org/10.1175/1520-0469(1972)029<0038:TNDOCW>2.0.CO;2.
Song,R.T.,1971:A numerical study of the three-dimensional structure and energetics of unstable disturbances in zonal currents:Part II.J.Atmos.Sci.,28,565-586,https://doi.org/10.1175/1520-0469(1971)028<0565:ANSOTT>2.0.CO;2.
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,https://doi.org/10.1175/1520-0469(1986)043<2070:AAOTIO>2.0.CO;2.
Vallis,G.K.,2006:Atmospheric and Oceanic Fluid Dynamics:Fundamentals and Large-Scale Circulation.Cambridge University Press,770 pp.
Yin,J.H.,2002:The peculiar behavior of baroclinic waves during the midwinter suppression of the pacific storm track.PhDdissertation,University of Washington,137 pp.
Zhao,Y.-B.,and X.S.Liang,2018:On the inverse relationship between the boreal wintertime Pacific jet strength and stormtrack intensity.J.Climate,31,9545-9564,https://doi.org/10.1175/JCLI-D-18-0043.1.
Zhao,Y.-B.,X.S.Liang,and J.P.Gan,2016:Nonlinear multiscale interactions and internal dynamics underlying a typical eddyshedding event at Luzon Strait.J.Geophys.Res.Oceans,121,8208-8229,https://doi.org/10.1002/2016JC012483.
Zhao,Y.-B.,X.S.Liang,and W.J.Zhu,2018:Differences in storm structure and internal dynamics of the two storm source regions over East Asia.Acta Meteorologica Sinica,76(5),663-679,http://dx.doi.org/10.11676/qxxb2018.033.(in Chinese)
a Note that the time tendency in Eqs.(8)and(9)in Charney’s model is meaningless since the basic flow has been assumed to be steady. Nevertheless, it has nothing to do with the other terms in the energy equation, in which we are interested most.
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