1、Michael E. McIntyre,Dept of Applied Mathematics & Theoretical Physics,University of Cambridge, UK For more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”. A tale of two paradigms, with remarks on unconscious assumptions Bernhard Haurwit
2、z Memorial LectureIts a great honor to be giving the Bernhard Haurwitz MemorialLecture and Im very touched. And its wonderful to see allthe young faces - and the not-so-young who are personalfriends and colleagues of mine - and to learn something moreabout your important work, as well as, for my par
3、t, indulgingin a little personal nostalgia, as may be permitted at myadvanced age.I myself have been more into astrophysical and, to some extent,plasma-physics problems recently, but the bottom line isFor more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”stai
4、rcase”, ”Rosenbluth”.Our life support systemFor more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”.and the huge challenge of observing and understanding it better. Indeed, youyoung scientists, and technologists and smart thinkers gener
5、ally, with yourenergy, enthusiasm, and penetrating curiousity about how things work, are animportant part of our hope for the future survival of science and civilization -indeed the future flourishing of science and civilization. What does “understanding” mean? I think it means not only good observa
6、tionsand good quantitative modeling, but also viewing a problem from all possibleangles - words, pictures, mathematics, computer codes, metaphors. When I canget all these different viewpoints into agreement with each other, then I wouldsay I understand something - especially if it turns out to look
7、simple from oneor more viewpoints. And by then I can hope to have corrected most of themistakes.For more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”.Of course no-one should be afraid of making mistakes. They can be milestones on the
8、way to something interesting. I suspect that the ability to make mistakes isrelated to the ability to have new ideas. The great physicist John ArchibaldWheeler said that “genius is the ability to make all possible mistakes in theshortest possible time.” (Ordinary mortals like me take longer.)Here Il
9、l review some understanding about fluid motion that developed over thepast century. Bernhard Haurwitz was born in 1905, and published his famous book Dynamic Meteorology in 1941. I was born in 1941. So between us we spanabout a century of trying to understand the atmosphere and oceans. I want topick
10、 out what I see as some key advances in understanding - things that aresimple and well known today, though - to my continual surprise - not all ofthem clearly flagged up in the textbooks, even today. So its going to be simple- but also so important that I make no apology.Were dealing withFor more de
11、tail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”.fluid dynamics on a grand scaleAnd rotation and stable stratification areimportant in many cases, including the SunsinteriorFor more detail, websearch ”lucidity principles” then back to my ho
12、me page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”.radiative interior no significant evidencefor departures fromsolid rotation(Princeton, May 2011)convectionzone2/nHzSchou et al 98For more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth
13、”.radiative interior no significant evidencefor departures fromsolid rotation(Princeton, May 2011)tachoclineconvectionzone2/nHzSchou et al 98For more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”.Voyager 1 approaching (60 Jupiter days)
14、 unearthly!For more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”.Artists impression NASA/JPL-Caltech/T. Pyle (SSC)Protoplanetary accretion disks:For more detail, websearch ”lucidity principles” then back to my home page at ”Encycloped
15、ia”, ”staircase”, ”Rosenbluth”.For more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”. Today it hardly needs saying, following an aphorism of V.I. Arnold, that Rotating, stratified fluid dynamics cannot be understood without potential
16、vorticity, PVFor more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”. Today it hardly needs saying, following an aphorism of V.I. Arnold, that Rotating, stratified fluid dynamics cannot be understood without potential vorticity, PV(Disk
17、 people call it “vortensity”)For more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”. Today it hardly needs saying, following an aphorism of V.I. Arnold, that Rotating, stratified fluid dynamics cannot be understood without potential vo
18、rticity, PVTokamaks too?(Disk people call it “vortensity”)For more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”. Today it hardly needs saying, following an aphorism of V.I. Arnold, that Rotating, stratified fluid dynamics cannot be un
19、derstood without potential vorticity, PVTokamaks too?(Disk people call it “vortensity”) Heres its mostbeautiful definition:For more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”.In both single-layer and multi-layer systems,we can defin
20、e the exact PV as the suitably normalized Kelvin circulationof an infinitesimal material circuit lying in a stratification surface.In both single-layer and multi-layer systems,we can define the exact PV as the suitably normalized Kelvin circulationof an infinitesimal material circuit lying in a stra
21、tification surface.“Suitably normalized”: multiply by mass of pillboxbetween adjacent stratification surfaces:For more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”. Kelvincirculation isFor more detail, websearch ”lucidity principles”
22、then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”.In both single-layer and multi-layer systems,we can define the exact PV as the suitably normalized Kelvin circulationof an infinitesimal material circuit lying in a stratification surface.“Suitably normalized”: multiply by mass o
23、f pillboxbetween adjacent stratification surfaces: Kelvincirculation is Corollary:exact PV =For more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”.In both single-layer and multi-layer systems,we can define the exact PV as the suitably
24、normalized Kelvin circulationof an infinitesimal material circuit lying in a stratification surface.“Suitably normalized”: multiply by mass of pillboxbetween adjacent stratification surfaces: Kelvincirculation is Corollary:exact PV =For more detail, websearch ”lucidity principles” then back to my ho
25、me page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”.In both single-layer and multi-layer systems,we can define the exact PV as the suitably normalized Kelvin circulationof an infinitesimal material circuit lying in a stratification surface.“Suitably normalized”: multiply by mass of pillboxbetween a
26、djacent stratification surfaces:Note: (1) the PV is a material invariant for frictionless, adiabaticfluid motion, under any scenario of stretching or tiltingof fluid elements and stratification surfaces.So the PV is mixable along stratification surfaces (though not across!)Note: (1) the PV is a mate
27、rial invariant for frictionless, adiabaticfluid motion, under any scenario of stretching or tiltingof fluid elements and stratification surfaces.So the PV is mixable along stratification surfaces (though not across!) Kelvincirculation is Corollary:exact PV =For more detail, websearch ”lucidity princ
28、iples” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”.In both single-layer and multi-layer systems,we can define the exact PV as the suitably normalized Kelvin circulationof an infinitesimal material circuit lying in a stratification surface.“Suitably normalized”: multiply by
29、 mass of pillboxbetween adjacent stratification surfaces:Note: (1) the PV is a material invariant for frictionless, adiabaticfluid motion, under any scenario of stretching or tiltingof fluid elements and stratification surfaces.So the PV is mixable along stratification surfaces (though not across!)i
30、mpermeabilitytheorem etc Kelvincirculation is Corollary:exact PV =For more detail, websearch ”lucidity principles” then back to my home page at ”Encyclopedia”, ”staircase”, ”Rosenbluth”.In both single-layer and multi-layer systems,we can define the exact PV as the suitably normalized Kelvin circulat
31、ionof an infinitesimal material circuit lying in a stratification surface.“Suitably normalized”: multiply by mass of pillboxbetween adjacent stratification surfaces:Note: (1) the PV is a material invariant for frictionless, adiabaticfluid motion, under any scenario of stretching or tiltingof fluid e
32、lements and stratification surfaces.So the PV is mixable along stratification surfaces (though not across!)And (2) the PV is invertible: the PV field has nearly all the dynamical information. (Invertibility depends on the flow being balanced.)impermeabilitytheorem etc Kelvincirculation is Corollary:
33、exact PV =In both single-layer and multi-layer systems,we can define the exact PV as the suitably normalized Kelvin circulationof an infinitesimal material circuit lying in a stratification surface.“Suitably normalized”: multiply by mass of pillboxbetween adjacent stratification surfaces:Note: (1) t
34、he PV is a material invariant for frictionless, adiabaticfluid motion, under any scenario of stretching or tiltingof fluid elements and stratification surfaces.So the PV is mixable along stratification surfaces (though not across!)And (2) the PV is invertible: the PV field has nearly all the dynamic
35、al information. (Invertibility depends on the flow being balanced.)impermeabilitytheorem etc Kelvincirculation is Corollary:exact PV =Recall scale effect: small-scale PV anomalies weak velocities.In both single-layer and multi-layer systems,we can define the exact PV as the suitably normalized Kelvi
36、n circulationof an infinitesimal material circuit lying in a stratification surface.“Suitably normalized”: multiply by mass of pillboxbetween adjacent stratification surfaces:Note: (1) the PV is a material invariant for frictionless, adiabaticfluid motion, under any scenario of stretching or tilting
37、of fluid elements and stratification surfaces.So the PV is mixable along stratification surfaces (though not across!)And (2) the PV is invertible: the PV field has nearly all the dynamical information. (Invertibility depends on the flow being balanced.)impermeabilitytheorem etc Kelvincirculation is
38、Corollary:exact PV =What do PV fields look like? Heres an example (nostalgic for me):In both single-layer and multi-layer systems,we can define the exact PV as the suitably normalized Kelvin circulationof an infinitesimal material circuit lying in a stratification surface.“Suitably normalized”: mult
39、iply by mass of pillboxbetween adjacent stratification surfaces:McIntyre and Palmer (1983), revisitedPVUCourtesy Dr A J Simmons,European Centre for MediumRange Weather Forecasts:Initial statePV on the 850K stratification surface:McIntyre and Palmer (1983), revisitedPVUCourtesy Dr A J Simmons,Europea
40、n Centre for MediumRange Weather Forecasts:Final statePV on the 850K stratification surface:McIntyre and Palmer (1983), revisitedPVUCourtesy Dr A J Simmons,European Centre for MediumRange Weather Forecasts:turbulenthereFinal statePV on the 850K stratification surface:McIntyre and Palmer (1983), revi
41、sitedPVUCourtesy Dr A J Simmons,European Centre for MediumRange Weather Forecasts:Final stateturbulentherewavelike herePV on the 850K stratification surface:Courtesy Dr A J Simmons,European Centre for MediumRange Weather Forecasts:Inhomogeneous!PV at 850K, mid-Jan. 1979 Quasi-elastic“eddy-transport
42、barrier”Yes, its turbulent strongly nonlinear but also highly inhomogeneous,well outside the scope of homogeneous turbulence theory and itsextensions.Yes, its turbulent strongly nonlinear but also highly inhomogeneous,well outside the scope of homogeneous turbulence theory and itsextensions. In part
43、icular,- the structure is completely missed by power spectra (e.g. Armi and Flament 1985, J. Geophys. Res.)Yes, its turbulent strongly nonlinear but also highly inhomogeneous,well outside the scope of homogeneous turbulence theory and itsextensions. In particular,- the structure is completely missed
44、 by power spectra (e.g. Armi and Flament 1985, J. Geophys. Res.)- the structure has wavelike and turbulent regions that fit together in a “wave-turbulence jigsaw”:PV contours undulate reversibly:PV contours deform irreversibly: longitudelatitudeYes, its turbulent strongly nonlinear but also highly i
45、nhomogeneous,well outside the scope of homogeneous turbulence theory and itsextensions. In particular,- the structure is completely missed by power spectra (e.g. Armi and Flament 1985, J. Geophys. Res.)- the structure has wavelike and turbulent regions that fit together in a “wave-turbulence jigsaw”
46、:PV contours undulate reversibly:PV contours deform irreversibly: longitudelatitude Quasi- elastic“barrier”Yes, its turbulent strongly nonlinear but also highly inhomogeneous,well outside the scope of homogeneous turbulence theory and itsextensions. In particular,- the structure is completely missed
47、 by power spectra (e.g. Armi and Flament 1985, J. Geophys. Res.)- the structure has wavelike and turbulent regions that fit together in a “wave-turbulence jigsaw”:PV contours undulate reversibly:PV contours deform irreversibly:(wave breaking inhomogeneous PV mixing via scale effect) longitudelatitud
48、e Quasi- elastic“barrier”Yes, its turbulent strongly nonlinear but also highly inhomogeneous,well outside the scope of homogeneous turbulence theory and itsextensions. In particular,- the structure is completely missed by power spectra (e.g. Armi and Flament 1985, J. Geophys. Res.)- the structure ha
49、s wavelike and turbulent regions that fit together in a “wave-turbulence jigsaw”:PV contours undulate reversibly:PV contours deform irreversibly:NB: its impossible to make sense of the dynamics, even grossangular-momentum budgets including Starrs “negative viscosity”(anti-friction) without recognizi
50、ng this inhomogeneous jigsaw structure.(wave breaking inhomogeneous PV mixing via scale effect) longitudelatitude Quasi- elastic“barrier”Yes, its turbulent strongly nonlinear but also highly inhomogeneous,well outside the scope of homogeneous turbulence theory and itsextensions. In particular,- the
