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A Molecular View of Vorticity & Turbulence Four Lectures at NCAR, 28-29 November 2007. Adrian Tuck NOAA-ESRL/CSD6 Meteorological Chemistry Program. Slide 1. CREDITS. •Susan Hovde. •Many people in the erstwhile NOAA Aeronomy Laboratory.
Meteorological Chemistry Program
•Many people in the erstwhile NOAA Aeronomy Laboratory.
•Many people connected with the NASA ER-2 & WB57F, and the NOAA G4.
Alder & Wainwright (1970), Phys. Rev. A,1, 18-21.
[emergence of fluid flow from molecular dynamics]
Schertzer & Lovejoy (1987), J. Geophys. Res., 92, 9693-9714.
[generalized scale invariance, statistical multifractals]
Tuck et al. (2004), Q. J. R. Meteorol. Soc., 130, 2423-2444.
[scale invariance in jet streams]
Tuck et al. (2005), Faraday Discuss., 130, 181-193.
[correlation between temperature intermittency and ozone photodissociation rate]
Further references and bibliography are in slides 79-84
Some equations and text are in slides 70-78
Eady (1951), Q. J. R. Meteorol. Soc., 77, 316: Discussion remark. ‘I congratulate Dr. Batchelor on his scholarly presentation of the similarity theory of turbulence initiated by Kolmogoroff. The argument which derives the consequences of statistical “de-coupling” between the primary turbulence-producing processes and the secondary small-scale features of the turbulence appears to be sound but does it get us very far? In meteorology and climatology we are concerned principally with the transfer properties of the turbulence, determined mainly by the large-scale primary processes to which the similarity theory does not pretend to apply. It is the great virtue of similarity theories that no knowledge of the mechanism is involved and we do not have to assume anything about the nature of “eddies”; anything which has “size” (such as a Fourier component) will do in our description of the motion. But this emptiness of content is also their weakness and they give us very limited insight. It is true that a similarity theory that could be applied to the primary turbulence-producing processes would be of great value but there is no reason to expect that anything simple can be found; when several non-dimensional parameters can be formed, similarity theory, by itself, cannot do much.[continued]
Similarity theories are attractive to those who follow Sir Geoffrey Taylor in rejecting crude hypotheses regarding “eddies”, mixing lengths, etc. But those who try to determine the properties of turbulence without such (admittedly unsatisfactory) concepts must show that they have sufficient material (in the shape of equations) to determine the answers. If this is not the case it will be necessary to develop some new principle in addition to the equations of motion and the nature of this principle may be brought to light in a study of the mechanism of the primary turbulence-producing process i.e. by trying to refine or modify what we mean by an “eddy” rather than by completely rejecting the concept.’
A wider context for the importance of understanding the mechanisms of turbulence can be found in Eady and Sawyer (1951), Q. J. R. Meteorol. Soc.,77, 531-551: ‘Dynamics of flow patterns in extratropical regions’.
Temperature & its H scaling exponent
Wind speed & its H scaling exponent
10˚- 46˚N,140˚- 172˚W
Alder & Wainwright (1970): A flux applied to an
equilibrated population of Maxwellian molecules.
Vortices and fluid flow emerge in 10-12s and 10-9 m.
scores of ER-2 flight segments, Arctic summer 1997 & winter
1998 - 1999 (WAM and ACCENT)
All DC-8 total water, ‘horizontal’, 44˚S - 90˚S, Aug-Sep 1987
All NOAA G4 ‘horizontal’ data, 10˚N-46˚N, 140˚W-172˚W
20040229 - 20040315
All 261 dropsondes, Winter Storms 2004, 10˚N-46˚N, 140˚W-172˚W, 20040229 - 20040314, NOAA G4
140˚W-172˚W, 20040229 - 20040314, NOAA G4
Gulfstream Ascents & Descents
WB57F Ascents & Descents
Correlation of H for ER-2 wind speed and temperature with jet strength
Dropsonde (25˚N,157˚W) on 20040229. The ‘Russian doll’ structure.
2004. Scaling is not Kolmogorov or gravity wave; Bolgiano-Obukhov
applies in lower troposphere, but none are correct at jet altitudes.
Isentropes observed by MTP.Figure 22
Scaling of WB57F observations and of MM5 simulation, 19980411.
values of generalized scale invariance exponents: conservation,
intermittency and Lévy.
ER-2 temperature data from SOLVE, Arctic Jan-Mar 2000. H1, C1 and . Archived (truncated) data spoils calculation of (T).
the intermittency of observed temperature. Arctic summer 1997
and winter 2000.
its intermittency. Arctic summer 1997 and winter 2000.
crossing terminator. Temperature changes between night and day,
nothing else does.
nitrous oxide do not change across the terminator.
racetrack flights in static air mass, Arctic summer 19970509.
racetrack flights in static air mass, Arctic summer 19970911,14,15.
Lapse rate PDFs at different vertical resolutions, dropsondes from
NOAA G4, 20040229 - 20040315, eastern Pacific Ocean.
a flux applied to an equilibrated Maxwellian population results in
the emergence of vortices on scales of 10-12 seconds & 10-8 meters.Figure 8
The correspondence and coupling of the microscopic and macroscopic
processes in the atmosphere.
distribution of photofragments, O3 photodissociation, Hartley band.
Marenco et al. (1994),JGR, 99, 16617-16632.
H[ClO] > 0.56.
H[ClO] < 0.56.
March 2000. An early ClO source & NOy sink from PSCs evolve
to a sink and to a passive scalar (tracer) respectively.
Scatterplot, scaling exponents of ClO & O3, Arctic vortex 2000.
1 = 20000120, 11 = 20000312. Ozone sink was present 20000120.
Evans & Searles (2002), Adv. Phys.,51,1529-1585. The high speed
molecules, a minority, produce order (‘flow’) while the average
majority produce dissipation (‘temperature’).
THEORY: Nonlinear interaction among high speed molecules subject to an anisotropy sustains vortices and the overpopulation of fast molecules in the PDF - fluid flow emerges from the Maxwellian ‘billiard balls’. Temperature remains defined but is not the mean of the Maxwell-Boltzmann distribution. The high speed molecules produce larger scale order (negative entropy), the ones near the mean are responsible for dissipation (positive entropy).
EVIDENCE: Correlation of H1(windspeed) with horizontal and vertical measures of jet stream strength. Correlation of temperature intermittency with ozone photodissociation rate.
Jet stream speeds reach Mach 0.7 - half the speed of the most probable speed of N2 molecules.
ATMOSPHERIC TURBULENCE: A Molecular Dynamics Perspective, Oxford University Press,
due to appear January 2008.
A F Tuck
Oxford University Press
Target: January 2008