A molecular view of vorticity turbulence four lectures at ncar 28 29 november 2007
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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.

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A Molecular View of Vorticity & Turbulence Four Lectures at NCAR, 28-29 November 2007

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A Molecular View of Vorticity & TurbulenceFour 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.

•Many people connected with the NASA ER-2 & WB57F, and the NOAA G4.

Slide 2


Key References

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

Slide 3


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]

Slide 4


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’.

Slide 5


ER-2 flight into the polar night jet, Stavanger to Wallops Is.: T

Slide 6


ER-2 flight into the polar night jet, Stavanger to Wallops Is.: √(u2+v2)

Slide 7


19890220 Wind VectorsCentred At (550 N,460 W)

Slide 8


19890220 Wind Shear Vectors

Slide 9


Scaling Calculation for19890220 Wind Speed

Slide 10


Scaling Calculation for19941005 Wind Speed(44°S,173°E) to (65°S,180°E)

Slide 11


Dropsonde from NOAA G4: (15˚N, 166˚W), 20040304

Temperature & its H scaling exponent

Slide 12


Dropsonde from NOAA G4: (15˚N, 166˚W), 20040304

Wind speed & its H scaling exponent

Slide 13


All ER-2 flight segments, 1987 - 2000, 90˚N -72˚S

˚

Slide 15


All 261 dropsondes, 20040229 - 20040315,

10˚- 46˚N,140˚- 172˚W

Slide 16


Figure 8

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.

Slide 16


Intermittency, sharp gradients

Slide 17


Intermittency, sharp gradients

Slide 18


Intermittency, sharp gradients

Slide 19


Long-tailed PDFs of temperature: millions of 5 Hz points from

scores of ER-2 flight segments, Arctic summer 1997 & winter

2000.

Slide 20


All ER-2 ‘horizontal’ segments >2000 s, 1987-2000

Slide 21


All WB57F ‘horizontal’ data near tropical tropopause

1998 - 1999 (WAM and ACCENT)

Slide 22


All DC-8 ‘horizontal’ data, 44˚S - 90˚S, Aug-Sep 1987 (AAOE)

Slide 23


All DC-8 total water, ‘horizontal’, 44˚S - 90˚S, Aug-Sep 1987

Slide 24


All NOAA G4 ‘horizontal’ data, 10˚N-46˚N, 140˚W-172˚W

20040229 - 20040315

Slide 25


All ER-2 ozone & nitrous oxide, 59˚N-70˚S, heavy SH weighting

Slide 26


All 261 dropsondes, Winter Storms 2004, 10˚N-46˚N, 140˚W-172˚W, 20040229 - 20040314, NOAA G4

Slide 27


All 261 dropsondes, Winter Storms 2004, 10˚N-46˚N,

140˚W-172˚W, 20040229 - 20040314, NOAA G4

Slide 28


Aircraft ascents and descents,Jan-Mar 2004,10˚- 60˚N,84˚- 158˚W

Gulfstream Ascents & Descents

WB57F Ascents & Descents

Slide 29


Scaling from G4 in Winter Storms 2004

Slide 30


Figure 18

Correlation of H for ER-2 wind speed and temperature with jet strength

Slide 31


Correlation of H for dropsonde wind speed with jet strength, WS 2004

Slide 32


Dynamical stability [Ri>0.25] at 500 & 150 m(left),50 & 10 m(right)

Dropsonde (25˚N,157˚W) on 20040229. The ‘Russian doll’ structure.

Slide 33


Vertical scaling of horizontal wind, 235 dropsondes, Winter Storms

2004. Scaling is not Kolmogorov or gravity wave; Bolgiano-Obukhov

applies in lower troposphere, but none are correct at jet altitudes.

Slide 34


WB57F, Rocky Mountains 19980411. Severe turbulence & lee waves.

Isentropes observed by MTP.

Figure 22

Slide 35


Lee waves near Riverton, Wyoming. Severe turbulence (WAM).

Slide 36


Figure 24

Scaling of WB57F observations and of MM5 simulation, 19980411.

Slide 37


Scaling of WB57F and MM5, WAM Rocky Mountain Lee Wave Flight 19980411

Slide 38


Simulated monofractal signals: random, antipersistent & persistent.

Slide 39


Simulated statistical multifractal signal, with typical observed

values of generalized scale invariance exponents: conservation,

intermittency and Lévy.

Slide 40


ER-2 temperature data from SOLVE, Arctic Jan-Mar 2000. H1, C1 and . Archived (truncated) data spoils calculation of (T).

Slide 41


Scaling exponents H1, C1and for SOLVE ER-2, full precision at 5 Hz

Slide 42


ER-2, O3 SOLVE data. Scaling exponents H1, C1and.

Slide 43


ER-2, O3 scaling exponents, AAOE, Antarctic vortex, Aug-Sep 1987.

Slide 44


Long-tailed PDFs of temperature, Arctic winter & summer, trop. trop.

Slide 45


Scaling & intermittency of temperature, ER-2, Arctic, 19970506

Slide 46


Correlation of the observed photodissociation rate of ozone with

the intermittency of observed temperature. Arctic summer 1997

and winter 2000.

Slide 47


Correlation of average temperature along an ER-2 flight segment with

its intermittency. Arctic summer 1997 and winter 2000.

Slide 48


ER-2, Arctic summer 1997. Racetrack segments in static air mass,

crossing terminator. Temperature changes between night and day,

nothing else does.

Slide 49


ER-2, Arctic summer 1997. Unlike temperature, wind speed and

nitrous oxide do not change across the terminator.

Slide 50


Shift to warmer temperatures on sunlit side of terminator, ER-2

racetrack flights in static air mass, Arctic summer 19970509.

Slide 51


Shift to warmer temperatures, sunlit side of terminator, ER-2

racetrack flights in static air mass, Arctic summer 19970911,14,15.

Slide 52


Lapse rate PDFs at different vertical resolutions, dropsondes from

NOAA G4, 20040229 - 20040315, eastern Pacific Ocean.

(a)

(b)

Slide 53


Maxwellian Velocity Distribution

Slide 54


Maxwellian speed PDFs, m = 28: T dependence

Slide 55


Maxwellian speed PDFs: mass dependence

Slide 56


NOAA-NCEP GFS 0.50 RESOLUTION ANALYSIS, FLECHES & ISOTACHS

Slide 57


Alder & Wainwright (1970): molecular dynamics simulation of

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

Slide 58


O

O +

O

3

2

The correspondence and coupling of the microscopic and macroscopic

processes in the atmosphere.

Slide 59


Baloïtcha & Balint-Kurti (2005), PCCP, 7, 3829-3833.Speed

distribution of photofragments, O3 photodissociation, Hartley band.

Slide 60


Historical montane surface site observations of ozone:

Marenco et al. (1994),JGR, 99, 16617-16632.

Slide 61


Scaling of ER-2 ClO, Arctic vortex, 20000123. A source is operative,

H[ClO] > 0.56.

Slide 62


Scaling of ER-2 ClO, Arctic vortex, 20000226. Source no longer

operative.

Slide 63


Scaling of ER-2 ClO, Arctic vortex, 20000312. A sink is operative,

H[ClO] < 0.56.

Slide 64


ER-2 scaling exponents for ClO and NOy, Arctic vortex, January -

March 2000. An early ClO source & NOy sink from PSCs evolve

to a sink and to a passive scalar (tracer) respectively.

Slide 65


Figure 46

Scatterplot, scaling exponents of ClO & O3, Arctic vortex 2000.

1 = 20000120, 11 = 20000312. Ozone sink was present 20000120.

Slide 66


H1 scaling exponents for chemical speciesER-2 during SOLVE

Slide 67


Figure 47

Evans & Searles (2002), Adv. Phys.,51,1529-1585. The high speed

molecules, a minority, produce order (‘flow’) while the average

majority produce dissipation (‘temperature’).

Slide 68


Summary

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.

Slide 69


Slide 70


Slide 71


Slide 72


Slide 73


Slide 74


Slide 75


Slide 76


Slide 77


Slide 78


References

Slide 79


Slide 80


Slide 81


Slide 82


Slide 83


ATMOSPHERIC TURBULENCE: A Molecular

Dynamics Perspective

A F Tuck

Oxford University Press

Target: January 2008

Slide 84


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