Part I: Dry Convection

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1 Turbulent dispersion and chemical transformation in the atmospheric boundary layer: Part I: Dry Convection DISPERSION Thanks: Alessandro Dosio Jordi Vilà-Guerau de Arellano WA G E N I N G E N U N I VE R S I T Y M E TE O R O L O G Y A N D A I R Q U A L I TY Stefano Galmarini

2 Laminar Lasagna (LES) Turbulent ratatouille (DNS)

3 How do the Atmospheric Boundary Layer dynamics influence the transport, mixing, chemical transformation and removal of atmospheric (reactive) compounds? Greenhouse gases (CO 2, N 2 O, CH 4,...) Reactive compounds(o 3, NO x, VOC,...)

4 Scope of the 2 lectures Discuss in detail how boundary layer structure determines the dispersion and transformation of atmospheric compounds

5 Organization of the 2 lectures Basic concepts (Part 1) cloudy CBL (Part 2) clear CBL (part 1) SBL (part 2)

6 Basic concepts Emphasis on connecting ABL dynamics (mainly atmospheric turbulence) to the dispersion and transformation of atmospheric compounds Dispersion: Lagrangian approach Taylor s diffusion equation Chemical transformation: Eulerian approach Conservation equation of reactants

7 Plume Dispersion is described by Mean (1 st moment) Spread (2 nd moment) C ( x!, t)! ( x!, t ) S ( x!, t) Symmetry (3 rd moment)

8 Taylor s diffusion equation: Autocorrelation Quantifying the persistence of the velocities fluctuations 2 ) ( ) ( ) ( j j j j u t u t u R!! + = 0 ) ( 1 (0) 0 =! =! " = " = R R # # (Taylor, 1921)

9 Taylor s diffusion equation: Lagrangian time scale Integral time scale that characterizes the energy containing eddies L # " 0 L T $ R (! ) d! j j Remember than L j T > T E j

10 Taylor s diffusion equation: dispersion Connecting flow properties to dispersion properties (σ) If turbulent field is homogenous: 2 2 " ( T ) = 2u dt R (! ) d! j j j T o t # # o Through out the lecture, examples of R(τ) and T L under different ABL conditions

11 Chemical transformations are easier to be treated in a fix system of coordinates (Eulerian)

12 Conservation eq. reactants: reaction term Relevance of the chemical term! C! t + u j! C! x j = R( c,..., c 1 n ) Similar to: radiative flux divergences phase changes

13 Conservation eq. reactants: physical influences Turbulence and UV-radiation influence R " C " t + U " C " u jc j + = j A! k( BC + bc) " x " x j j (Averaged equation) Photolysis j control by UV radiation Co-variance quantifies how atmospheric turbulence mixes reactants

14 Outline Refreshing the main characteristics of the convective boundary layer Turbulent dispersion Reactivity

15 Convective Boundary Layer characteristics Large diurnal variability (3) Entrainment (exchange fluxes) FREE TROPOSPHERE/RESIDUAL LAYER ABL (2) Turbulent mixing (turbulent fluxes) (1) Land-atmosphere interaction (including surface/emission variability) SURFACE

16 How does the CBL structure influence the dispersion and transformation of atmospheric compounds? Turbulent dispersion and mixing driven by vigorous thermals and subsidence motions

17 Plume morphology

19 Using LES to understand and obtain the statistical properties of plume dispersion Calculation Taylor s diffusion equation 2 2 " ( T ) = 2u dt R (! ) d! j j j T o t # # o σ is calculated explicitly by LES Each term calculated by LES

20 Lagrangian autocorrelation velocities Horizontal Vertical e t e! /!t / T L T L cos( wt) T t 2 2 j j # # j ) o o " ( T ) = 2u dt R (! d! Approximately, follows a Markov process (homogeneous and stationary) Influence by large-eddy structure.

21 Lagrangian time scale Horizontal T t 2 2 j j # # j ) o o " ( T ) = 2u dt R (! d! # " 0 L L Tj $ R j (! ) d! Vertical

22 Lateral dispersion (y-comp) T t 2 2 j j # # j ) o o " ( T ) = 2u dt R (! d! Continuous line y '2 ( t) Dotted line σ y Dashed line Taylor eq. Water-tank data y '2 ( t) directly calculated from Lagrangian particles

23 Lateral dispersion LES results validated against other studies σ y ~ t LES (aver. cases B1- B5) σ y /z i σ y ~t Meandering (large scale) * Taylor Willis & Deardorff (1981) Nieuwstadt & De Valk (1987) Lamb (1982)! Weil (2002) Meandering 2 2 = m + y s 2 t * Weil (2002)

24 Vertical dispersion (z-comp) " = 2w 2 T dt! 2 # # o o R(! ) d! Continuous line z '2 ( t) Dashed line Taylor eq. Water-tank data Overestimation of Taylor s theory z '2 ( t) directly calculated from Lagrangian particles

25 Redefining the Lagrangian time scale To account for free and bounded motion Free Bounded

26 Free movement (τ<t o ) (before reaching the boundary) ' L w T ( t) = T ( t) = " R (! ) d! L w t 0 L Bounded movement (τ>t o ) (after reaching the boundary) T ' L ( t) = 0 " = 2w 2 T o dt! 2 # # o R(! ) d! Not a theoretical explanation!!!

27 Vertical dispersion (z-comp) " = 2w 2 T dt! 2 # # o o R(! ) d! Continuous line z '2 ( t) Dashed line Taylor eq. Water-tank data Dashed-dotted new T L

28 Previous simulation were done in free convective conditions. What is the role of wind and shear in dispersion under convective conditions?

30 Buoyancy Profiles velocity variances Moderate Shear Strong Shear Near Neutral Increase shear at the boundaries Z/Zi z/z i Z/Zi σ v /w m Decrease flow anisotropy σ w /w m

31 Vertical velocity horizontal cross-sections (z/z i =0.175) Buoyancy Convective cell pattern Moderate shear Strong shear Near neutral Two-dimensional roll pattern

32 Lateral dispersion (σ) NN SS MS σ y /z i B t*

33 and now we move to chemistry

34 Do we need to treat chemical species differently that inert atmospheric compounds? or What s the importance of the reactive term in the conservation equation?

35 Conservation eq. reactants: physical influences Turbulence and UV-radiation influence R " C " t + U " C " u jc j + = j A! k( BC + bc) " x " x j j (Averaged equation) Photolysis j control by UV radiation Co-variance quantifies how atmospheric turbulence mixes reactants

36 Essential processes to be represented in the ABL FREE TROPOSPHERE/RESIDUAL LAYER (3) Entrainment (exchange fluxes) ABL (2) Turbulent mixing (turbulent fluxes) SURFACE (1) Land-atmosphere interaction (including surface/emission variability)

37 (1) Land/Atmosphere exchange Is the flux of chemically reactive species constant with height in the Atmospheric Surface Layer?

38 In the atmospheric surface layer flux is (almost) constant with height " w '#' " z! 0 " =!, U, V, q, CO2,...

39 But for chemically active species " w' $ ' # ± R " z $! 0 Chemical reaction term (production/destruction)! = O, NO, NO, RH, NH, CO,

40 Chemical/aerosols transformations lead to a flux divergence A + B -> C C -> A + B " w' c' =! jc + k [ ] ab + a' b' " z As a result, the flux of chemically active species can vary with height in the ASL

41 Flux divergence of the system NO-O 3 -NO 2 Monin-Obukhov similarity theory applied to reactive species NO + O 3 -> NO 2 NO 2 -> NO + O 3 Departure log profile Departure constant flux NO/NO x NO/NO x (Fitzjarrald and Lenschow, 1983)

42 Do we have experimental evidence? Not so much but interesting Grass Day time Unstable stratification Inside canopy Day time Stable stratification 11 m surface (Rummel et al. 2002) Practical implications of the flux divergence of chemically active species

43 (2) Turbulent mixing Does atmospheric turbulence control the chemically reactivity?

44 Segregation of chemical species due to the boundary layer structure A + B k C B 0.9 z/z i A + B Products 0.1 z/z i A

45 Horizontal cross section vertical velocity and reaction zones 0.1 z/z i 0.9 z/z i Reaction zone in the updraft Reaction zone in the downdraft

46 A similar turbulent control can occur in chemically reactive plumes Chemical species can be segregated and then reactivity is controlled by turbulent dispersion!!

47 How efficient is turbulence in mixing the reactants? When does turbulence control the reactivity?

48 In particular, for reactions with a similar chemical time scale to the turbulent mixing time scale Definition Damköhler number: Da =!! t c

49 Classification regimes (rough): Da << 1 Chemistry is slow compared with turbulence => SPECIES ARE WELL MIXED Da = O(1) Chemistry and turbulence similar time scales => CONTROL Ability of turbulence to efficiently mix reactants Da >> 1 Chemistry is faster than turbulence => NOT DEPENDING ON THE TURBULENCE

50 How can we quantify the effect of segregation/heterogeneous mixing? " c " t =! " w' c' " z! jc + k [ ] ab + a' b' Coefficient Intensity segregation Is = a' b' AB Co-variance between reactants A + B -> Products

51 Classification regimes: Da << 1 SPECIES ARE WELL MIXED then Is =0 Da => O(1) CONTROL by TURBULENCE then (non-premixed) -1 < Is < (premixed) Depends on the way species are introduced

52 Observations of the intensity of segregation NO-plume released in the atmospheric (Komori, 1991) surface layer and reacting with ozone OBSERVATIONS Negative value => Slow down of the reaction rate Is Is= -.15 => Reaction rate 15% slower NO/O 3 (Komori et al., 1991)

53 Intensity of segregation depends on: I: Ability of turbulence to mix chemical species II: Horizontal/vertical variability emissions

54 I: Ability of turbulence to mix chemical species O 3 NO 2 NO + O 3 NO 2 + O 2 Simple chemistry mechanism. Binary irreversible reaction/nonpremixed

55 Setting up numerical experiments using LES to investigate the combined effect of turbulence and emission heterogeneity Uniform/Homogeneous Non-uniform/Heterogeneous Same amount of species is emitted!!!

56 Location of the reaction rate: Horizontal cross section z/zi= % of the emission in L=700 m y=6.4 km L X=6.4 km 6.4 km

57 Different length scale of the surface emission L=700 m L=1700 m L=2400 m

58 Quantifying the effect of the emission heterogeneity by the intensity of segregation Uniform Non-uniform L=700 m L=1700 m L=2400 m

59 The heterogeneity of emission can control the reactivity of concentration A + B -> P Volume (whole PBL) concentration Species A Non-uniform L=700 m L=1700 m L=2400 m Uniform

60 Horizontal variability emissions and canopy effects (Patton et al., 2000)

61 (3) Entrainment/Exchange What is the role of entrainment on the exchange of reactants? To be studied during the tutorial 7 (optional)!!!

62 Boundary layer dynamics control dispersion and reactivity of atmospheric compounds

63 Challenges ahead (I) To integrate the dispersion chemical transformation in all the relevant spatial/temporal scales Canopy Micrometeorology Boundary layer dynamics Stratification effects Orography Mesoscale Stratification and rotation effects

64 Challenges ahead (II) To account for the interaction/feedbacks of physical/chemical processes Atmospheric dispersion near the surface and in stable stratified conditions Clouds Deposition/Sedimentation heavy particles (pollen) Heterogeneous chemistry..

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