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  • On the vertical structure of the tropospheric eddy momentum flux

    Farid Ait Chaalal(1,3) and Tapio Schneider(2,3)(1)Brown University, Providence, USA (2)ETH, Zurich, Switzerland

    (3)Caltech, Pasadena, USA

    19th Conference on Atmospheric and Oceanic Fluid Dynamics1721 June 2013, Newport, Rhode Island

  • Eddy momentum flux maximum in the upper troposphere

    Held, 2000: upper level zonal mean flow favors linear wave meridional propagation

    Upper level enhancement not captured without nonlinear saturation (Simmons and Hoskins, 1978; Merlis and Schneider, 2009)

    106ms2

    Motivation

    Eddy momentum flux convergence in the atmosphere (colors), zonal wind (contours, m/s) andtropopause (grey line).ERA 40 1980-2001

    Latitude

    Sigm

    a

    10

    10

    303010

    60 30 0 30 60

    0.2

    0.8

    50

    0

    50

    10

    2020

    0

    0

  • Surface friction?

    Large scale eddy-eddy interactions?

    Outline

    Why is eddy momentum flux concentrated in the upper troposphere?

  • An idealized dry GCM

    GFDL pseudospectral dynamical core

    Radiation: Newtonian relaxation toward temperature profile

    Convection: relaxation of vertical lapse rate toward 0.7 (dry adiabatic)

    Uniform surface, no seasonal cycle

    Run at T85 with 30 vertical sigma-levels

    600 days average after 1400 days spin-up

    (Schneider and Walker, 2006)

  • The role of surface friction

    Colors: eddy momentum flux divergenceContours and dashed lines: zonal mean flow (m/s)Dotted line: potential temperature (K)Grey line: tropopause (2K/km lapse rate)

    Simulation with positive 90 K pole-to-equator temperature contrast h.

    Simulation with negative h = -90 K.Poles heated, tropics cooled.

    106ms2

    LatitudeSigm

    a

    10

    2030

    40 40

    300

    320

    350

    60 30 0 30 60

    0.2

    0.8

    10

    5

    0

    5

    10

    Latitude

    Sigm

    a

    30 30

    10

    10

    20 20

    300

    320

    350

    60 30 0 30 60

    0.2

    0.8

    50

    0

    50106ms2

  • Removal of eddy-eddy interactions

    Quasi-linear (QL) model (OGorman and Schneider, 2007)

    Retained:Wave-mean flow interaction (mean flow = zonal average)Interaction of waves of opposite zonal wavenumber

    (Reynolds stress)

    Neglected:All other eddy-eddy interactions

    (Statistics equivalent to 2nd order cumulant expansion, see Brad Marstons talk)

  • Full

    No eddy-eddy

    Meridonal circulation

    Contours: zonal mean flow (m/s)

    Dotted lines: potential temperature (K)

    Grey line: tropopause

    Latitude

    Sigm

    a30 30

    2020

    10 10

    300

    320

    350

    60 30 0 30 60

    0.2

    0.8

  • Eddy Momentum Flux Divergence

    Latitude

    Sigm

    a30 30

    10

    10

    20 20

    300

    320

    350

    60 30 0 30 60

    0.2

    0.8

    50

    0

    50

    Colors: eddy momentum flux convergence

    Contours: zonal mean flow (m/s)

    Dotted lines: potential temperature (K)

    Grey line: tropopause

    Eddy momentum flux convergence

    Full

    No eddy-eddy

    106ms2

  • Restoring barotropic triads

    Latitude

    Sigm

    a

    10 10

    1010

    40 40

    300

    320

    350

    60 30 0 30 60

    0.2

    0.8

    50

    0

    50

    Latitude

    Sigm

    a30 30

    10

    10

    20 20

    300

    320

    350

    60 30 0 30 60

    0.2

    0.8

    50

    0

    50

    106ms2Colors: eddy momentum flux convergence

    Contours: zonal mean flow (m/s)

    Dotted lines: potential temperature (K)

    Grey line: tropopause

    Full

    Withbarotropic

    triads

  • Baroclinic wave lifecycle experiments

    Initialize a zonal wavenumber 6 perturbation in the zonally averaged circulation (fully non-linear model)

    Experiments run with full model, no eddy-eddy model, and model with only barotropic triads

    Why eddy momentum flux not maximum in the upper troposphere in the QL model ?

    Why enhancement captured when barotropic triads are restored?

    Also: eddy kinetic energy larger in the QL model usually, larger momentum flux expected

    Removal of eddy-eddy interactions

  • 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 755

    0

    5

    10

    x 105 full model

    Days

    W/kg

    0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 755

    0

    5

    10

    x 105

    Days

    W/kg

    only barotropic eddyeddy

    0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 755

    0

    5

    10

    x 105

    Days

    W/kg

    no eddyeddy

    Baroclinic conversion.Eddy available potential energy to eddy kinetic energy

    Barotropic conversion.Zonal kinetic energy to eddy kinetic energy

    Full

    No eddy-eddy Only barotropic eddy-eddy

    Energy conversion

  • 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 755

    0

    5

    10

    x 105

    Days

    W/kg

    only barotropic eddyeddy

    0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 755

    0

    5

    10

    x 105

    DaysW/kg

    no eddyeddy

    0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 755

    0

    5

    10

    x 105 full model

    Days

    W/kgColors: QG potential vorticity fluxContours: zonal mean flow (m/s)Arrows: QG Eliassen-Palm vector

    Full No eddy-eddy Only barotropic eddy-eddy

    105ms2

    Latitude Latitude Latitude

    Sig

    ma

    Maximum of barotropic conversion

  • 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 755

    0

    5

    10

    x 105

    Days

    W/kg

    only barotropic eddyeddy

    0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 755

    0

    5

    10

    x 105

    DaysW/kg

    no eddyeddy

    0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 755

    0

    5

    10

    x 105 full model

    Days

    W/kg

    Sig

    ma

    Latitude Latitude Latitude

    Minimum of baroclinic conversion

    Colors: QG potential vorticity fluxContours: zonal mean flow (m/s)Arrows: QG Elliassen-Palm vector

    Full No eddy-eddy Only barotropic eddy-eddy

    105ms2

  • Potential vorticity rearrangement and mixing

    Days

    W/kg

    15 20 25 30 355

    0

    5

    10x 10

    Days

    W/kg

    15 20 25 30 355

    0

    5

    10x 10

    For a theoretical study of critical layers (SWW solution) in the QL approximation:Haynes and McIntyre, 1987

    Full(350 K

    isentrope)

    No eddy-eddy

    (320 K isentrope)

    Day 26 Day 30 Day 35

    Day 17 Day 22 Day 30

    PV fields on isentropes

    210PVU

  • Potential vorticity rearrangement and mixing

    Days

    W/kg

    15 20 25 30 355

    0

    5

    10x 10

    15 20 25 30 355

    0

    5

    10

    x 105

    Days

    W/kg

    only barotropic eddyeddy

    Noeddy-eddy

    (320 K isentrope)

    Only barotropic eddy-eddy

    (320 K isentrope)

    Day 17 Day 22 Day 30

    Day 25 Day 28 Day 32

    PV fields on isentropes

    210PVU

  • Conclusions

    Surface friction not an important factor

    Wave packets generated in LT propagate upward until they reach UT and tropopause, where horizontal propagation is favored

    Vorticity rearragement and mixing through eddy-eddy interaction near critical layers essential

    Keeping only barotropic triads captures the enhancement

    Understanding nonlinear barotropic critical layer dynamics might suffice

    Why is eddy momentum flux concentrated in the upper troposphere?

  • Conclusions

    What still favors meridional propagation of waves in the upper-troposphere? (tropopause as a wave guide? ...)

    Index of refraction for zonal wavenumber 6 baroclinic waves.

    Latitude

    Sigm

    a

    30 30

    1010

    60 30 0 30 60

    0.2

    0.8

    0

    5

    10

    15

    20

    Why is eddy momentum flux concentrated in the upper troposphere?

    FullNo

    eddy-eddy

  • Dry GCM without eddy-eddy interactions

    Removal of the eddy-eddy interactions (OGorman and Schneider,2007).Advection of a quantity a = a+ a0 by the meridional flow v = v + v 0(zonal mean/eddy decomposition):

    @a

    @t= v @a

    @y= v @a

    @y v @a

    0

    @y v 0 @a

    @y v 0@a

    0

    @y

    transformed into

    @a

    @t= v @a

    @y v @a

    0

    @y v 0 @a

    @y v0@a

    0

    @y

    Statistics of such a model are equivalent to a second order cumulantexpansion (third order cumulants set to 0 in the second orderequations).

    Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 4 / 19

    @a

    @t= v@a

    @y= v@a

    @y v@a

    0

    @y v0 @a

    @y v0 @a

    0

    @y

    @a

    @t= v@a

    @y= v@a

    @y v@a

    0

    @y v0 @a

    @y v0 @a

    0

    @y

    Removal of the eddy-eddy interactions

  • Latitude

    Sigm

    a

    0 0

    5

    10

    30

    40 40

    300

    320

    350

    60 30 0 30 60

    0.2

    0.8

    10

    5

    0

    5

    10

    The role of surface friction

    Latitude

    Sigm

    a0

    0

    5

    10

    30

    40 40

    300

    320

    350

    60 30 0 30 60

    0.2

    0.8

    10

    5

    0

    5

    10

    Simulation with h = -90 K

    Latitude

    Sigm

    a

    10

    5

    10

    5 50 50

    4030

    10300

    320

    350

    60 30 0 30 60

    0.2

    0.8

    10