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Large-Scale Tropical Atmospheric Dynamics: Asymptotic Nondivergence & Self-Organization

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Large-Scale Tropical Atmospheric Dynamics:

Asymptotic Nondivergence

& Self-Organization

(& Self-Organization)

by Jun-Ichi Yano

With

Sandrine Mulet, Marine Bonazzola, Kevin Delayen, S. Hagos, C. Zhang,

Changhai Liu, M. Moncrieff

Madden-Julian Oscillation (MJO)

:Madden & Julian (1972)

30-60 days

Dominantly

Divergent-Flow

Circulations

?

(e.g., Yanai et al., 2000)

(Free-Ride,

Fraedrich &

McBride 1989):

(TOGA-COARE IFA Observation)

moisture

Heat Budget

Condensation(K/day)

Convective

Heating(K/day)

Vertical Advection+Radiation

Vertical Advection

Vertical Advection

=Diabatic Heating

Thermodynamic equaton:

i.e., the vertical velocity vanishes to leading order

i.e., the horizontal divergence vanishes to leading order of asymptotic expansion

i.e., Asymptotic Nondivergence

Scatter Plots

between

Vorticity and

Divergence

divergence

vorticity

500hPa

divergence

vorticity

250hPa

divergence

vorticity

Asymptotic Tendency for Non-Divergence:

Divergence/Vorticity(Total)

horizontal scale (km)

Time scale (days)

Asymptotic Tendency for Non-Divergence:

Divergence/Vorticity(Transient)

horizontal scale (km)

Time scale (days)

(Free-Ride,

Fraedrich &

McBride 1989):

(TOGA-COARE IFA Observation)

moisture

Heat Budget

Condensation(K/day)

Convective

Heating(K/day)

Effectively Neutral

Stratification:hE=0 :

Vertical Advection+Radiation

Vertical Advection

1. Vertical Advection

=Diabatic Heating

:No Waves (Gravity)!

Dry Equatorial Waves with hE=25 m

(Wheeler & Kiladis 1999)

Equatorially

asymmetric

Equatorially

symmetric

Frequency

Frequency

Zonal Wavenumber

Zonal Wavenumber

- Vertical Scale of the wave: D
- Gravity-Wave Speed: cg=(ghE)1/2~ND

Scale Analysis (Summary):Yano and Bonazzola

(2009, JAS)

(Simple)

(Asymptotic)

R.2. Vertical

Advection:

- L~3000km, U~3m/s (cf., Gill 1980):

Wave Dynamics (Linear)

- L~1000km, U~10m/s (Charney 1963):

Balanced Dynamics (Nonlinear)

R.1. Nondimensional: =2L2/aU

Are the Equatorial Wave Theories consistent with the Asymptotic Nondivergence?

A simple theoretical analysis:

RMS Ratio between the Vorticity and the Divergence for Linear Equaotorial Wave Modes:

<(divergence)2>1/2/<(vorticity)2>1/2

?

(Delayen and Yano, 2009, Tellus)

but

Asymptotic Nondivergence is much weaker than those expected from linear wave theories

(free and forced)

Nonlinearity defines the divergence/vorticity ratio

(Strongly Nonlinear)

Asymptotically Nondivergent Dynamics

(Formulation):

- Leading-Order Dynamics:

Conservation of Absolute Vorticity

- Higher-Order:

Perturbation“Catalytic” Effect of Deep Convection

Slow Modulation of the Amplitude of the Vorticity

Balanced Dynamics (Asymptotic: Charney)

Qw

Q=Q(q,… )

- divergence equation (diagnostic)

barotropics -plane vorticity equation

Rossby waves (without geostrophy): vH(0)

}

- hydrostatic balance:

- continuity: w weak divergence

weak forcing on vorticity (slow time-scale)

- thermodynamic balance: w~Q:

(free ride)

- dynamic balance: non-divergent

- vorticity equation (prognostic)

- moisture equation (prognostic): q

Asymptotically Nondivergent Dynamics

(Formulation):

- Leading-Order Dynamics:

Conservation of Absolute Vorticity:

:Modon Solution?

Absolute

Vorticity

Streamfunction

A snap shot from TOGA-COARE (Indian Ocean):

40-140E, 20S-20N

?

(Yano, S. Hagos, C. Zhang)

“Asymptotic nondivergence” is equivalent to “Longwave approximation” to the linear limit.

(man. rejected by Tellus 2010, JAS 2011)

Last Question: What is wrong with this theorem?

Last Remark

However, “Asymptotic nondivergence” provides a qualitatively different dynamical regime under Strong Nonlinearity.

Reference: Wedi and Smarkowiscz (2010, JAS)

(Yano, Liu, Moncrieff 2012 JAS)

Point of view of Water Budget

Precipitation

Rate, P

?

Column-Integrated Water, I

(Yano, Liu, Moncrieff 2012 JAS)

?

Self-Organized Criticality

Homeistasis

(Self-Regulation)

(Yano, Liu, Moncrieff 2012 JAS)

(Yano, Liu, Moncrieff, 2012, JAS)

(Yano, Liu, Moncrieff, 2012, JAS)

- Criticality (Stanley 1972)

- Bak et al (1987, 1996)

- Dissipative Structure (Gladsdorff and Prigogine 1971)

- Synergetics (Haken 1983)

- Butterfly effect (Lorenz 1963)

- etimology:

homeo (like)+stasis(standstill)

- Psyology: Cannon (1929, 1932)

- Quasi-Equilibrium (Arakawa and

Schubert 1974)

- Gaia (Lovelock and Margulis 1974)

- Self-Regulation (Raymond 2000)

- cybernetics (Wiener 1948)

- Buffering (Stevens and Feingold 2009)

- Lesiliance (Morrison et al., 2011)

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