9 de setembro de 2010 LNCC

From observation to modeling: Lessons and regrets from 36 years in the field.

David FitzjarraldAtmospheric Sciences Research CenterUniversity at Albany, SUNYAlbany, New York USA

Experimentos do campo faz-se envelhecer1989

Observações

Teoria/modelos simples

Modelos mais complexos (DNS, LES, meso)

Resultados:

C = <C> + C’

Ya conheciamos(o ‘obvio’) Inovação (merece publicar)

conhecimento

A região de Xalapa, Veracruz, México

20°N

19°N

96°W97°W

a cidade deXalapa ficaalredor deun volcán

Um projeto simple,1980-81.

Experimento do campojulho 1980 & fevereiro 1981

Balão cativo

Vento catabático na presença no fluxo em oposição

Julho 1980Los alisios

uphill downhill

Fevereiro 1981 sem alisios, vento descendente depois a inversão pasa abaixo

Vento catabático sem oposição

First simplification: 1Dmomentum equation along a slope:

[1] [2] [3] [4] [5]

[1] acceleration [3] stress divergence

[2] advection of momentum [4] buoyant forcing

[5] pressure forcing

€

∂ui∂t

+ u j∂ui∂x j

= −∂τ ij∂x j

+ gθv '

θv

∂h

∂x i−

1

ρ

∂p'

∂x i

x3

x1h

  The Prandtl katabatic wind solution (1940’s) 

Prandtl assumed that the steady downslope momentum balance is made between “vertical” (perpendicular to the slope, called z here) turbulent flux of momentum (Fm ) and the “buoyancy force” (Archimedean acceleration):

Turbulent flux divergence buoyancy force along slopeMomentum (steady) : 0 = -∂Fm/∂z + [b q’ sin a] a

[Here q’ is the deviation of the potential temperature from a base state and b is the buoyancy parameter g/Qv.]

The whole analysis works because the base state is assumed to have a Theta(z’) that changes only in the true vertical, not perpendicular to the slope (n). 

The thermal balance is assumed to be between along-slope (labeled s) heat advection and turbulent flux divergence:horizontal thermal advection vertical turbulent heat flux divergence:

U∂Q/∂s    ≈ U[g sin a] = -∂FQ/∂n ,

[ where g is the base state potential temperature gradient, ∂Q/∂z’ , where z’ is the true vertical. ]

Prandtl (1953)

Prandtl’s analytic solution

Maximum wind speed independent of slope angle

Most results can be obtained through dimensional analysis alone! (Comes from the simplification.)

notes from USP IAGJune1984

Prandtl

July 1980

February 1981

Xalapa datarevisited,scaled by heightof wind speed maximum

Effects of entrainment larger than Prandtl can predict

Fedorovich & Shapiro (2009)

Redoing this problem using DNS & (inevitably) LES

Fedorovich & Shapiro (2009)

DNS simulation: confirms that maximum wind ≠ f(slope)

A 2nd simple model approach:

By integrating equations in the vertical, we form an analogy with open channel hydraulics

The hydraulic jump

Supercritical “shooting”

Subcritical “tranquil”

Modelo integrado no vertical Manins & Sawford (1979)

Uh = integral mass transport

Manins & Sawford (1979)

‘shooting’ (supercritical) flows vs. ‘tranquil’ (subcritical)

Manins & Sawford (1979)

Entrainment assumptions

Manins & Sawford (1979)

Manins & Sawford (1979)

Uh

U

Ri

UDQ

€

C = S1RiM = S1A

S2 tanα

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 2

Conditions on Ri for steady state

Fitzjarrald (1984)

Dimensionless equation set; ua is the ambient wind.

Changes in time

Stability of models

Solutions in time

Steady solutions

shooting

shooting

tranquil

Fitzjarrald, 1984

downhilluphill

Some thoughts in 2010:

Prandtl solution gave good insight.

When do we know that we are publishing new information?

Question of shooting vs tranquil flows (from the bulk models)observationally unresolved.

Oscillations simulated with DNS, but no observations yet