Laboratory and Field Measurements of Environmental Stratified Flows

Marko Princevac

July 28, 2006

Stellar Hydro Days, 26-28 July, 2006

Los Alamos

Outline

• Slope Flows

• Entrainment in Katabatic Current

• Eddy Diffusivity

• Waves vs. Turbulence

• Morning Inversion Break-up

Slope Flows – Thermally Driven

Phoenix

Terrain induced flow

Synoptic flow

Upslope flow

T

U

Q

vs.updraft regions

downdraft regions

Thermal blob

(I)

(IV)

(III)

(II)

(I)

(IV)

(III)

(II)

Detachment occurs when

33

10

cTgRaRa c

Competing tendencies

(I)

(IV)

(III)

(II)

B

P

2u

1u

B

gTgB 30

30~

222

210

2 ~~ uupP

rc P

c

Ra

P

B

41

~

Critical angle experiment

Heating System

Water-Glycerin solution

10 < Pr < 10000

Critical angle vs. Pr

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1 10 100 1000 10000Pr

Cri

tica

l An

gle

rc P

c

Ra

P

B

41

~

Katabatic (Downslope, Drainage) Flow

HUeU eU

eU

eU eU

)(tUU

UH

h S

H L H

0q

Downslope flow - Idealized Topography

HHcH LbU 2

z

UW

x

UU

t

U

Dt

DUˆˆ

zbH ˆ/

bx

UU H

~ˆ

ACS –VTMX ASU Site

Slope Site - VTMX

Downslope flow – Field Results

y = -0.0094x + 0.6523

R2 = 0.0551

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 2 4 6 8 10 12 14 16

b/(NE2h)

c

HHcH LbU ~2

10/15 TS1

0

50

100

150

200

250

300

350

400

450

500

0 1 2 3 4 5 6

Wind Speed [m/s]

Alti

tude

AG

L [m

]

0:22

0:42

1:09

1:30

1:49

2:07

2:30

2:56

10/15 TS1

0

50

100

150

200

250

300

350

400

450

500

288 290 292 294 296 298

Potential Temperature [K]

Alti

tude

AG

L [m

]

0:22

0:42

1:09

1:30

1:49

2:07

2:30

2:56

Downslope flow - Pulsation

T=55 min

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

275.15 275.2 275.25 275.3 275.35 275.4 275.45 275.5

JDay

Win

d S

pe

ed

[m

/s])!(tUU

z

UW

x

UU

t

U

Dt

DUˆˆ

zbH ˆ/

z

bW

x

bU

t

b

Dt

bDˆˆ

HEH UN

z

q 20

ˆ

Downslope flow - Pulsation

have oscillatory solution with the frequency

EN ~ or periodEN

T

2~

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

275.15 275.2 275.25 275.3 275.35 275.4 275.45 275.5

JDay

Win

d S

pe

ed

[m

/s]

bt

U

UNt

bE2

}

,

linearized

0222

2

UNt

UE

Downslope flow - Pulsation

Down-slope Wind

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

275.15 275.25 275.35 275.45

JDay

Win

d S

pe

ed

[m

/s]

Wind Speed

Sin T=55 min T=55 min

ENT

2

~

ACS =4 deg: T=20 – 50 min

SS =1.8 deg: T=50 – 130 min

Down-slope Wind

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

287.15 287.25 287.35 287.45

JDay

Win

d S

pe

ed

[m

/s]

Wind Speed

Sin T=30 min

Downslope flow - Entrainment

x U

z

h(x)

U(z,x)

UE

E

ue

eu

eu

eu

(z,x)

TS4

TS3

TS2

TS1

x

Uhue

u

uE e

Entrainment coefficient Richardson number

2'u

hgRi

gg 'EUUu

Richardson Number

Gradient Richardson Number

0.01

0.1

1

10

100

1000

10000

RIg

Efficient Mixing -KH Regime

Near Neutral

Waves - very little turbulence

Very stable RegimeNon-turbulent

22

zV

zU

zg

Rg

Entrainment

x

Uhue

dt

dhuB

C

wcuF

Entrainment velocities

u

uE e

Entrainment coefficient

Entrainment law

RiEE

Downslope flow – Laboratory Entrainment

Turner (1986)

Ri

RiE

51

1.008.0

310~Re Uh

Downslope flow - Entrainment

x

Uhue

Distance [km] measured from TS1 to the west

10 9 811 3 25 47 6 1 0

1400

1600

1800

2000

2200

2400

BinghamCanyon

Field data – 4 locations kilometer apart

x

Uhue

2u

hgRi

10/15 TS2

0

50

100

150

200

250

0 2 4 6

Wind Speed

Alt

itu

de

0:22

0:42

1:09

1:30

1:49

2:07

2:30

2:56

10/15 TS2

0

50

100

150

200

250

288 290 292 294 296 298

Potential Tem perature

Alt

itu

de

0:22

0:42

1:09

1:30

1:49

2:07

2:30

2:56

Downslope flow - Entrainment

y = 0.054x-0.7494

R2 = 0.7666

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Ri

E

u

uE e

Turner (1986) - laboratory

Field observations

Ri

RiE

51

1.008.0

75.005.0 RiE 7104~Re Uh

310~Re Uh

Downslope flow – Eddy diffusivities

zU

wuK M

dzd

wK H

Eddy diffusivity of momentum

Eddy diffusivity of heat

High Re (107 – 108)

Turbulent transport (u’w’, v’w’, w’’…) dominates molecular ()

ACS Tower

z

U

z

V

dz

d

''wu

''wv

''w

zU

wuK M

dzd

wK H

22

zV

zU

zg

Rig

Downslope flow – Eddy diffusivities

22

zV

zU

zg

Rig

)s(m45.012 RiK

0.22

gM

)s(m07.01245.0

RiK gH

)s(m07.012 K H

Wave Dominated Transport ?

Monti et al. 2002

Molecular

~ 10-5 (m2s-1)

Waves vs. Turbulence

Waves vs. Turbulence

Frequency, Wave Number Frequency, Wave Number

E E

41

3

KL

Characteristics of Turbulent Flows

- Irregularity, randomness Waves also

- Diffusivity Waves also

- Rotational Waves also – generally

(exception example: surface waves)

- Dissipative Waves are essentially nondissipative

Data Filtering

0 100 200 300 400 500 600-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3av. per. 1 min, filter 6 order, 0.25 min cut-off

V

samples

zU

wuK M

dzd

wK H

...wavesMK ...wavesHK

...turbMK ...turbHK

Filters – low-pass

f

E

Low-pass filter

pass band transition band

stop band

slope

cut off frequency

pass-band ripples stop-band

ripples

f

E

unfiltered signal

Common Digital Filters

Flattest Pass-band

Frequency

Gain

Butterworth

Smoothest transition

Frequency

Gain

Bessel

Steepest slope

Frequency

Gain

Elliptic

Signal Spectra – where to cut?

? ?

Shortest internalwave period

Buoyancy frequency N corresponds to maximum possible wave frequency

dz

dgN

2

N= 0.05-0.1 rad/sec

min212

N

T

Cutting Frequency

“waves” “turbulence”

Period > 1 min Period < 1 min

Filtering cut-off period of 1 minute

0 500 1000 1500 2000 2500 3000-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

W

samples

5 minute averaging

5 minute mean is subtracted

before filtering

Elliptical filter

1 min cut off

KM from filtered and non-filtered data

1 E -2 1 E -1 1 E + 0 1 E + 1 1 E + 2R i

1 E -3

1 E -2

1 E -1

1 E + 0

1 E + 1

KM

(m

s )-2

g

1 m

1 m fil . 1 m

5 m

5 m fil . 1 m

1 5 m

1 5 m fil. 1 m

L O W E R S O N IC

zU

nsKM

''

KH from filtered and non-filtered data

1 E -2 1 E -1 1 E + 0 1 E + 1 1 E + 2R i

1 E -3

1 E -2

1 E -1

1 E + 0

1 E + 1

KH

(m

s )-2

g

1 m

1 m fil . 1 m

5 m

5 m fil . 1 m

1 5 m

1 5 m fil. 1 m

L O W E R S O N IC

dzd

nKH

'

TKE vs. “Wave” kinetic energyNon-filtered data Total KE

(fluctuations)Filtered data “wave-less” KE

(fluctuations)

“Wave” KE = Total – Wave-less

KETotal

KEWave

_

_

Rig=1

22

zV

zU

zg

Rig

1 E -2 1 E -1 1 E + 0 1 E + 1 1 E + 2R i

0 .0 0

0 .0 5

0 .1 0

0 .1 5

0 .2 0

0 .2 5

u (

m s

)

g

*

-1

1 m

1 m fil . 1 m

5 m

5 m fil . 5 m

5 m fil . 1 m

1 5 m

1 5 m fil . 1 5 m

1 5 m fil . 1 m

L O W E R S O N IC

1 E -2 1 E -1 1 E + 0 1 E + 1 1 E + 2R i

1 E -3

1 E -2

1 E -1

1 E + 0

1 E + 1

KH

(m

s )-2

g

1 m

1 m fil . 1 m

5 m

5 m fil . 1 m

1 5 m

1 5 m fil. 1 m

L O W E R S O N IC

1 E -2 1 E -1 1 E + 0 1 E + 1 1 E + 2R i

-0 .2

-0 .1

0 .0

0 .1

T*

g

1 m

1 m fil . 1 m

5 m

5 m f il . 1 m

U P P E R S O N IC

1 E -2 1 E -1 1 E + 0 1 E + 1 1 E + 2R i

0 .0 0

0 .0 5

0 .1 0

0 .1 5

0 .2 0

0 .2 5

0 .3 0

0 .3 5

TK

E (

m s

)

g

2 -

2

1 m

1 m fil . 1 m

5 m

5 m fil . 5 m

5 m fil . 1 m

1 5 m

1 5 m fil. 1 5 m

1 5 m fil. 1 m

L O W E R S O N IC

Turbulent Prandtl Number (inversed)

1 E -2 1 E -1 1 E + 0 1 E + 1 1 E + 2R i

1 E -3

1 E -2

1 E -1

1 E + 0

1 E + 1

KH

/KM

g

1 m

1 m fil . 1 m

5 m

5 m fil . 1 m

1 5 m

1 5 m fil. 1 m

S F 2 0 0 1

U P P E R S O N IC

TKE from filtered and non-filtered data

1 E -2 1 E -1 1 E + 0 1 E + 1 1 E + 2R i

0 .0 0

0 .0 5

0 .1 0

0 .1 5

0 .2 0

0 .2 5

0 .3 0

0 .3 5

TK

E (

m s

)

g

2 -

2

1 m

1 m fil . 1 m

5 m

5 m fil . 5 m

5 m fil . 1 m

1 5 m

1 5 m fil. 1 5 m

1 5 m fil. 1 m

L O W E R S O N IC

222 '''2

1nvuTKE

Nocturnal pooling

Experimental setup

Observed flow patterns

Simple slope flow followed by recirculation

Slope flow followed by recirculation plus layer “thickening” at the valley bottom

Same as previous plus horizontal intrusions in stable core

No large recirculation – all compensation of mass is via intrusions at different levels

Governing Parameters

Initial Stability (stratification) - N

Slope Angle -

Heat Flux (buoyancy flux) - qo

Inversion Height - h

Combination of dimensionless parameters:

and

oq

hNB

23

po c

gQq

*

T(z)

h

q

w

Cold Pool Breakup

Low B

Cold Pool Breakup

High B

Flow dependence

Low B regime

High B regime

Bc=1000-2000

Lower values for smaller slope angles

Angle Bmin Bmax

10o 107 2497

20o 212 8198

30o 24 5564

oq

hNB

23

Inversion breakup in SLC valley

oq

hNB

23

Wheeler Farm cross-section (40o38’ N)

Wheelers Farm

40o38’ N, 111o52’ W

1350 m MSL

Wheeler Farm Site

2,410 m MSL 2,223 m MSL

Potential Temperature Profile: VTMX Starting on 10/08 (LT)

0

500

1000

1500

2000

2500

3000

3500

4000

10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0

Pot. Temperature (C)

Hei

gh

t A

GL

(m

)

6:00 PM

7:00 PM

9:00 PM

11:00 PM

1:00 AM

3:00 AM

6:00 AM

8:00 AM

9:00 AM

10:00 AM

4 pm 8th

Bouancy Flux After Sun Rise

q0 =1.4*10^-3B = 873

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

8 8.5 9 9.5 10 10.5 11

Local Time (hrs)

Bu

oy

an

cy

Flu

x

Expected Cold Pool Destruction for SLC

1000B

Summary

- Upslope flowP

2u

1u

B

rc P

c

Ra

P

B

41

~

Valley floor lower (elevation) gentle slope

higher(elevation) steep

slope

(open terrain)

Synoptic flow

UH

UF

h S

Hh

V

H HL

z

>

>

x

hsf

sinkflow

wavefronts

>

>

(x - x )>

HV

HVxx=>

L V

- Downslope flow velocity

HHcH LbU ~2

Summary

Down-slope Wind

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

275.15 275.25 275.35 275.45

JDay

Win

d S

pe

ed

[m

/s]

ENT

2

~

- Downslope flow periodicity

x U

z

h(x)

U(z,x)

UE

E

ue

eu

eu

eu

(z,x)

TS4

TS3

TS2

TS1

- Entrainment

75.005.0 RiE

Summary

- Inversion breakup mechanisms

oq

hNB

23

K

/

/ |d

V/d

z|

g

M

w2~

R i

K

/

/ |d

V/d

z|

Hw2

~

F ie ld E x p e rim en t

E q u a tio n (3 .7 )

F ie ld ex p e rim en t

E q u a tio n (3 .8 )

0 .0 1 0 .1 1 1 0 1 0 0

1 0

1

0 .1

0 .0 1

0 .0 0 1

1 0

1

0 .1

0 .0 1

0 .0 0 1

(

)(

)

34.034.0~02.0

2

g

w

M RidzVd

K

5.049.0

208.008.0~

gg

w

H RiRidzVd

K

- Eddy diffusivity

Valley floor lower (elevation) gentle slope

higher(elevation) steep

slope

(open terrain)

Synoptic flow

UH

UF

h S

Hh

V

H HL

z

>

>

x

hsf

sinkflow

wavefronts

>

>

(x - x )>

HV

HVxx=>

L V

x U

z

h(x)

U(z,x)

UE

E

ue

eu

eu

eu

(z,x)

TS4

TS3

TS2

TS1

[S]

[M]

[I]

[E]

zh

SS

SS

z

U

h

x

x

h

S

I

E

S

MS

MI

S

C

(z)

C

S

S

SF

~

K

/

/ |d

V/d

z|

g

M

w2~

R i

K

/

/ |d

V/d

z|

Hw2

~

F ie ld E x p e rim en t

E q u a tio n (3 .7 )

F ie ld ex p e rim en t

E q u a tio n (3 .8 )

0 .0 1 0 .1 1 1 0 1 0 0

1 0

1

0 .1

0 .0 1

0 .0 0 1

1 0

1

0 .1

0 .0 1

0 .0 0 1

(

)(

)

x=LV

x

z

(z)

0

FxU(x,z,t)

Cooling Slope Front

Mixing

Next Scale

Filters – ideal

f

E

unfiltered signal

“Brick-wall” filter

(hypothetical ideal filter)

Low-pass example

f

E

cut off frequency

Filters – high-pass

f

E

High-pass filter

stop band transition band

pass band

slope

cut off frequency

stop-band ripples pass-band

ripples

f

E

unfiltered signal

Filters – pass-band & stop-band

Pass-band filter

f

E

unfiltered signal

f

E

pass-band

width

cut off frequency

Stop-band filter

f

E

stop-band

width

cut off frequency

Friction velocity: filtered and non-filtered

1 E -2 1 E -1 1 E + 0 1 E + 1 1 E + 2R i

0 .0 0

0 .0 5

0 .1 0

0 .1 5

0 .2 0

0 .2 5

u (

m s

)

g

*

-1

1 m

1 m fil . 1 m

5 m

5 m fil . 5 m

5 m fil . 1 m

1 5 m

1 5 m fil . 1 5 m

1 5 m fil . 1 m

L O W E R S O N IC

4 22

* '''' nvnsu

Normalized momentum flux

1 E -2 1 E -1 1 E + 0 1 E + 1 1 E + 2R i

-2

-1

0

1

2

s'n'

/u*^

2

g

1 m

1 m fil . 1 m

5 m

5 m fil . 1 m

L O W E R S O N IC

Temperature scale

1 E -2 1 E -1 1 E + 0 1 E + 1 1 E + 2R i

-0 .2

-0 .1

0 .0

0 .1

T*

g

1 m

1 m fil . 1 m

5 m

5 m fil . 1 m

U P P E R S O N IC

**

''

u

nT

Summary

- Removing “waves” decreases momentum transport (KM) for high Rig

1 E -2 1 E -1 1 E + 0 1 E + 1 1 E + 2R i

1 E -3

1 E -2

1 E -1

1 E + 0

1 E + 1

KM

(m

s )-2

g

1 m

1 m fil . 1 m

5 m

5 m fil . 1 m

1 5 m

1 5 m fil. 1 m

L O W E R S O N IC

- Removing “waves” does not affect heat transport (KH)

1 E -2 1 E -1 1 E + 0 1 E + 1 1 E + 2R i

1 E -3

1 E -2

1 E -1

1 E + 0

1 E + 1

KH

(m

s )-2

g

1 m

1 m fil . 1 m

5 m

5 m fil . 1 m

1 5 m

1 5 m fil. 1 m

L O W E R S O N IC

Downslope flow – Normalized Eddy diffusivities

K

/

/ |d

V/d

z|

g

M

w2~

R i

K

/

/ |d

V/d

z|

Hw2

~

F ie ld E x p e rim e n t

E q u a tio n (3 .7 )

F ie ld e x p e rim e n t

E q u a tio n (3 .8 )

0 .0 1 0 .1 1 1 0 1 0 0

1 0

1

0 .1

0 .0 1

0 .0 0 1

1 0

1

0 .1

0 .0 1

0 .0 0 1

(

)(

)

34.034.0~02.0

2

g

w

M RidzVd

K

5.049.0

208.008.0~

gg

w

H RiRidzVd

K

dzVdL ws

~wsV

dzVdK w

M ~34.02

NK w

H

2

08.0