Observation and simulation of flow in vegetation canopies

Roger H. ShawUniversity of California, Davis

•Kinetic energy spectral densities that are strongly peaked•Strong correlations between streamwise and vertical velocities•Large velocity skewness (Sku>0; Skw<0)•Transport dominated by organized structures•Larger contributions from sweep motions than ejections

Canopy turbulence

“We will understand the movement of the stars long before we understand canopy turbulence”

Galileo Galilei

Time traces of velocity components

Z=2.4h

Z=0.9h

Scalar ‘ramps’ correlated through the depth of the canopy show wholesale ‘flushing’ of

the canopy airspace by large scale gusts.

Scalar

Vertical velocity

Streamwise velocity

Turbulent kinetic energy budget determined from LES

Large-eddy simulation of surfaceand canopy layers

•Based on NCAR code developed by Moeng (1984)•Modified to include drag effects on both the resolved-scale flow and SGS motions•An experimental tool and framework for investigation of observed phenomena

2

Resolved- and subgrid-scales

in large-eddy simulation (LES)

W av en u m b er

Ene

rgy

spec

tral

den

sity

x

R eso lv ed -sca les

S u b g rid -sca le s

LES resolved- and subgrid-scales

X = 96 grids

Z=30grids

A sketch of simulated domain

canopy( green region ) = 1/3 vertical domainshear dominant ( neutral )

F ig u re 1

canopy

• periodic horizontal boundary conditions

• frictionless lid at upper boundary (no flux)

• uniform force to drive the flow

• scalar source through depth of canopy

Canopy specification:

•Represented at each grid point by element area density a (m2/m3)•Area density horizontally uniform but a(z)•Canopy elements rigid•Volume occupied by solid elements is considered to be negligible

Static pressure perturbation

2

Resolved- subgrid- and wake-scales

Mean flow KE

Resolved-scale TKE

Subgrid-scale TKE

Internal energy

1 2 3

Mean flow KE

Resolved-scale TKE

Subgrid-scale TKE

Wake-scale TKE

Internal energy

Viscous drag

Form drag

1 2 3

4 5 6 7

8 9 10

Drag parameterization:

i d sf iF C C au V

1.328 2.326sfC

RR

Blasius solution for flow parallel to a flat plate:

inertialcascade

formdrag

SGS energy pool

inertialcascade

formdrag

SGS energy wake energyw

sgs

ii ij m fd sf

i j i i

ue e eu K

t x x x x

Subgrid-scale energy equation

where

3/ 2 8 8

; ;3 3fd d sf sf

c eC aVe C aVe

Wake-scale energy equation

3 8

3w w w

i d d m wi i i

e e eu C aV C aVe K

t x x x

where

3/ 2w

wf

c e

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

N o rm a lize d T K E e / u *2

0

1

2

3

Nor

mal

ized

hei

ght z

/h

W a k e

S u b g r id

T o ta l

R e s .

1 e -0 0 6 1 e -0 0 5 0 .0 0 0 1 0 .0 0 1 0 .0 1 0 .1 1

N o rm a lize d d if f u s iv ity K / h u *

0

1

2

3

Nor

mal

ized

hei

ght z

/h

W a k e

S u b g rid

R e s .

T o ta l

- 2 - 1 0 1 2 3

S G S k in e tic e n e rg y b u d g e t

0

1

2

3

Nor

mal

ized

hei

ght z

/h R e so lv e d sh e a r

D iss ip a tio n

D if f u s io n

W a k e e f f ec t

•Additional variable ew to represent kinetic energy associated with wake motions•Dissipation of ew controlled by dimension of canopy elements

•Additional variable ew to represent kinetic energy associated with wake motions•Dissipation of ew controlled by dimension of canopy elements•Rate of conversion of kinetic energy from resolved scales to wake scales is large•Effective diffusivity of wake-scale turbulence can be ignored

•Additional variable ew to represent kinetic energy associated with wake motions•Dissipation of ew controlled by dimension of canopy elements•Rate of conversion of kinetic energy from resolved scales to wake scales is large•Effective diffusivity of wake-scale turbulence can be ignored•Important to include the conversion of resolved and SGS energy to wake-scale kinetic energy

•Additional variable ew to represent kinetic energy associated with wake motions•Dissipation of ew controlled by dimension of canopy elements•Rate of conversion of kinetic energy from resolved scales to wake scales is large•Effective diffusivity of wake-scale turbulence can be ignored•Important to include the conversion of resolved and SGS energy to wake-scale kinetic energy•Viscous drag and direct dissipation in viscous boundary layers of leaves is of little consequence

0 1 2 3 4 5 6 7 8 9

x /h

0

1

2

3

4

5

6

7

8

9

y/h

P e rtu rb a tio n sca la r co n c en tra tio n c /c*

0 1 2 3 4 5 6 7 8 90

1

2

3

z/h

N o rm a liz e d sc a la r c o n c e n tra tio n

0 1 2 3 4 5 6 7 8 90

1

2

3

z/h

N o rm a liz e d p re ssu re

0 1 2 3 4 5 6 7 8 9

x /h

0

1

2

3

z/h

N o rm a liz e d s tre a m w ise v e lo c ity p e rtu rb a tio n

Conditional sampling of LES output and composite averaging of flow structures

1. Pressure signal at z/h=1 used as detection function2. Structures aligned according to peak in pressure signal3. Composite averages of various elements of the structures

Approximately 1,600 events extracted from one 30-minutetime series (but not all independent)

- 4 - 3 - 2 - 1 0 1 2 3 4

S tream w ise p o s itio n x /h

1

2

3

Hei

ght z

/h

P ertu rb a tio n s ta tic p re ssu re

- 4 - 3 - 2 - 1 0 1 2 3 4

S tream w ise p o s itio n x /h

0

1

2

3

Hei

ght z

/h

S tream w ise v e lo c ity p e rtu rb a tio n

- 4 - 3 - 2 - 1 0 1 2 3 4

S tream w ise p o s itio n x /h

1

2

3

Hei

ght z

/h

V ertica l v e lo c ity

- 4 - 3 - 2 - 1 0 1 2 3 4

S tream w ise p o s itio n x /h

1

2

3

Hei

ght z

/h

S ca la r co n cen tra tio n p e rtu rb a tio n

270 seconds (17 frames)

-4 -2 0 2 4

-2

0

2

-4 -2 0 2 4

-2

0

2

y/h

x/h

0

1

2

-4

-2

0

2

4

-5

-4

-3

-2

-1

0

1

2

3

4

XY

Z

x

0

1

2

-4

-2

0

2

4

-5

-4

-3

-2

-1

0

1

2

3

4

XY

Z

y

0

1

2

-2

0

2

4

-4

-3

-2

-1

0

1

2

3

4

XY

Z

z

0

1

2

-4

-2

0

2

4

-2-1

01

2

X

Y

Z

0

1

2

-4

-2

0

2

4

-2-1012

X

Y

Z

0

1

2

-4

-2

0

2

4

-2

-1

0

1

2

X

Y Z

The structure of the large-eddy motion as a solution to the eigenvalue problem:

Where ij is the spectral density tensori is the eigenvector is the associated eigenvalue

*, , , , , , , ,j iij x y x y x y x yD

k k z z k k z k k k k z

u -v e lo c ity

w -v e lo c ity

sca la r

- 8 - 6 - 4 - 2 0 2 4 6 8

rx /h

00.51

1.52

z/h

- 8 - 6 - 4 - 2 0 2 4 6 8

rx /h

00.51

1.52

z/h

- 8 - 6 - 4 - 2 0 2 4 6 8

rx /h

00.51

1.52

z/h