Coherent structures in wall turbulence

Short term goal: understand and control near wall processes

(relevant for drag, lift, resuspension, etc)

Long term goal: shift turbulent closure to larger scales, in order to solve

large domain accurately (atmosphere, rivers, oceans)

Smallest scale of the flow: kolmogorov scale

(in the near atmosphere about 1mm)

Largest scale of the flow: several times the boundary layer height

(in the atmosphere may go up to O(1-10 Km )

There are 6-7 orders of magnitude !

However IF, we understand how turbulent structures behave and IF

these structures truly play a major role (statistically) on momentum,

scalar and energy fluxes, mixing, etc. ...

Then we could propose low dimensional models, smart closures,

control systems

Flow visualization and sketches

Kline 1967 (near wall streaks) (log and outer layer)

(1981)

flow

flow

Acarlar and Smith, 1987, downstream of a fixed hemisphere

downstream of a low momentum

fluid ejection

Laminar flow upstream

flow

flow

Robinson 1991

Kline 1967 Flow visualization (hydrogen bubbles, flow markers)

Hairpin vortex detection: track of a strongly 3D structure on the

2D streamwise - wall normal laser sheet: Adrian et al 2000

vortex Q2 event

Shear layer

The Biot-Savart law is used to calculate the velocity

induced by vortex lines.

For a vortex line of infinite length, the induced velocity

at a point is given by:

V = 2 πΓ /d where

Γ is the strength of the vortex

d is the shortest distance from a point P to the

vortex line

For a arch-like vortex line, there is a combined

induction towards its center

(ejection of low momentum fluid u’v’ Q2 event

• Single hairpin vortices can explain the observed

features of low and high speed streaks, bursting

phenomena and lift up of structures (viscous &

buffer layer)

• What is still missing so far is the outer layer,

• Structures were observed to form bulges with

ramp-like features.

A brief summary . . .

Numerical Simulation (Zhou, Adrian et al. 1996, 1999)

isovorticity surface

Self sustaining mechanism

(see also Waleffe 1990) and

vortex alignment

Limitation : low Re

with initial perturbation

Experimental evidence of hairpin packets

in smooth wall turbulence (Adrian, Meinhart, Tomkins JFM, 2000)

flow

Instantaneous flow fields: U-Uc (convection velocity)

Vortex marker: swirling strength

Ramp packet

Q2

Q4 Q4

flow

Detection of zones of uniform

momentum associated to the

streamwise alignment of

hairpin vortex: mutual

induction of Q2 event

flow

Vortex identification Okubo-Weiss parameter Swirling Strength analysis

zu

xw

s

zw

xu

n

sn

S

S

where

SSS

:

222

22

zSQ

z

w

x

wz

u

x

u

u

From the local velocity

gradient tensor

Imaginary eigenvalues

cicrc i

We select the region

where

0ciSee also Chong & Perry, 1990

Jeong and Hussain 1995

Numerical simulation Adrian, PoF 2008 multimedia appendix

Flow visualization,

flow

First snow PIV

visualization of

coherent

structures in the ASL

Can I use the

snowflake as

tracers or not

Far wake features : wake meandering

Rotor

Kang and Sotiropoulos 2014, Howard et al 2015b

large scale oscillation of the far wake

Statistical Signature

1)Relevance

2)Physical mechanisms

3)Connection with quadrant analysis (Lu &

Willmart, 1973, Wallace 1972, Nezu &

Nakagava 1977)

4)Vortex identification in 2D and 3D

5)Zones of uniform momentum

6)Consistency with observed resuspension

events (strong correlation between c’w’ and u’w’ events)

Besides instantaneous realizations…

Is it possible to obtain some quantitative

information about turbulent structures ?

2 point correlation

vu, ji,for

y'σyσ

',,ρ

d)(normalize

t coefficienn correlatio

', ,',,

n tensorcorrelatiopoint 2

ji

ij

*

yyrR

yrxuyxuyyrR

xij

xjixij

Linear stochastic estimate

Estimate of the flow field

Statistically conditioned

To the realization of a

known event :

1) II quadrant (u < 0, v > 0)

2) IV quadrant (u > 0, v < 0)

3) Vortex

identified by the swirling strength :

complex part of the eigenvalue of

the local velocity gradient tensor.

See also Proper

Orthogonal

Decomposition

(Holmes & Lumley )

A B

Comparison A B center

(reduction of the streamwise lengthscale:

lost of coherence within the structures

of the packets)

(see also Krogstad e Antonia 1994 rough wall)

Two point correlation

streamwise velocity fluctuation

Comparison A B center

B

A

Linear Stochastic Estimate:

Question:

What is the average flow field statistically conditioned to the realization of a

vortex with a spanwise axe (identified as the signature of the hairpin vortex

On the laser sheet)?

The best (linear) estimate is given by

Adrian, Moin & Moser, 1987

Adrian 1988, Christensen 2000

Note:

Information about conditioned

probabilistic variables are obtained from

unconditioned statistical moments

y,rxu y'x,λ'xu xλ

),(xcon

xλxλ xλ

'xu xλ xλL xλ'xu

xj

j

jj

yx

Linear stochastic

Estimate :

known event

assumed at a fixed y’

Flow field obtained from a statistical

analysis (conditioned to the realization of

a E event) E

E

See Christensen 2000

Kim and Adrian 1999

Spanwise alignment of hairpin structures leading to

long coherent regions of uniform momentum Kim & Adrian 1999

VLSM Contribution :

turbulent kinetic energy and Reynolds stresses

Guala et al. 06

Pipe : Guala et al, 06

channel:

• Pipe flow

• Turbulent Boundary layers

• channel flow

Turb. B. layer: Balakumar, (2007)

Net force exerted by Reynold stress in the mean momentum equation

• Large scale motion participate significantly to the Reynolds stress, thus contribute not only to TKE but also to TKE production.

• In terms of momentum balance, close to the wall, VLSM push the flow forward, while smaller scales slow down the flow.

• Such features are observed for turbulent pipe, channel and boundary layers flows

A brief summary . . .

Marusic & Hutchins 2008

Atmospheric Surface Layer

Reτ=O(106)

Hutchins & Marusic 2007

Large scale influence on the near

Wall turbulence intensity:

Amplitude modulation

Note that in different research field

some type of very large scale

motions are addressed with

different names

e.g. streamwise rolls (atmospheric

science) or secondary current

(river hydraulics)

Low Re

High Re

High Re

Low Re

VLSM : A visual inspection

Lekakis 88, Metzger et al. 07; Guala, Metzger, McKeon 08

PIPE FLOW ATMOSPHERIC

SURFACE LAYER (ASL)

Chacin & Cantwell 2000 (Turb. Boundary Layer)

Soria 94

Chong & Perry 90

Luthi 2005

PTV isotropic turbulence

A different view

Coherent structures vs vortices Open questions:

1) How spanwise mean vorticity relates to streamwise fluctuating vorticity ?

2) How vortex stretching is affected by a non zero mean strain

( and perhaps also mean vorticity) ?

3) Do they both scale with Kolmogorov (core) and the integral lengthscale ?

4) Are they more or less stable as compared to worms in isotropic 3D turbulence ?

Other Questions

1) How roughness in general can perturb self organization, how about complex

terrain ?

2) What are the relevant scales for coherent structures (inner, outer)?

3) Can we really define a coherent structure

4) Can we describe coherent structures evolution in

unambiguous quantitative (not handwavy) terms ?

5) How VLSM rtelate to hairpin packets (is it Reynolds dependent)?

6) why near wall peak can be affected by outer layer structures?

7) which terms of which equation are responsible?

8) can we go beyond geometrical characteristics (exp) and vorticity contour (num) ?