Coherent structures in wall...
Transcript of Coherent structures in wall...
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 IFthese 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
Acarlar and Smith, 1987, downstream of a fixed hemisphere
downstream of a low momentum fluid ejection
Laminar flow upstream
Hairpin vortex detection: track of a strongly 3D structure on the 2D streamwise - wall normal laser sheet: Adrian et al 2000
vortexQ2 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 vortexd is the shortest distance from a point P to the vortex lineFor 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 surfaceSelf 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)
Instantaneous flow fields: U-Uc (convection velocity) Vortex marker: swirling strength
Ramp packet
Q2
Q4Q4
Detection of zones of uniform momentum associated to the streamwise alignment of hairpin vortex: mutual induction of Q2 event
Vortex identificationOkubo-Weiss parameter Swirling Strength analysis
zu
xw
s
zw
xu
n
sn
SSwhere
SSS
:
222
22zSQ
zw
xw
zu
xu
u
From the local velocity gradient tensor
Imaginary eigenvalues
cicrc i
We select the region where
0ciSee also Chong & Perry, 1990Jeong and Hussain 1995
Statistical Signature
1)Relevance 2)Physical mechanisms3)Connection with quadrant analysis (Lu &
Willmart, 1973, Wallace 1972, Nezu & Nakagava 1977)
4)Vortex identification in 2D and 3D5)Zones of uniform momentum6)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)(normalizet coefficienn correlatio
', ,',,
n tensorcorrelatiopoint 2
jiij
*
yyrR
yrxuyxuyyrR
xij
xjixij
Linear stochastic estimate
Estimate of the flow fieldStatistically conditionedTo 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 )
AB
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)
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 vortexOn the laser sheet)?
The best (linear) estimate is given by
Adrian, Moin & Moser, 1987 Adrian 1988, Christensen 2000Note: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
jjj
yx
Linear stochasticEstimate :
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
Spanwise alignment of hairpin structures leading to long coherent regions of uniform momentum Kim & Adrian 1999
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 . . .
Hutchins & Marusic 2007
Large scale influence on the near Wall turbulence intensity: Amplitude modulation
Note that in different research fieldsome type of very large scale motions are addressed with different namese.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 94Chong & Perry 90
Luthi 2005PTV isotropic turbulence
A different view
Coherent structures vs vorticesOpen 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 Questions1) 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) ?