Stratified turbulent flows in Ocean and Atmosphere : Processes, observations and CFD

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Stratified turbulent flows in Ocean and
Atmosphere Processes, observations and CFD
Laboratoire de Sondages Electromagnétiques de
lEnvironnement Terrestre (Université de Toulon
et du Var)
Philippe Fraunié Sabeur BERRABAA Jose Manuel
Redondo et al
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Observations
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Basic processes
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KH instability
Kelvin-Helmholtz instability Richter (1969)
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Holmboe instability

• Ri gt ¼
• Su gt 2 Sb
• Possibility of Holmboe instability

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Holmboe instability
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Richardson number
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Global Richardson number
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Turbulence scales
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Measurements in Atmosphere

• Profiles of temperature mesured by baloons
  weakly and srongly stratified layers (Dalaudier
  et al., 1994)

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Measurements in Oceans

• Temperature profiles in Malta sea Contribution
  of K.-H. instabilities to mixed layers (Woods,
  1969)
• Korotayev et Panteleyev (1977), Indian and
  Pacific oceans, Alford et Pinkel (2000)
  California

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Measurements in Ocean

• Temperature profiles in Japan sea Contribution
  of internal waves to mixed layers (Navrotsky,
  1999)

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Laboratory Experiments the layering effect

• Generation of turbulence (grids) in a stratified
  flow at rest

• Interaction between
• turbulence and
• stratification

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Computational Fluid Dynamics

• Focused on Kelvin-Helmholtz instability (Palmer
  et al., 1996)
• Only few numerical experiments concerning
  internal waves (Koudella et Staquet, 1996
  Bouruet-Aubertot et al., 2001)

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Navier-Stokes solver

• Based on JETLES DNS Code (Versico, Orlandi)
  adapted to stratified flows
• cartésian coodinates
• sreamwise non périodic bc (Ox)
• transport equations for salinity and
  temperature)
• LES
• Smagorinsky subgrid model

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LES equations

• Continuity equation
• Momentum equations

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Transport of scalar fields

• Temperature and Salinity
• State Equation

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LES numerical code

• Continuity equation
• Momentum equations

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Turbulence closure

• Smagorinsky model

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Discretization

• Time marching three steps Runge-Kutta scheme,
  third order accurate
• Spacial discretization second order centered
  finite differences

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Algorithm
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Computational domain
Taille du domaine 2 lt Lx lt 4 m Ly 0.1 m
0.1 lt Lz lt 0.2 m
Taille de la barre
Maillage dx 3.9 mm dy 3.1 mm dz 1
mm
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Boundary conditions
En surface et au fond
A la frontière droite
A la frontière gauche
avec
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Homogeneous flow Von Karman streets
Champs diso-vitesses horizontales,
diso-vitesses verticales et diso-vorticités
daxe (Oy)
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3D structures low Reynlods number
Surfaces diso-vorticité
- en rouge et bleu, les surfaces
- en vert et noir, les surfaces
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3D structures larger Reynolds number
Surfaces diso-vorticité
- en rouge et bleu, les surfaces
- en vert et noir, les surfaces
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2D du computational domain
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Turbulence collapse  (1)
Champs diso-vorticité daxe (Oy)
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Turbulence collapse  (2)
Transformée de Fourier de lévolution temporelle
des composantes de vitesse dans le sillage
proche - Diminution du nombre de Strouhal
avec
laugmentation de la stratification
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Turbulence collapse (3)  physical process 

• Temporal evolution of the near wake width for
  Richardson numbers less than 1/4
• the wake grows following a t1/3 law as for
  homogeneous flow
• coolapse occurs when the wake width is maximum
• the wake widh decreases up to an constant value

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Physical collapse (4)
ooo Ri0 0.03 ooo Ri0 0.039
D après Lin et al. (1992)
Lépaisseur du sillage proche atteint une valeur
maximale pour NBVt ? 2 ? Ri0 lt 1/9
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Physical collapse (5)

• NBVt (maximum wake width) depends on Ri0 (Xu et
  al., 1995)
• Ri0 lt 1/9 NBVt varies in the range 1.5 - 2.5
• 1/9 lt Ri0 lt 1/4 NBVt varies between 3 and 5
• Ri0 gt 1/4 the wake width is constant

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Physical collapse (6)

• La taille de la zone perturbée dans le cas
  
• névolue pas contrairement au cas

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Gravity internal wave weak initial
stratification (1)

• Iso-density fields for différent Richardson
  numbers
• Ondulation occurs at the starting point

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Gravity internal wave weak initial
stratification (2)

• Profiles of local Richardson number
• Waves occur for Ri gt 1 stratification dominates
  turbulence

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Gravity internal wave strong initial
stratification (1)
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Gravity internal wave strong initial
stratification (2)

• Iso-density and diso-vorticity - transverse axis
  (Oy)
• ondulatory motion imposed by internal waves
• Remember Lee waves (Atkinson)

?
?
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Mixing Processes in the near wake weak initial
stratification (1)

• Iso-vorticity - transverse axis (Oy) in the near
  wake
• Shear instability

overturning
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Mixing Processes in the near wake weak initial
stratification (2)

• Overturning time evolution of two density
  surfaces
• Roll up

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Mixing Processes in the near wake weak initial
stratification (3)
Local convective instability
Unstable situation
Overturning
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Mixing Processes in the near wake strong
initial stratification (1)

• Time evolution of two density surfaces
• Breaking internal waves

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Mixing Processes in the far wake weak initial
stratification
Sillage lointain

• Iso-density field in the far wake
• Mushroom type structures collapse due to
  stratification

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Mixing Processes in the far wake strong initial
stratification (1)
Sillage lointain

• Iso-density field in the far wake
• Mixed fluid inside the elliptic zones

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Mixing Processes in the far wake strong initial
stratification (2)

• Iso-density fields at different times
• interaction betyween shifted internal waves

Breaking
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Layering effect computational domain
Succession de passages dune ou de plusieurs
barres
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 sheets layers 

• Density profiles for weak and strong initial
  stratification
• Layering effect weakly depends on initial
  stratification

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Strongly stratified layers

• ?

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Stratified layers of another type

• Unstable stratification
• Convergence of density isolines

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Successive wakes

• Density profiles and gradients after each
  cylinder tow
• Sratification increases after each towing

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Successive wakes

• Time evolution of the density gradient
• The maximum value increases
• Damped oscillations

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Infinitesimal perturbation (1)
Champ de densité après trois passages de la
perturbation
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Successive infinitesimal perturbation (2)

• Density profiles and gradients after 4 tows
• Growth of the perturbation after each towing

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Time evolution of the density and velocity
gradients

• Oscillation is damped
• The stratification is evolving following three
  steps
• The layering increase is due to the initial state
  before new perturbation

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Vertical cylinder computational domain
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Laboratory experiments

• Density profile
• Towed vertical cylinder

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Vertical cylinder

• zig-zag instability
• Layering effect

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Conclusion

• Caractéristics of stratified flows
• turbulence collapse
• internal waves occuring
• Mixing processes
• overturning collapse
• breaking internal waves
• Layering effect
• sheets layers
• reorganizing layers

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Perspectives

• CFD improvements
• boundary conditions (open problem)
• long time computation statistics and budgets
• subgrid models (Babiano et al)

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Energy spectrum
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Velocity components and gradients
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Processus de mélange dans le sillage proche
zones mélangées

• Evolution temporelle dun profil vertical de
  densité dans les cas de faible et de forte
  stratification