Presentacin de PowerPoint

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MULTIFRACTAL CHARACTERIZATION OF TURBULENT EDDY
CASCADES José Manuel REDONDO () Universitat
Politècnica de Catalunya, Barcelona, Spain.


Turbulence Course


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• Introduction
• Experiments
• Cloud observations
• Atmospheric Turbulence
• Simulations LES/KS
• Multi-Fractal Dimension
• Intermittency
• Discussion Conclusions

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Introduction
? The Atmospheric turbulence behaviour is
strongly affected by gravitational forces due to
stratification and may be quantified by the
Richardson number (Ri) and by the fractal
dimension (D1). ? It can be also reflected in
satellite images providing more aspects of these
phenomena (D2 i D3). ?We will compare
micrometeorological data and satellite images and
provide some conditional statistics of the
relationship D(Ri). ? The data at
microatmospherical scalecomess from the
experimental measurements obtained in the
campaign SABLES-98 (period September 10 to 28 of
1998) at the north-west high Iberian Peninsula
plateau (Valladolid CIBA). ? Macroatmospherical
information comes from Meteosat images in Visible
and Infrared channels using fractal geometry. ?
In both cases local meteorological conditions
have been taken into account.
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Small Scale Turbulence
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Convective Rayleigh Taylor Mixing
Experiments in a Perspex tank H500mm Lx400mm Ly
200mm Linden, Redondo Youngs (1994) J. Fluid
Mech. 265 Dalziel, Linden Youngs (1997) 6th
IWPCTM
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Cloud Analysis
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Cloud Fractal Analysis
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Cloud Fractal Analysis
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Important parameters to consider in Rayleigh
Taylor Instability study

• The Atwood Number, A
• The width of the mixing zone, d
• The non-dimensional time, t-t0
• The Fractal Dimension

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2D LES SGS Smagorinsky Lilly Unsteady,
1st-Order, Implicit Boussinesq model 256²
elements mesh Atwood 5x10-²
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2D LES of the RT Front
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max
Velocity Magnitude
Volume of Fluid
Vorticity Magnitude
00,33
01
-10684
min
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Experimental results vs LES
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MULTI- FRACTAL DIMENSION ANALYSIS
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D
? 4.5 ? 4.0 ? 3.5 ? 3.0 ? 2.5 ? 2.0
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Fractal dimension by scalar valuesOverall
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Volume of fluid and Vorticity
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Fractal dimension by scalar valuesMushroom
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Fractal Dimension for the Overall, Mushroom and
Front
D
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Fractal Dimension for the Experiments
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3D Simulation
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Experimental Visualizations

• LIF Fluoresceine Visualization Elevation and
  Plane Views

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Cloud Fractal Analysis
In nature we have the combination of different
sort of clouds that do not exactly follow the
theoretical profile.
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Cloud Fractal Analysis
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Cloud Fractal Analysis
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Results (See description of SABLES-98, Carlos
Yagüe)
- Between the 10th to 13th of September of
1998 . Unstable situation (without rains). . In
agreement with the synoptic situation and the
type of clouds present those days.
- Between the 22nd and 28th of September .
Intermediate situation, depending of the day.
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Cloud Results
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Results
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Multi fractal Results
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Results
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• Stratification causes strong vertical anisotropy!
• Redondo(1990)

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Discussion and Conclusions
In the case of a stable system, a non
stratified fluid has a limit on the maximum
fractal dimension of D12.4 (Villermaux and
Inocenti 1999) with a power law dependence with
Ri. In this situation mixing prevails and the
vertical scales of motion can not be suppressed.
The fluid loses the isotropy and modifies its
geometrical self-similarity when Ri increases.
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Discussion and Conclusions
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Discussion and Conclusions
Using fractal geometry as well, we can
establish now a theoretical baseline pattern for
the turbulence behaviour that is reflected in
satellite images we can obtain a cloud
classification relating D3 and the sum (integral)
of the different fractal dimensions D2 for
different levels of cloud intensity (or
temperature related to the height). Both
micro and macro scales in the atmosphere seem
connected, especially in cases of stable
stratification. The relevant parameter is the
Richardson number (flux or gradient) measured at
the ABL low level. The correlation between
the Ri and the fractal dimension detected from IR
or Visible images is good i.e. Stratum
corresponds to high Ri values as well as low
fractal dimension values D3 for the whole range
of cloud intensities and also for the integrated
D2(i) multifractal signature.
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Using multi-fractal geometry we can also
establish certain regions of higher local
activity used to establish the geometry of the
turbulence mixing A taxonomy of changes in the
equilibrium (or not) cascade may lead to more
physically realistic (and understandable) models
to paramerize sub-grid scalinga Care has to be
taken when interpreting the direct 3D Kolmogorov
cascade and the Inverse 2D Kraichnan Cascade. As
an example of Convective RT flow Fractal
dimension anlaysis probed that the mixing occurs
mainly at the sides of the blobs and that in the
front there is no mixing The fractal dimension
differs for the various scalar fields even when
there is presence of similar topology and
structure. These differences seem to be related
with a complex system of cascades of direct and
inverse vorticity. The range of scales is very
active and complex and in the future the
application of Fractal Analysis can be helpful to
decompose and analyse these scales. A three
dimensional simulation (even better if DNS is
used) analyzed with Fractal Analysis may give a
better approach to the experimental results.