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   -> Volume 5, Issue 5

Thesis: A study of coherent structures using Wavelet analysis
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Author Message (Jon Harald Kaspersen)

PostPosted: Wed Dec 04, 2002 9:53 am    
Subject: Thesis: A study of coherent structures using Wavelet analysis
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Thesis: A study of coherent structures using Wavelet analysis

My Ph.d thesis is available in postscipt format. It can be obtaind by
sending me an e-mail. My e-mail adress is :
The comlete thesis with figures occupies about 15Mb.

A study of coherent structures using Wavelet analysis

A new algorithm to detect coherent structures based on Wavelet
transformations has been proposed and discussed. Data from ZPG flows
and DNS channel flow have been used to investigate the performance of
the new detection procedure. Results from the new algorithm have also
been compared with results from existing algorithms. The general
performance of the new Wavelet detection algorithm has been found to
be very good. The advantage of the new detection scheme is that it
does not require any predefined threshold or integration time. The
time between the events and their duration are found to be in good
agreement with these obtained from the other detection methods
investigated. Reynolds number dependency was found when the time
between events were scaled with inner or outer variables. A better
collapse of the data was found when the results were scaled with mixed
variables. The duration of events was then found to be independent of
Reynolds number, and to follow the Kolmogorov length scale variation
in the logarithmic part of the boundary layer.

The scaleograms resulting from the Wavelet transform show clearly that
coherent structures exist in turbulent flows. These structures are
shown to contribute considerably to the shear stresses. The
contribution from the organized motion to the normal stresses close to
the wall appears to be considerably smaller. The DNS channel flow
seems to be more organized than the ZPG flows. A coherent
contribution to the shear stress of about 60\% was found in parts of
the DNS channel flow compared to 45\% in the boundary layer.

The topology of the ZPG flows has been studied using a multiple hot
wire arrangement. Conditionally averaged streamlines based on
detections from the Wavelet method are presented. It is shown that
the shear stresses associated with these flow patterns are rather
insensitive to the detection scale chosen. Contour plots of
conditional large scale vorticity and strain show that the coherent
structures produce large amounts of both vorticity and strain in the
vicinity of the detection point. As expected this is also the case
for the conditional shear stress.

Conditional vector and streamline plots revealed that for the strong
events, an ejection is always followed by a sweep. The streamwise
distance from an ejection to a sweep was found to be Reynolds number
dependent. At high Reynolds numbers this distance was found to be
$frac{U_{c}Delta t}{delta} approx 1$.

Correlations between conditionally averaged $u$ velocities at
$frac{y}{delta} approx 0.2$ and friction velocity measured with a
single hot wire close to the wall, showed that the streamwise extent
of the wall events scaled with outer variables. The structures
inclination angle with respect to the horizontal was found to be
slightly Reynolds number dependent. An average inclination angle of
about $15^o$ was found.

Jon Harald Kaspersen

Dr. Jon Harald Kaspersen
Dept. Applied Mechanics, Thermo- and Fluiddynamics
The Norwegian Institute of Technology
University of Trondheim
7034 Trondheim, Norway

e-mail :
Phone : +47 73 59 37 08
Fax : +47 73 59 37 13
All times are GMT + 1 Hour
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