To: Ray Fonck, Roger Durst, Steve Paul, Norton Bretz, Jim Callen, 
	Mike Zarnstorff, Kevin McGuire
From: Greg Hammett
Date:  2/10/93

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Before reading on, take a look at the accompaning "statistical
visualization" of BES turbulence measurements.  Ignore the "intermittent"
color plot and just concentrate on the other color plot and the two black
and white plots.

What is different between these plots and the old ones I sent you a couple
of months ago?  In particular, why are the eddies now smaller than they
used to be?

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Before giving the answer, I'll point out that the B&W contour option is
just another option in the NCSA ximage package (in case you want to try
it).  The answer is that the underlying density data n(x,y) for these plots
is identical to the old plots I sent you a couple of months ago.  You can
even overlay the various plots.  The only difference between the two B&W
plots is that one has 15 contour levels and the other has 7 levels, and the
new color plots uses a new color palette I put together.

The way our brain percieves contour plots is not necessarily
straightforward.  In the case of the B&W contours, our brain tends to focus
on the shortest scale eddies displayed or where the contours are closest
together, and ignores the fact that there are some very long contour paths
which enclose several eddies, unless the short eddy scales are suppressed
by plotting fewer contours on the page.

Likewise, there seems to be a difference between the way our brain
percieves the B&W vs. various type of color contours.  Our eye tends to
focus on the typical "small" eddies in the B&W plot (with 15 levels) and
concludes "Oh, the average eddy is about 2 cm long radially, consistent
with the BES correlation measurements".  However, when our eye looks at the
old color contours, it instead focusses just on "red" regions vs. "blue"
regions and concludes "Wow, some of these blue or red regions are extremely
long in the radial direction, much longer than the the BES measured radial
correlation.  Something doesn't seem right."

The problem is that with the old color plots our eye focusses on just red
vs.  blue and ignores the finer scale variations in color which occur on a
shorter scale (despite the fact that I tried to emphasize the shorter
scales in the color plots by putting 16 bands of alternating light and dark
hues into the color palette), while in the B&W plots our eye ignores the
few long contours which surround several eddies of the same polarity.  Both
pictures are "correct" but we need to be aware of the differences in our
perception when we look at them.  

To try to merge the advantages of the color plots with the black&white
plots, I developed a new color palette (I tried lots of the standard
existing palettes, and finally had to write a fortran program to cook up my
own).  The new palette has more of a range of colors (my eye sees 5 main
colors: blue, green, yellow, orange, and a hot pink) to allow our eys to
see more color contrasts (the old palette looked mostly just blue or
orange-red).  It also explictly overlays 15 black bands (instead of the old
15 bands of slightly darker hues) to really emphasize the finer,
shorter-scale, details.  I like these new color plots.  They are a bit
jazzier in color, still convey the excitement and importance of this
research to the novice, while providing the extra clues an expert might
appreciate (such as whether or a certain contour encloses a hill or a
valley).

Finally, I have checked that the code is working properly by calculating
the 2-point correlation function directly from the "simulated data" by
summing over lots of points separated by a given distance.  This agrees to
within a few percent the 2-point correlation function found by Fourier
transforming the power spectra.  The agreement won't be exact because of
the sample size.  Compared to the 2 cm correlation length, the 40 cm by 40
cm box contains about 20*20=400 independent sample volumes, so roughly
1/sqrt(400) = 5% fluctuations are to be expected.