Coherent Wall Structures: Dynamics and Contribution to Turbulent Activity - Transport and Coherent Structures in Wall Turbulence - page 211

would give an ejection frequency of approximately

2

[4.2]

e −

L 2

f = f

1

e 0

in the case of a normal probability density of u . The
hypothesis that u is Gaussian implies an exponential
decrease. Similarly, if f L 1 and f L are, respectively, the
frequencies of crossings at the corresponding levels, the
above relation results in

( ) ( )

2 2

.

ln f f =− L L 2

LL 1

1

We have attempted to determine the extent to which an
expression as simple as the above one could, at
least approximately, predict the frequency of the ejections
identified by highly nonlinear schemes such as VITA.
VITA 7 is based on the local variance

()

, but the threshold

σ V t

is based on uu rather than on

σ V σ V . Therefore, it is
more appropriate to contrast the measurements to the
relation

2 2

LLuu −

( )

ln ff =

1

LL

2 σσ

1

VV

Figure 4.11 recaps the results obtained at y + =

10

and . The value of L 1 is the threshold used for

each scheme, i.e.

Re

τ =

500

for
quadrant- II , and 0.35 for VITA. We can see a
reasonable correspondence with the Gaussian distribution
for low values of L . The difference between the frequency of
the quadrant- II events and the prediction [4.2] is only 10%
where

for ul and mu ,

− 1.3 − − l LH == 1

1

. The prediction stumbles when the value of the
threshold is high - particularly for nonlinear schemes such
as VITA and quadrant detection, as might have been
expected.

L = 1.6

7 See Chapter 3.