Coherent Wall Structures: Dynamics and Contribution to Turbulent Activity - Transport and Coherent Structures in Wall Turbulence - page 210

the wall than that observed with the quadrant- II and u

l
methods. Additionally, the maximum frequency in the inner
layer is 0.025 for QII , but only half as great for VITA. It
should be noted that VITA is not directly sensitive to
ejections, but to layers of significant instantaneous shear,
resulting from (or giving rise to) these events. This does not,
in itself, constitute an explanation, but highlights the
difference between the different identification methods.

−

The frequency of the events detected depends on the
threshold used. The frequency of the zero crossings of
turbulent signals in a wall flow is near to its Gaussian value
[SRE 93, TAR 99]. For a Gaussian signal, the Taylor λ T and

the Liepmann A scales are equal:

u

2

1

[4.1]

λ = = A i =

T

2 π f

( )

2

du dt

0

where f 0 is the frequency of zero crossings of the temporal
signal 6 [RIC 45]. The reasonable correspondence that we
observe between

λ T and A both for the zero crossings of u
and v , which are, nevertheless, profoundly non-Gaussian,
probably arises from the central limit theorem [KAI 93].
Using the u -level scheme to detect a signal whose detection
function is

⎧ ⎪

1, i f L uut L u << ( )

Dt () =

1 2

⎨
⎪ ⎩

0, else.

6 These concepts can easily be generalized to apply to spatial signals.
Thus, we can define directional zero crossings in the streamwise and
spanwise directions in a homogeneous plane.