Conditional statistics of velocity fluctuations in turbulence

• Published in: Physica. D Vol. 113; no. 1; pp. 73 - 78
• Main Authors: Naert, A., Castaing, B., Chabaud, B., Hébral, B., Peinke, J.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-02-1998; Elsevier
• Subjects: Physics
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/S0167-2789(97)00196-6

Using experimental data recorded in a low temperature helium jet, we have studied the statistics of velocity increments:
v
r
(
x) =
v(
x+
r) −
v(
x) conditioned on a “rate of energy transfer” anzatz,
e
r
:
P(
v
r
|
e
r
). For a fixed value of
e
r
, the histograms of
v
r
are found Gaussian at all scale, i.e. there is no intermittency at fixed
e
r
. Intermittency is caused by the fluctuations of the latter quantity. If
P(
v
r
|
e
r
) is Gaussian, it is characterized uniquely by its variance
σ
2 = 〈
v
r
2|
e
r
〉 − 〈
v
r
|
e
r
〉
2 and mean
v
0 = 〈
v
r
|
e
r
〉. We show that σ is related to
e
r
by a power law, valid at any scale, and that
v
0 is close to logarithmic in
e
r
in the inertial range. With these two relationship, the statistics of
v
r
at fixed
e
r
are completely determined by
e
r
. Therefore, the relevant quantity to describe intermittency is the transfer rate of energy, acting as a driving process for the velocity fluctuations.