Conditional statistics of velocity fluctuations in turbulence

✍ Scribed by A. Naert; B. Castaing; B. Chabaud; B. Hébral; J. Peinke

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 461 KB
• Volume: 113
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(97)00196-6

✦ Synopsis

Using experimental data recorded in a low temperature helium jet, we have studied the statistics of velocity increments: Vr (x) = v(x +r) -v(x) conditioned on a "rate of energy transfer" anzatz, er : P(vr ]er). For a fixed value ofer, the histograms of Vr are found Gaussian at all scale, i.e. there is no intermittency at fixed er. Intermittency is caused by the fluctuations of the latter quantity. If P (Vr ]er) is Gaussian, it is characterized uniquely by its variance ~r 2 = (V2rler) -(vr ]er)2 and mean vo = (vr let). We show that a is related to er by a power law, valid at any scale, and that vo is close to logarithmic in er in the inertial range. With these two relationships, the statistics of vr at fixed er are completely determined by er. Therefore, the relevant quantity to describe intermittency is the transfer rate of energy, acting as a driving process for the velocity fluctuations.