M ay 2 00 5 Transverse velocities , intermittency and asymmetry in fully developed turbulence

Self-similar properties of turbulence, suggested by Kolmogorov [2], have been intensively studied for a long time. The theory predicted simple scaling for the longitudinal velocity increments ur = u(x+r)−u(x), namely, 〈|ur| 〉 ∼ r. It became clear, however, that there are corrections to these scalings, usually attributed to intermittency. The only exception is the so-called 4/5thKolmogorov law [3] which is exact in inertial range. According to the law, the third moment, that is the structure function, 〈u3r〉 = Buuu(r) = −4/5εr in inertial range, and this scaling has no intermittency corrections [4]. Nevertheless, more detailed study of this third order structure function proved to be useful in understanding the intermittency. It is indeed important to understand what contribution into the third moment give the tails. It is natural to assume that the main events from the core of P (ur), the PDF, mainly contribute. This is certainly the case for even order structure functions, or for moments like 〈|ur| 〉. As to the odd order moments, we note that 〈u3r〉 6 = 0, while 〈ur〉 = 0. This means that the PDF is asymmetric. However, the core of the PDF may be more or less symmetric, in which case the contribution of the tails would be substantial. And indeed, this asymmetry, described by a ramp-model, also suggest intermittency (in addition to the asymmetry) [1], [5]. Further studies showed that indeed the tails of P (ur), responsible for the intermittency, give a substantial contribution to Buuu [6]. Another way to check this connection between asymmetry and intermittency is to compare directly the PDF for positive and negative parts of ur, and we can see that the asymmetry of the PDF stretches far into the tails [6]. The transverse velocities give additional information about both asymmetry and intermittency, and this paper is devoted to their study. The transverse (vertical) component of the velocity increments vr = v(x+ r)− v(x) is also supposed to possess asymmetry, although 〈v r 〉 = 0. Assuming isotropic turbulence, the only non-vanishing correlation is (see [7], [4])