Abstracts - KTH Mechanics

Anisotropic fluctuations in a turbulent boundary layer
B. Jacob ∗ , C. M. Casciola † , A. Talamelli ‡ and P. H. Alfredsson §
The aim of the present work is an experimental investigation of both large- and
small-scale turbulent properties of the boundary layer over a flat plate at Reθ ≈
15000. We focus on the scaling behaviour of the two-points correlation tensor of
order p, defined by: S (p)
α1...αn(r) =〈 δuα1(r) ... δuαn(r)〉, at different distances from
the wall. By projecting each component of the tensor on the so-called sectors of the
group of rotations SO(3), it is possible to extract the isotropic contribution and
to distinguish between different kinds of anisotropies. The contribution from the
isotropic sector is completely described throughout the entire inner region by two
sets of universal exponents, pertaining respectively to the small- and the large-scale
ranges 1 . Preliminary measurements 2 seem to suggest a similar behaviour also for the
pure anisotropic terms of the correlation tensor, like S111112(r3) orS111222(r3). A first
direct evidence is provided in Fig.1, which shows how the data in the upper part of
the logarithmic layer can be exactly described by the same scaling exponents of the
homogeneous shear flow. The behaviour in the buffer region, where the increase of
the mean shear and the proximity of the wall are expected to drastically change the
turbulence dynamics, will also be discussed in the presentation.
∗ INSEAN, Rome, Italy.
† DMA, University “La Sapienza”, Rome, Italy.
‡ DIEM, University of Bologna, Forlì, Italy.
§ KTH Mechanics, Stockholm, Sweden.
1 Casciola et al., Phys. Rev. Letters 95, 024503 (2005).
2 Jacob et al., Phys. Fluids 16, 11 (2004).
10 3
10 2
10 1
10 0
10 0
r (mm)
3
10 1
-S 111112
-S 111222
Figure 1: Scaling behaviour at two different wall-normal distances of the anisotropic
components of the 6-th order correlation tensor. Squares and dashed line: S111112(r3)
and S111222(r3) aty + ≈ 700, respectively. Circles and dotted line: S111112(r3) and
S111222(r3)aty + ≈ 300, respectively. The solid line corresponds to the scaling ∼ z ζ6,2 ,
with ζ6,2 =2.2 the exponent of the homogenous shear flow. The streamwise, wall
normal and transverse directions are denoted by 1, 2 and 3 respectively.
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