DOI: 10.1615/TSFP3
DERIVATIVES IN TURBULENT FLOW IN AN ATMOSPHERIC SURFACE LAYER WITHOUT TAYLOR HYPOTHESIS
ABSTRACT
Derivatives play an outstanding role in the dynamics of
turbulence for a number of reasons. The importance of
velocity derivatives became especially clear since the papers by Taylor (1938) and Kolmogorov (1941). Taylor
emphasized the role of vorticity, whereas Kolmogorov
stressed the importance of dissipation, and thereby of strain. However, the most common method of obtaining the
derivatives in the streamwise direction is the use of Taylor hypothesis (Taylor, 1935, see references in Tsinober et al, 2001), the validity of which is a widely and continuously debated issue. It is related to a more general issue, the so called random Taylor hypothesis or the sweeping decorrelation hypothesis which concerns the relation between the (Eulerian) 'components' a1 = du/dt and
ac = (u·∇)u of the full (Lagrangian) acceleration (see Tsinober et al. (2001) for a discussion and numerical study of this problem). In fact the issue is even more general in the sense that it concerns the relation between the Eulerian components dQ/dt and (u·∇)Q of the material derivative of any quantity Q (scalar, vector or tensor) in a turbulent flow.
Using conventional hot- and cold-wire techniques it is not possible to distinguish between the temporal and the streamwise spatial derivatives thus enforcing the use of the Taylor hypothesis.
This presentation contains results obtained with a system
enabling to evaluate separately the temporal and streamwise
spatial derivatives, the latter being obtained without
employing the Taylor hypothesis. Along with experimental
we present also some numerical results clearly showing
strong anti-correlation and consequently cancellation
between the local, dQ/dt, and advective, (u·∇)Q,
components of different quantities in turbulent flows.