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DERIVATIVES IN TURBULENT FLOW IN AN ATMOSPHERIC SURFACE LAYER WITHOUT TAYLOR HYPOTHESIS

Barak Galanti
High Performance Computing Unit of the IUCC, Tel-Aviv University, Tel-Aviv 69978, Israel

Gregory Gulitsky
Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel

Michael Kholmyansky
Faculty of Engineering, Tel Aviv University Tel Aviv 69974, Israel

Arkady Tsinober
Department of Fluid Mechanics and Heat Transfer, School of Mechanical Engineering, Tel-Aviv University, Tel-Aviv, Israel; and Institute for Mathematical Sciences and Department of Aeronautics, Imperial College, London, United Kingdom

Svyatoslav Yorish
Faculty of Engineering, Tel Aviv University Tel Aviv 69974, Israel

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.