DERIVATIVES IN TURBULENT FLOW IN AN ATMOSPHERIC SURFACE LAYER WITHOUT TAYLOR HYPOTHESISBarak Galanti AbstraktDerivatives 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' a_{1} = du/dt and
a_{c} = (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. |
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