Temporal surrogates of spatial turbulent statistics: The Taylor hypothesisrevisited

The Taylor hypothesis, which allows surrogating spatial measurements requir ing many experimental probes : by rime series from one or two probes, is ex amined on the basis of a simple analytic model of turbulent statistics. The main points are as follows: (i) The Taylor hypothesis introduces systemati c errors in the evaluation of scaling exponents. (ii) When the mean wind (V ) over bar(0) is not infinitely larger than the root-mean-square longitudin al turbulent fluctuations upsilon(T), the effective Taylor advection veloci ty V-ad Should take the latter into account. (iii) When two or more probes are employed the application of the Taylor hypothesis and the optimal choic e of the effective advecting wind V-ad need extra care. We present practica l considerations for minimizing the errors incurred in experiments using on e or two probes. (iv) Analysis of the Taylor hypothesis when different prob es experience different mean winds is offered. [S1063-651X(99)14010-8].