Accelerations in isotropic and homogeneous turbulence and Taylor's hypothesis

The validity of Taylor's hypothesis is analyzed by comparing the root mean square (rms) values of full (Lagrangian) and inertial accelerations in an i sotropic and homogeneous turbulent flow. Full, local, and inertial accelera tions in turbulence were decomposed into solenoidal and potential component s, which made it possible to avoid dealing, at least directly, with the pre ssure-gradient term in the Navier-Stokes equation. The evaluations of the c orrelation functions and spectra of the accelerations are presented. These evaluations have been obtained using the Batchelor [Proc. Cambridge Philos. Soc. 47, 359 (1951)] longitudinal structure function that describes statis tical properties of the turbulent velocity field. This function is equally valid for both inertial and dissipative subranges. It was shown that the ra tio of the rms values of the full and inertial accelerations depends on the Reynolds number R-lambda only and decreases at large R-lambda as R-lambda( -1/2). At R-lambda of about 20 this ratio is close to 0.72. At R-lambda of 1000 the ratio is less than 0.1. The validity of Taylor's hypothesis depend s on the ratio of the rms values of the accelerations. The results indicate that Taylor's hypothesis is valid for large R-lambda (exceeding about 1000 ) and becomes questionable at R-lambda below 100. At large R-lambda the ful l acceleration in homogeneous and isotropic turbulence turned out to be ind ependent of the Reynolds number. (C) 2000 American Institute of Physics. [S 1070-6631(00)50111-1].