Random Taylor hypothesis and the behavior of local and convective accelerations in isotropic turbulence

The properties of acceleration fluctuations in isotropic turbulence are stu died in direct numerical simulations (DNS) by decomposing the acceleration as the sum of local and convective contributions (a(L)=partial derivativeu/ partial derivativet and a(C)=u.delu), or alternatively as the sum of irrota tional and solenoidal contributions [a(I)=-del (p/rho) and a(S)=nu del (2)u ]. The main emphasis is on the nature of the mutual cancellation between a( L) and a(C) which must occur in order for the acceleration (a) to be small as predicted by the "random Taylor hypothesis" [Tennekes, J. Fluid Mech. 67 , 561 (1975)] of small eddies in turbulent flow being passively "swept" pas t a stationary Eulerian observer. Results at Taylor-scale Reynolds number u p to 240 show that the random-Taylor scenario <a(2)><<<a(C)(2)> approximate to <a(L)(2)>, accompanied by strong antialignment between the vectors a(L) and a(C), is indeed increasingly valid at higher Reynolds number. Mutual c ancellation between a(L) and a(C) also leads to the solenoidal part of a be ing small compared to its irrotational part. Results for spectra in wave nu mber space indicate that, at a given Reynolds number, the random Taylor hyp othesis has greater validity at decreasing scale sizes. Finally, comparison s with DNS data in Gaussian random fields show that the mutual cancellation between a(L) and a(C) is essentially a kinematic effect, although the Reyn olds number trends are made stronger by the dynamics implied in the Navier- Stokes equations. (C) 2001 American Institute of Physics.