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

The properties of acceleration fluctuations in isotropic turbulence are studied in direct numerical simulations (DNS) by decomposing the acceleration as the sum of local and convective contributions (a_L = ∂u/∂t and a_C = u. ∇u), or alternatively as the sum of irrotational and solenoidal contributions [a₁ = - ∇(p/p) and a_s =ν∇²u]. 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" past a stationary Eulerian observer. Results at Taylor-scale Reynolds number up to 240 show that the random-Taylor scenario 〈a²〉≪〈a²_c〉 ≈〈a²_L〉, accompanied by strong antialignment between the vectors a_L and a_C, is indeed increasingly valid at higher Reynolds number. Mutual cancellation between a_L and a_C also leads to the solenoidal part of a being small compared to its irrotational part. Results for spectra in wave number space indicate that, at a given Reynolds number, the random Taylor hypothesis has greater validity at decreasing scale sizes. Finally, comparisons 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 Reynolds number trends are made stronger by the dynamics implied in the Navier-Stokes equations.