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

Abstract

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 (aL=∂u/∂t and aC=u⋅∇u), or alternatively as the sum of irrotational and solenoidal contributions [aI=−∇(p/ρ) and aS=ν∇2u]. The main emphasis is on the nature of the mutual cancellation between aL and aC 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〉≪〈aC2〉≈〈aL2〉, accompanied by strong antialignment between the vectors aL and aC, is indeed increasingly valid at higher Reynolds number. Mutual cancellation between aL and aC 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 aL and aC is essentially a kinematic effect, although the Reynolds number trends are made stronger by the dynamics implied in the Navier–Stokes equations.