Acceleration and dissipation statistics of numerically simulated isotropic turbulence

Abstract

Direct numerical simulation (DNS) data at grid resolution up to 20483 in isotropic turbulence are used to investigate the statistics of acceleration in a Eulerian frame. A major emphasis is on the use of conditional averaging to relate the intermittency of acceleration to fluctuations of dissipation, enstrophy, and pseudodissipation representing local relative motion in the flow. Pseudodissipation (the second invariant of the velocity gradient tensor) has the same intermittency exponent as dissipation and is closest to log-normal. Conditional acceleration variances increase with each conditioning variable, consistent with the scenario of rapid changes in velocity for fluid particles moving in local regions of large velocity gradient, but in a manner departing from Kolmogorov's refined similarity theory. Acceleration conditioned on the pseudodissipation is closest to Gaussian, and well represented by a novel "cubic Gaussian" distribution. Overall the simulation data suggest that, with the aid of appropriate parameterizations, Lagrangian stochastic modeling with pseudodissipation as the conditioning variable is likely to produce superior results. Reduced intermittency of conditional acceleration also makes the present results less sensitive to resolution concerns in DNS. © 2006 American Institute of Physics.