The Structural and Statistical Character of Acceleration in Wall Turbulence

Abstract-
Robust large eddy simulation (LES) of turbulence requires accurate modeling of the small-scale features of the flow, including their interactions with the larger scales. Formulations based upon optimal estimation of the large-scale evolution minimize the mean-square error associated with computing the short-term dynamics of the resolved scales. Optimal formulations show great promise (Langford and Moser, 1999), since this evolution term embodies the stochastic nature of the small scales. However, in order for optimal formulations to be extended to higher Reynolds numbers, the statistical and structural nature of the evolution must be documented.

To this end, particle-image accelerometry measurements are made in the streamwise-wall-normal plane of turbulent channel flow at Ret = 550, 1140 and 1750. Temporal and convective derivatives of velocity are computed from this data in order to evaluate the small-scale behavior of these quantities as well as of the velocity itself. Instantaneous velocity fields indicate that the flow is dominated by small-scale vortex cores believed to be associated with hairpin/hairpin-like vortices. These vortices have been observed in realizations of the random velocity in other wall turbulence studies. In the present work, a deterministic "vortex signature" is revealed by conditional averaging techniques. This average signature is consistent with the hairpin vortex signature defined by Adrian and co-workers. Further, vortex organization in the outer layer is found to leave a distinct imprint upon the statistics of the flow, indicating that this coherent organization is a dominant feature of the flow.

Instantaneous time-derivative fields are spatially intermittent and dominated by strong events that are spatially coincident with the small-scale vortex cores seen in the associated velocity fields. Stochastic estimation of the temporal derivative signature associated with the presence of a vortex core, coupled with Taylor's hypothesis considerations, shows that these small-scale vortices remain relatively frozen in time. The bulk convective derivative of velocity (i.e., the temporal derivative computed in a reference frame traveling at the bulk velocity) is found to be nearly an order of magnitude smaller than the temporal derivative of velocity and is mostly associated with the growth of the vortices away from the wall. Based upon the trends noted in the instantaneous data, scaling of the temporal and convective derivative statistics is considered to determine a consistent Reynolds-number scaling of the statistics involved in optimal LES subgrid-scale models.

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