Investigations into velocity spikes provide high-order statistics on turbulent flow

Large amounts of the energy the world spends on moving fluids is lost to fluid turbulence near the wall of the surface by which it flows. While many aspects of fluid motion can accurately be simulated already, some discrepancies between direct numerical simulation and experimental analysis still exist for high-order statistical descriptions of certain flow behaviors. A new analysis on one discrepancy, the higher-order statistics of wall-normal velocity fluctuations, is leading to a better understanding of fluid turbulence in anything from pipes to planes to boats.

The authors examined the high-order statistics of large, local wall-normal velocity fluctuations in turbulent flow using time series and instantaneous flow-field realizations. Described in the Physics of Fluids, the work included direct numerical simulations (DNS) of turbulent pipe flow, and investigated the dependency of the high-order statistics over a range of Reynolds numbers, the dimensionless quantity that compares inertial to viscous forces in a flowing fluid.

The work reports DNS results with respect to the convergence and scaling behavior of the turbulent high-order statistics, particularly the wall-normal kurtosis component at the wall where rare velocity spikes contribute to slow convergence.

The streamwise variance, skewness and the wall-normal kurtosis of the velocity exhibited logarithmic dependence on the Reynolds number. This is due to the interaction of large-scale motions with the near-wall structures — velocity spikes in the case of the kurtosis behavior, and wall-layer streaks for the streamwise variance and skewness dependencies. How these very large-scale motions become energetic, however, is still an open question.

Source: “On the convergence and scaling of high-order statistical moments in turbulent pipe flow using direct numerical simulations,” by C. Bauer, D. Feldmann, and C. Wagner, Physics of Fluids (2017). The article can be accessed at https://doi.org/10.1063/1.4996882 .