Simulation of homogeneous turbulent shear flows at higher Reynolds numbers: numerical challenges and a remedy

Abstract

In a recent study, Isaza and Collins [J. Fluid Mech., 637 (2009), pp. 213–239] found the asymptotic state of homogeneous turbulent shear flows (HTSFs) to be sensitively dependent on the initial shear parameter (), and yet be almost independent of the initial Reynolds number (R _λ≡qλ/ν). The stringent resolution criteria they employed, however, restricted their studies to relatively low Reynolds numbers. In this paper, we present higher resolution direct numerical simulations of HTSFs over a wider range of Reynolds numbers, aided in part by an improved parallelisation scheme that utilises two-dimensional domain decomposition. We maximise the time-window for our simulations by determining appropriate settings for the initial energy spectrum, viscosity and domain configuration, thereby ensuring that we attain the highest possible asymptotic Reynolds number at the chosen grid resolution. In the course of our study, we find that the pseudo-spectral method suffers from Gibbs oscillations while resolving the thin vortical structures that tend to form in HTSFs. The nonlinear growth of these oscillations leads to spurious energy buildup in the high-wavenumber region of the spectrum, and contaminates the flow field. Consequently, the growth of the integral length scale is found to be numerically stunted, well before the intended final Reynolds number is attained. The issue is rectified by the application of exponential-type spectral filters, which stabilise the simulations and extend the runtime window, permitting attainment of larger asymptotic Reynolds numbers. Various large-scale flow statistics are then studied, and their dependence on the initial value of the shear parameter and Reynolds number corroborates the findings of Isaza and Collins.

Keywords:

• homogeneous turbulent shear
• direct numerical simulations
• shear parameter
• Gibbs oscillations
• spectral filter

Acknowledgments

[Acknowledgements] The authors thank P.J. Ireland and M. Henke for several useful discussions and suggestions. This work was supported by the National Science Foundation (NSF) through grant CBET-0967349. We also acknowledge the high-performance computing support provided by the Extreme Science and Engineering Discovery Environment (XSEDE) programme, which receives its support from NSF grant OCI-1053575; the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory sponsored by the Office of Science at the US Department of Energy under Contract No. DE-AC05-00OR22725; and the National Center for Atmospheric Research (NCAR) Computational and Information Systems Laboratory, sponsored by the NSF.