A restricted nonlinear large eddy simulation model for high Reynolds number flows

ABSTRACT

Recent numerical studies of the restricted nonlinear (RNL) model have demonstrated its ability to reproduce important features of wall turbulence despite a severe reduction in the number of degrees of freedom. In these prior studies, the RNL model included full resolution of the viscous term. In this work, we extend the RNL model to arbitrarily high Reynolds numbers by developing a RNL large eddy simulation (LES) framework along with a method to systematically identify an appropriate streamwise wavenumber support based on spectral properties of wall turbulence. This method leads to a band-limited RNL–LES system which is successful in reproducing some of the most important statistical features captured in previous low to moderate Reynolds number simulations, e.g. the mean velocity and second-order moment profiles. The RNL–LES framework offers a new approach to understanding the connection between coherent structures and the momentum transfer mechanisms of wall turbulence at arbitrarily high Reynolds numbers, where resolution of the viscous terms can become computationally expensive even with the relatively low computational complexity afforded through the dynamical restriction of the RNL model.

KEYWORDS:

• Restricted nonlinear model
• large eddy simulation
• wall-bounded turbulent flow
• reduced-order modelling

Acknowledgments

We acknowledge the high-performance computing resources of the Maryland Advanced Research Computing Center (MARCC) as well as the open source plotting tools provided by the Matplotlib [52] development team. We also acknowledge the many developers of the open source Lesgo CFD code, maintained at Johns Hopkins University and available at: https://lesgo-jhu.github.io/lesgo. We gratefully acknowledge the WINDINSPIRE program (NSF OISE 1243482), as well as NSF program CBET 1652244, which have provided many opportunities to present and discuss the research leading to this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Romanov proved that the laminar solution to Couette flow is linearly stable [53].

Additional information

Funding

This work was supported by the U.S. National Science Foundation [grant number OISE 1243482], [grant number CBET 1652244].