Invariant-based calibration of coefficients in nonlinear eddy viscosity turbulence closure

Abstract

Based on the standard quasi-linear pressure–strain correlation model a nonlinear eddy viscosity turbulence closure is developed. In two-dimensional mean-flows it is uniquely determined by three model coefficients. The model coefficients are allowed to adapt to flow conditions described by the invariants of mean-flow deformation and Reynolds stress anisotropy. The adaption is done in a straightforward and inexpensive manner. In the rapid distortion limit the coefficients are based on recent numerical and theoretical predictions for initially anisotropic turbulence. The model performance is furthermore calibrated against DNS data of canonical flows of engineering and geophysical interest. Those are the boundary layer of channel flow, homogeneous shear flow and Ekman flow. The resulting turbulence model is demonstrated to be superior to those based on well-known pressure–strain correlation models. An interpolation procedure is suggested to cover the entire Reynolds stress anisotropy-invariant map.

Keywords:

• homogeneous turbulence
• Reynolds-averaged Navier–Stokes
• turbulence modeling: Reynolds averaged
• turbulent mixing

Acknowledgment

We are indebted to Dr. Roderick Johnstone for kindly providing his Ekman flow DNS that were used in this work.