Generating Homogeneous Anisotropic Turbulence in the Rapid Distortion Limit

Closure models for RANS and LES must represent turbulence with a wide range of anisotropies. One way to generate anisotropic turbulence is through rapid distortion theory (RDT), which can then be used to calibrate and/or validate these closures. In homogeneous turbulence, RDT is much cheaper than DNS and can therefore be used to generate a large number of different anisotropies. Here we discuss an efficient numerical technique using RDT to solve for the velocity spectrum tensor for a wide range of mean velocity gradients. In RDT, the velocity spectrum tensor evolves as a linear ODE coupled with the wavenumber evolution. Due to the scale-invariance of the RDT evolution, it is sufficient to solve them on a single spherical shell, from which the spectrum tensor can be recovered. The solution on a spherical shell is optimally represented in terms of spherical harmonics, which motivates solving the RDT system for a set of Gauss quadrature points known as Spherical Designs[1]. To support model development, an ensemble of RDT solutions was computed for a sampling of the mean velocity gradient tensor. The resulting anisotropies were analyzed, and their application to RANS modeling will be discussed.

[1]. In Proc. Sympos. Pure Math (Vol. 34, pp. 255-272)