Statistics of the turbulent kinetic energy dissipation rate and its surrogates in a square cylinder wake flow

A numerical simulation based on the lattice Boltzmann method is carried out in the wake of a square cylinder with the view to investigating possible surrogates for the instantaneous turbulent kinetic energy dissipation rate, e, as well as its mean value, e¯. Various surrogate approximations of e, based on local isotropy (eiso), local axisymmetry along the streamwise direction x (ea, x) and the transverse direction y (ea, y), local homogeneity (ehom), and homogeneity in the transverse plane, (e4x), are assessed. All the approximations are in agreement with e¯ when the distance downstream of the obstacle is larger than about 40 diameters. Closer to the obstacle, the agreement remains reasonable only for e¯a,x, e¯hom and e¯4x. The probability density functions (PDF) and joint PDFs of e and its surrogates show that e4x correlates best with e while eiso and ehom present the smallest correlation. The results indicate that e4x is a very good surrogate for e and can be used for correctly determining the behaviour...