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, ε, as well as its mean value, ε¯ . Various surrogate approximations of ε, based on local isotropy (ε_{a, ya, x} and the transverse direction y (ε_{a, yhom}) and homogeneity in the transverse plane, (ε ), are assessed. All the approximations are in agreement with ε¯ when the distance downstream of the obstacle is larger than about 40 diameters. Closer to the obstacle, the agreement remains reasonable only for ε¯_a,x , ε¯_hom and ε¯_4x. The probability density functions (PDF) and joint PDFs of ε and its surrogates show that ε_4x correlates best with ε while ε_iso and ε_hom present the smallest correlation. The results indicate that ε4x is a very good surrogate for ε and can be used for correctly determining the behaviour of ε.