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, [12pt]{minimal}{document}ε ̄{document}ε¯. Various surrogate approximations of ε, based on local isotropy (εiso), local axisymmetry along the streamwise direction x (εa, x) and the transverse direction y (εa, y), local homogeneity (εhom), and homogeneity in the transverse plane, (ε4x), are assessed. All the approximations are in agreement with [12pt]{minimal}{document}ε ̄{document}ε¯ when the distance downstream of the obstacle is larger than about 40 diameters. Closer to the obstacle, the agreement remains reasonable only for [12pt]{minimal}{document}ε ̄a,x{document}ε¯a,x, [12pt]{minimal}{document}ε ̄ₕₒₘ{document}ε¯hom and [12pt]{minimal}{document}ε ̄₄ₓ{document}ε¯4x. The probability density functions (PDF) and joint PDFs of ε and its surrogates show that ε4x correlates best with ε while εiso and εhom 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.