Question

Which of these terms corresponds to the cross stresses?

(a) \(\rho\overline{u_i^{‘}\overline{u_j}}\)

(b) \(\rho\overline{\overline{u_i}u_j^{‘}}\)

(c) \(\rho\overline{\overline{u_i}u_j^{‘}} + \rho\overline{u_i^{‘}\overline{u_j}}\)

(d) \(\rho\overline{\overline{u_i}u_j^{‘}}\, – \rho\overline{u_i^{‘}\overline{u_j}}\)

I got this question during an internship interview.

Question is taken from Turbulence Modelling topic in section Turbulence Modelling of Computational Fluid Dynamics

Answer 1

Right answer is (c) \(\rho\overline{\overline{u_i}u_j^{‘}} + \rho\overline{u_i^{‘}\overline{u_j}}\)

The best explanation: The cross-stresses among the other SGS stresses occur due to the interaction between two variables. It can be given by the equation \(\rho\overline{\overline{u_i}u_j^{‘}} + \rho\overline{u_i^{‘}\overline{u_j}}\). The filtered and the unfiltered variables come together in each of these terms.