Question

Which of these conditions satisfy realizability?

(a) \(-\rho \overline{u_{i}^{‘} u_{j}^{‘}}\)<1

(b) \(-\rho \overline{u_{i}^{‘} u_{j}^{‘}}\)>1

(c) \(-\rho \overline{u_{i}^{‘} u_{j}^{‘}}\)>0

(d) \(-\rho \overline{u_{i}^{‘} u_{j}^{‘}}\)<0

The question was asked in an international level competition.

I want to ask this question from Turbulence Modelling in section Turbulence Modelling of Computational Fluid Dynamics

Answer 1

Right answer is (d) \(-\rho \overline{u_{i}^{‘} u_{j}^{‘}}\)<0

Easiest explanation: According to the realizability conditions, the properties which are physically non-negative must be numerically non-negative too. So,\(-\rho \overline{u_{i}^{‘} u_{j}^{‘}}\)>0. Therefore, \(-\rho \overline{u_{i}^{‘} u_{j}^{‘}}\) should be less than zero.