The Closure Problem of RANS

In RANS modeling the problem of figuring out a way to calculate ${\tau }_{ij}^{turb}$ in the Momentum Equations is called the closure problem

$$\boxed{\frac{\partial {\bar{u}}_i}{\partial t}+\frac{\partial {\bar{u}}_i{\bar{u}}_j}{\partial x_j}=-\frac{1}{\rho }\frac{\partial \bar{p}}{\partial x_i}+\frac{\partial }{\partial x_j}\left[v\frac{\partial u_i}{\partial x_j}+{\tau }_{ij}^{turb}\right]}$$