Derive the pde for the dimensionless mean kinetic energy (k equiv frac{1}{2}leftlangle v_{alpha}^{prime} v_{alpha}^{prime} ightangle) assuming a

Derive the pde for the dimensionless mean kinetic energy \(k \equiv \frac{1}{2}\left\langle v_{\alpha}^{\prime} v_{\alpha}^{\prime}\rightangle\) assuming a viscous, incompressible Newtonian fluid. Identify production, viscous destruction and the total turbulent flux terms.