The symbols used to follow the meaning employed in the literature on turbulent flows. Lower case symbols indicate velocity fluctuations, while the upper case symbol is for the time-averaged velocity In the above equation, the turbulent kinetic energy is a time-averaged quantity

The time- averaged rate of strain and fluctuating rate of strain are

The first term on the right hand side of the turbulent kinetic energy equation is advection. Under the assumption of a negligible w-velocity (w=0) it reduces to: