Reynolds Equation and Mixing Length Model

Energy Equation in a Pure Shear Flow

The exact (unclosed) energy equation is given by

Note that the last term is zero.

For a pure shear flow,

 and .

The energy equation then becomes

.

The energy equations for , , and  are given as

( ): 

( ): 

( ): 

It is observed that the entire production is for  and there is no direct production of  and . Therefore,  and  receive their energy from the pressure-velocity interaction terms. That is,  and  must be positive and  must be negative. In most flows,  is twice as large as  and .