choice 1: $$ k_{res} = \frac{1}{2}U^2$$ , which is basically the kinetic energy contained in the resolved velocity field, and choice 2: $$ k_{res} = \frac{1}{2} ({U-\bar{U}})^2$$, which is basically the kinetic energy contained in fluctuations about the average of the resolved field. In other words, the resolved "turbulence". The first is straightforward to implement, while for the second I basically use trace(Uprime2Mean). I haven't been able to decide which is the more appropriate metric here, so would appreciate help on this.