  A popular method of forcing the fluid in Direct Numerical Simulations of
turbulence is to take the body force proportional to the projection of the
velocity of the fluid onto its lowest Fourier modes, while keeping the injected
external power constant. In this paper we perform a simple but rigorous
analysis to establish bounds on the relationship between the energy dissipation
rate and the resulting Reynolds number for this type of forcing. While this
analysis cannot give detailed information of the energy spectrum, it does
provide some indication of the balance of energy between the lower, directly
forced, modes, and those excited by the cascade.
