  A method for finding reduced-order approximations of turbulent flow models is
presented. The method preserves bounds on the production of turbulent energy in
the sense of the $\curly{L}_2$ norm of perturbations from a notional laminar
profile. This is achieved by decomposing the Navier-Stokes system into a
feedback arrangement between the linearised system and the remaining, normally
neglected, nonlinear part. The linear system is reduced using a method similar
to balanced truncation, but preserving bounds on the supply rate. The method
involves balancing two algebraic Riccati equations. The bounds are then used to
derive bounds on the turbulent energy production. An example of the application
of the procedure to flow through a long straight pipe is presented. Comparison
shows that the new method approximates the supply rate at least as well as, or
better than, canonical balanced truncation.
