We apply the Linear-Quadratic-Gaussian design to fuid flows of engineering interest. The dynamic model is obtained from spatial discretization of the Navier-Stokes equations. Using spatial invariance, we transform the Riccati equations for the optimization problem in the 3D flow domain into a parameterized family of 1D problems that can be solved efficiently in parallell. The optimal control and estimation gains are shown to yield well-resolved localized convolution kernels when transformed back to physical space. The performance of the output feedback controller illustrated in direct numerical simulation of the 3D nonlinear Navier-Stokes equations.