Reduced-order Galerkin models of plane Couette flow

Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearized Navier-Stokes system for a few low wave numbers. Resulting Galerkin systems comprise ordinary differential equations, with a number of degrees of freedom ranging from 144 to 600, which may be integrated to large times without any indication of numerical instability. The reduced-order models so obtained are also found to match statistics of direct numerical simulations at Reynolds number 500 and 1200 with reasonable accuracy, despite a truncation of orders of magnitude in the degrees of freedom of the system. The present models offer thus an interesting compromise between simplicity and accuracy in a canonical wall-bounded flow, with relatively few modes representing coherent structures in the flow and their dominant dynamics.