Generalized mean-field model of oscillatory flow using continuous mode interpolation*

A `least order' Galerkin model is proposed for the transient and post-transient cylinder wake targeting model-based flow control. The underlying Galerkin approximation comprises two mean-flow dependent modes representing the developing von K\'arm\'an vortex street and the shift mode resolving mean-flow changes. A continuous mode interpolation between global stability eigenmodes and POD modes enables a uniformly accurate flow prediction during the whole transient from steady to periodic state. Additionally, the shift mode and the interpolated oscillatory modes are derived from first principles employing a generalized mean-field theory.