Dynamic mode shaping for fluid flow control: New strategies for transient growth suppression

Sub-critical transition to turbulence is often attributed to transient energy growth that arises from non-normality of the linearized Navier-Stokes operator. Here, we introduce a new dynamic mode shaping perspective for transient growth suppression that focuses on using feedback control to shape the spectral properties of the linearized flow. Specifically, we propose a dynamic mode matching strategy can be used to reduce non-normality and transient growth. We also propose a dynamic mode orthogonalization strategy that can be used to eliminate non-normality and fully suppress transient growth. We further formulate dynamic mode shaping strategies that aim to handle the practical challenges of high-dimensionality, nonlinearity, and uncertainty that are inherent to fluid flow control applications. Dynamic mode shaping methods are demonstrated on a number of simple illustrative examples that show the utility of this new perspective for transient growth suppression. The methods and perspectives introduced here will serve as a foundation for developing practical fluid flow control strategies in the future.