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 that 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. Further, we formulate dynamic mode shaping strategies that aim to handle some of the practical challenges inherent to fluid flow control applications, namely high-dimensionality, nonlinearity, and uncertainty. 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 realizing effective flow control in the future.

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