Model-based Design of Active and Passive Flow Control for Wall Turbulence

Abstract: Control of wall-bounded turbulent flows has been an important area of research for several decades. However, the development of effective control techniques has been hindered by the limited availability of computationally-tractable models that can guide design and optimization. In this talk, I will describe extensions of the resolvent analysis formalism that seek to address this limitation. Under the resolvent formulation, the turbulent velocity field is expressed as a superposition of propagating modes (‘resolvent modes’), identified via a gain-based decomposition of the Navier-Stokes equations. Control is introduced into this framework via changes to the boundary conditions or through additional forcing terms in the governing equations. This alters the structure and gain of resolvent modes, whereby a reduction in gain indicates mode suppression. I will show that this modeling framework reproduces observations from previous experiments and direct numerical simulations for passive techniques (e.g., riblets, compliant walls) as well as active feedback flow control (e.g., opposition control). Implications for the development of practicable control techniques will also be discussed.