We propose a system-theoretic approach for analyzing stability and transient energy growth performance of nonlinear fluid flow systems. The systems in consideration are composed of a non-normal linear element in feedback with a static and lossless nonlinearity—the NavierStokes equations being a special case. Specifically, we show that the input-output properties of the nonlinear element can be represented by a set of quadratic constraints. As a result, the nonlinear system can be analyzed by solving the Lyapunov inequalities of a linear system with a set of quadratic constraints that capture nonlinear behavior. Here, we investigate the proposed analysis framework on the Waleffe-Kim-Hamilton model—a low-dimensional mechanistic model of transitional and turbulent shear flows. Our proposed analysis framework can analyze global and local stability of a given equilibrium point of the nonlinear system. We show that nonlinear flow interactions have a destabilizing effect on the system response. The Lagrange multipliers in the proposed analysis provide additional information regarding the dominant nonlinear flow interaction terms.
|Original language||English (US)|
|Title of host publication||AIAA Scitech 2020 Forum|
|Publisher||American Institute of Aeronautics and Astronautics Inc, AIAA|
|State||Published - 2020|
|Event||AIAA Scitech Forum, 2020 - Orlando, United States|
Duration: Jan 6 2020 → Jan 10 2020
|Name||AIAA Scitech 2020 Forum|
|Conference||AIAA Scitech Forum, 2020|
|Period||1/6/20 → 1/10/20|
Bibliographical noteFunding Information:
This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-19-1-0034, monitored by Dr. Gregg Abate.
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