This article presents techniques for the analysis of fluid systems. It adopts an optimization-based point of view, formulating common concepts such as stability and receptivity in terms of a cost functional to be optimized subject to constraints given by the governing equations. This approach differs significantly from eigenvalue-based methods that cover the time-asymptotic limit for stability problems or the resonant limit for receptivity problems. Formal substitution of the solution operator for linear time-invariant systems results in the matrix exponential norm and the resolvent norm as measures to assess the optimal response to initial conditions or external harmonic forcing. The optimization-based approach can be extended by introducing adjoint variables that enforce governing equations and constraints. This step allows the analysis of far more general fluid systems, such as time-varying and nonlinear flows, and the investigation of wavemaker regions, structural sensitivities, and passive control strategies.
Analysis of Fluid Systems: Stability, Receptivity, Sensitivity: Lecture notes from the FLOW-NORDITA Summer School on Advanced Instability Methods for Complex Flows, Stockholm, Sweden, 2013
Manuscript received July 11, 2013; final manuscript received December 18, 2013; published online March 24, 2014. Assoc. Editor: Ardeshir Hanifi.
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Schmid, P. J., and Brandt, L. (March 24, 2014). "Analysis of Fluid Systems: Stability, Receptivity, Sensitivity: Lecture notes from the FLOW-NORDITA Summer School on Advanced Instability Methods for Complex Flows, Stockholm, Sweden, 2013." ASME. Appl. Mech. Rev. March 2014; 66(2): 024803. https://doi.org/10.1115/1.4026375
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