The aim of the present study is to extend the linear unsteady optimal-perturbation analysis of (Luchini 2000) to the nonlinear regime. In order to account for the nonlinear interactions, a Fourier expansion is applied in the streamwise direction and in time and the solution is decomposed in Fourier modes along both z and t. The optimal unsteady spanwise-sinusoidal leading-edge excitation that provides the maximum energy growth for a given initial energy and frequency can thus be determined. Of interest will be that the optimal growth decreases with both.
Time-Dependent Optimal Perturbations for the Algebraic Instability in the Nonlinear Regime
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Zuccher, S, & Luchini, P. "Time-Dependent Optimal Perturbations for the Algebraic Instability in the Nonlinear Regime." Proceedings of the ASME 2002 Joint U.S.-European Fluids Engineering Division Conference. Volume 1: Fora, Parts A and B. Montreal, Quebec, Canada. July 14–18, 2002. pp. 1387-1393. ASME. https://doi.org/10.1115/FEDSM2002-31049
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