Abstract
In this paper we study the structural sensitivity of the nonlinear periodic oscillation arising in the wake of a circular cylinder for Re47. The sensibility of the periodic state to a spatially localised feedback from velocity to force is analysed by performing a structural stability analysis of the problem. The sensitivity of the vortex shedding frequency is analysed by evaluating the adjoint eigenvectors of the Floquet transition operator. The product of the resulting neutral mode with the nonlinear periodic state is then used to localise the instability core. The results obtained with this new approach are then compared with those derived by Giannetti & Luchini [8]. An excellent agreement is found comparing the present results with the experimental data of Strykowski & Sreenivasan [7].
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References
J.-M. Chomaz, P. Huerre, and L. Redekopp. A frequency selection criterion in spatially developing flows. Stud. Appl. Math., 84:119–144, 1991.
E.A. Fadlun, R. Verzicco, P. Orlandi, and J. Mohd-Yusof. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comp. Phys., 161:35–60, 2000.
J. Kim, D. Kim, and H. Choi. An immersed-boundary finite-volume method for simulations of flow in complex geometries. J. Comp. Phys., 171:132–150, 2001.
S. Le Dizs, P. Huerre, J.-M. Chomaz, and P.A. Monkewitz. Linear global modes in spatially developing media. Phil. Trans. R. Soc. Lond., 354:169–212, 1996.
J. Mohd-Yusof. Combined immersed-boundary/b-spline methods for simulations of flows in complex geometries. Annual research briefs, Center for Turbulence Research, NASA Ames and Standford University, 1997. p. 317.
P.A. Monkewitz, P. Huerre, and J.-M. Chomaz. Global linear stability analysis of weakly nonparallel shear flows. J. Fluid Mech., 251:1–20, 1993.
P.J. Strykowski and K.R. Sreenivasan. On the formation and suppression of vortex “shedding” at low Reynolds number. J. Fluid Mech., 218:71–107, 1990.
F. Giannetti and P. Luchini. Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech., 581:167–197, 2007.
P.M. Morse and H. Feshbach. Methods of Theoretical Physics. McGraw-Hill, 1953.
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Luchini, P., Giannetti, F., Pralits, J. (2009). Structural Sensitivity of the Finite-Amplitude Vortex Shedding Behind a Circular Cylinder. In: Braza, M., Hourigan, K. (eds) IUTAM Symposium on Unsteady Separated Flows and their Control. IUTAM Bookseries, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9898-7_12
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DOI: https://doi.org/10.1007/978-1-4020-9898-7_12
Publisher Name: Springer, Dordrecht
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Online ISBN: 978-1-4020-9898-7
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