Nonlinear global modes in hot jets

Abstract : Since the experiments of Monkewitz et al. (J. Fluid Mech. vol. 213, 1990, p. 611), sufficiently hot circular jets have been known to give rise to self-sustained synchronized oscillations induced by a locally absolutely unstable region. In the present investigation, numerical simulations are carried out in order to determine if such synchronized states correspond to a nonlinear global mode of the underlying base flow, as predicted in the framework of Ginzburg - Landau model equations. Two configurations of slowly developing base flows are considered. In the presence of a pocket of absolute instability embedded within a convectively unstable jet, global oscillations are shown to be generated by a steep nonlinear front located at the upstream station of marginal absolute instability. The global frequency is given, within 10% accuracy, by the absolute frequency at the front location and, as expected on theoretical grounds, the front displays the same slope as a k--wave. For jet flows displaying absolutely unstable inlet conditions, global instability is observed to arise if the streamwise extent of the absolutely unstable region is sufficiently large: While local absolute instability sets in for ambient-to-jet temperature ratios S = 0.453, global modes only appear for S = 0.3125. In agreement with theoretical predictions, the selected frequency near the onset of global instability coincides with the absolute frequency at the inlet. For lower S, it gradually departs from this value. © 2006 Cambridge University Press.
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Journal of Fluid Mechanics, Cambridge University Press (CUP), 2006, 554 (may), pp.393-409. 〈10.1017/s0022112006008974〉
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Lutz Lesshafft, Patrick Huerre, P. Sagaut, M. Terracol. Nonlinear global modes in hot jets. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2006, 554 (may), pp.393-409. 〈10.1017/s0022112006008974〉. 〈hal-01023363〉

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