The short-wave asymptotic approximation of inviscid instabilities proposed by Bayly (Phys. Fluids 31, 1988) and Lifschitz \& Hameiri (Phys. Fluids A 3, 1991) is here applied to the dominant (three-dimensional) instability of two-dimensional flow in either an open or a closed driven cavity, and compared to the structural sensitivity obtained by direct-adjoint computation. The comparison shows that the structural sensitivity of the eigenmode is indeed localized around the critical streamline identified by short-wave asymptotics, and that the latter provides a reasonably good expression of even the first unstable eigenvalue at critical Reynolds number. Curiously enough, the same approximation appears also to apply with success to the two-dimensional instability of the same flow, despite the absence of a large spanwise wavenumber to be used as an expansion parameter. The theoretical justification of this extension, and the importance of phase quantization along the trajectory, will be discussed.
Short-wave analysis of 3D and 2D instabilities in a driven cavity
LUCHINI, Paolo;GIANNETTI, FLAVIO;CITRO, VINCENZO
2013-01-01
Abstract
The short-wave asymptotic approximation of inviscid instabilities proposed by Bayly (Phys. Fluids 31, 1988) and Lifschitz \& Hameiri (Phys. Fluids A 3, 1991) is here applied to the dominant (three-dimensional) instability of two-dimensional flow in either an open or a closed driven cavity, and compared to the structural sensitivity obtained by direct-adjoint computation. The comparison shows that the structural sensitivity of the eigenmode is indeed localized around the critical streamline identified by short-wave asymptotics, and that the latter provides a reasonably good expression of even the first unstable eigenvalue at critical Reynolds number. Curiously enough, the same approximation appears also to apply with success to the two-dimensional instability of the same flow, despite the absence of a large spanwise wavenumber to be used as an expansion parameter. The theoretical justification of this extension, and the importance of phase quantization along the trajectory, will be discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.