Towards the foundation of a global modes concept

A contribution is presented, intended to provide theoretical foundations for the ongoing efforts to employ global instability theory for the analysis of the classic boundary-layer flow, and address the associated issue of appropriate inflow/outflow boundary conditions to close the PDE-based global eigenvalue problem in open flows. Starting from a theoretically clean and numerically simple application, in which results are also known analytically and thus serve as a guidance for the assessment of the performance of the numerical methods employed herein, a sequence of issues is systematically built into the target application, until we arrive at one representative of open systems whose instability is presently addressed by global linear theory applied to open flows, the latter application being neither tractable theoretically nor straightforward to solve by numerical means. Experience gained along the way is documented. It regards quantification of the depar- ture of the numerical solution from the analytical one in the simple problem, the generation of numerical boundary layers at artificially truncated boundaries, no matter how far the latter are placed from the region of highest flow gradients and, ultimately the impracti- cally large number of (direct and adjoint) modes necessary to project an arbitrary initial perturbation and follow its temporal evolution by a global analysis approach, a finding which may question the purported robustness reported in the literature of the recovery of optimal perturbations as part of global analyses yielding under-resolved eigenspectra.

Técnica de Inversión Temporal para la Mejora del Enfocado de Imágenes SAR en Entornos Urbanos

Conventional SAR (Synthetic Aperture Radar) techniques only consider a single reflection of transmitted waveforms from targets. Nevertheless, today?s new applications force SAR systems to work in much more complex scenes such as urban environments. As a result, multiple-bounce returns are additionally superposed to direct echoes. We refer to these as ghost images, since they obscure true target image and lead to poor resolution. By applying Time Reversal concept to SAR imaging (TR-SAR), it is possible to reduce considerably ?or almost mitigate? ghosting artifacts, recovering the lost resolution due to multipath effects. Furthermore, some focusing indicators such as entropy (E), contrast (C) and Rényi entropy (RE) provide us a good focusing criterion when using TR-SAR.