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M. P. Juniper¹ and B. Pier²
¹Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK; ²Laboratoire de mécanique des fluides et d'acoustique, École centrale de Lyon – CNRS – Université Claude-Bernard Lyon 1 – INSA, 36 avenue Guy-de-Collongue, 69134 Écully cedex, France
European Journal of Mechanics B/Fluids 49, 426–437 (2015)
The structural sensitivity shows where a flow instability is most sensitive to changes in internal feedback mechanisms. It is formed from the overlap of the flow’s direct and adjoint global modes. These global modes are usually calculated with 2D or 3D global stability analyses but this can be very computationally expensive. For weakly non-parallel flows the direct global mode can also be calculated with a local stability analysis, which is orders of magnitude cheaper. In this theoretical paper we show that, if the direct global mode has been calculated with a local analysis, then the adjoint global mode follows at little extra cost. We also show that the maximum of the structural sensitivity is the location at which the local k+ and k- branches have the same imaginary value and that this differs slightly from the position of the saddle point in the complex streamwise coordinate plane. Finally, we use the local analysis to derive the structural sensitivity of two flows: a confined co-flow wake at Re=400, for which it works very well, and the flow behind a cylinder at Re=50, for which it works reasonably well. As expected, we find that the local analysis becomes less accurate when the flow becomes less parallel.
hal-01084708
2015b_juniper_ejmb.pdf