Frequency response of Lamb-Oseen vortex

In this numerical study we present the frequency response of the Lamb-Oseen (Gaussian) vortex for two synthetic jet configurations. The first one consists of an annular axial jet that is superimposed on the Gaussian vortex. The other configuration deals with an off-axis, single-point, axial jet (SPI). We detect that the system responds to the forcing for a given axial wavenumber, k, exciting natural modes of the vortex by a resonance mechanism. We propose an explanation for the physical mechanism responsible for the maximum energy gain obtained by comparing our results with the different branches found theoretically by Fabre et al (2006 J. Fluid Mech. 551 235–74). We find high energy gains in both cases ($G_{\infty }\simeq {10}^3$ for the annular jet and $G_{\infty }\simeq {10}^4$ for the SPI jet), so these types of forcing are able to produce responses of the system strong enough to reach a non-linear state. Axisymmetric modes, with azimuthal wavenumber m = 0, produce the highest energy gain while applying an annular forcing. However, other modes, such as the helical one m = 1 and also double helix modes with m = 2, contribute in the SPI configuration. We find that the best region to be tested experimentally in both cases is the region that corresponds to the L2 branch described by Fabre and his collaborators. Furthermore, and whenever using these L2 branch frequencies, the response of the system is always axisymmetric, independently of the type of excitation. Finally, we conclude that the energy gain with the SPI jet is one order of magnitude greater than for the annular jet, so that the single-point off-axis jet is a feasible candidate to design a control device. (paper)