International audienceThe decomposition of experimental data into dynamic modes using a data-based algorithm is applied to Schlieren snapshots of a helium jet and to time-resolved PIV-measurements of an unforced and harmonically forced jet. The algorithm relies on the reconstruction of a low-dimensional inter-snapshot map from the available flow field data. The spectral decomposition of this map results in an eigenvalue and eigenvector representation (referred to as dynamic modes) of the underlying fluid behavior contained in the processed flow fields. This dynamic mode decomposition allows the breakdown of a fluid process into dynamically revelant and coherent structures and thus aids in the characterization and quantification of physical mechanisms in fluid flow. © 2010 Springer-Verlag

The ability of hydrodynamically self-excited jets to lock into strong external forcing is well known. Their dynamics before lock-in and the specific bifurcations through which they lock in, however, are less well known. In this experimental study, we acoustically force a low-density jet around its natural global frequency. We examine its response leading up to lock-in and compare this to that of a forced van der Pol oscillator. We find that, when forced at increasing amplitudes, the jet undergoes a sequence of two nonlinear transitions: (i) from periodicity to T 2 quasiperiodicity via a torus-birth bifurcation; and then (ii) from T 2 quasiperiodicity to 1:1 lock-in via either a saddle-node bifurcation with frequency pulling, if the forcing and natural frequencies are close together, or a torus-death bifurcation without frequency pulling, but with a gradual suppression of the natural mode, if the two frequencies are far apart. We also find that the jet locks in most readily when forced close to its natural frequency, but that the details contain two asymmetries: the jet (i) locks in more readily and (ii) oscillates more strongly when it is forced below its natural frequency than when it is forced above it. Except for the second asymmetry, all of these transitions, bifurcations and dynamics are accurately reproduced by the forced van der Pol oscillator. This shows that this complex (infinite-dimensional) forced self-excited jet can be modelled reasonably well as a simple (three-dimensional) forced self-excited oscillator. This result adds to the growing evidence that open self-excited flows behave essentially like low-dimensional nonlinear dynamical systems. It also strengthens the universality of such flows, raising the possibility that more of them, including some industrially relevant flames, can be similarly modelled.

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In this paper, we report the results of an experimental sensitivity analysis on a thermoacoustic system -an electrically heated Rijke tube. We measure the change of the linear stability characteristics of the system, quantified as shifts in the growth rate and oscillation frequency, that is caused by the introduction of a passive control device. The control device is a mesh, which causes drag in the system. The rate of growth is slow, so the growth rate and frequency can be measured very accurately over many hundreds of cycles in the linear regime with and without control. These measurements agree qualitatively well with the theoretical predictions from adjoint-based methods of Magri & Juniper (J. Fluid Mech., vol. 719, 2013, pp. 183-202). This agreement supports the use of adjoint methods for the development and implementation of control strategies for more complex thermoacoustic systems.