Periodically arranged co-flowing jets

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Abstract
The problem of a periodic planar arrangement of a large number of co-flowing, interacting jets is investigated. It is shown that this interaction gives rise to strong nearfield oscillations of large-scale spatial coherence and to far-field inhomogeneities. In the experiments performed, the jets were produced behind a flat plate perforated by holes arranged in a square or triangular periodic pattern and placed perpendicular to a uniform flow. At moderate Reynolds numbers, the interaction results in a remarkable low-frequency oscillation of the merging distance of the jets downstream of the plate. A detailed description of the recirculating flow in the cavities between the jets emphasizes the role of the backflow in the cavities on the oscillatory behaviour. This description is supported by measurements of the local fluctuating velocity and pressure, two-point correlation measurements and quantitative flow visualizations. These experimental observations suggest a new formulation for the instability dynamics of such unstable recirculating flows. This formulation, based on the nonlinear delayed saturation of the jet's shear layer instability (NLDS model) predicts successfully the dependence of the oscillation of the merging distance on the jet Reynolds number and on the local geometrical features of the confinement of the jets. Furthermore, it is shown that the diffusion of mass coming from one jet, seeded with an inert dye, gives rise to an exponential diffusion front over a distance corresponding to a few mesh sizes indicating a strong local coupling of the jets. At the scale of the whole jet assembly, the oscillations are organized as large-scale travelling waves, propagating from the boundaries of the domain to its centre. This symmetry-breaking property is discussed and supplemented by a spatio-temporal simulation of an array of coupled oscillators.

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