A direct numerical simulation is presented of an elliptical instability observed in the laboratory within an elliptically distorted, rapidly rotating, fluid-filled cylinder (Malkus 1989). Generically, the instability manifests itself as the pairwise resonance of two different inertial modes with the underlying elliptical flow. We study in detail the simplest ‘subharmonic’ form of the instability where the waves are a complex conjugate pair and which at weakly supercritical elliptical distortion should ultimately saturate at some finite amplitude (Waleffe 1989; Kerswell 1992). Such states have yet to be experimentally identified since the flow invariably breaks down to small-scale disorder. Evidence is presented here to support the argument that such weakly nonlinear states are never seen because they are either unstable to secondary instabilities at observable amplitudes or neighbouring competitor elliptical instabilities grow to ultimately disrupt them. The former scenario confirms earlier work (Kerswell 1999) which highlights the generic instability of inertial waves even at very small amplitudes. The latter represents a first numerical demonstration of two competing elliptical instabilities co-existing in a bounded system.

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Synthetic-jet actuators (SJA) have been employed in a variety of roles including aerodynamic boundary layer control. In their most widespread configurations, these zero net mass-flow devices are actuated by a piezoelectric, periodically-oscillating which alternatively admits and then expels a gas from an enclosed cavity through a nozzle. The cyclic fluid motion in and out of the cavity forms a synthetic outward bound jet. The aim of the current paper is to present the development and validation of a modeling procedure based on finite elements, which includes multiphysics simulation. The SJA model was based on fully-coupled acoustic, structural and piezoelectric modeling. The predicted results were favorably compared to experiment. While coupled fluid-structural piezoelectric models are available, the proposed method is a much more convenient quick-design tool for SJA'S due to reduced computational times based onthe acoustic fluid approximation.