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Stabilization of linear systems by noise: Application to flow induced oscillations

In a recent paper, Popp and Romberg reported on stabilization by grid generated turbulence of a smooth circular cylinder immersed in the wake from an identical cylinder in an array of aluminium tubes. Although these results were obtained experimentally, so far they have not been explained from a stochastic point of view on a rigorous theoretical basis. This paper provides analytical results which may explain this stabilization phenomenon by modelling the immersed cylinder as a two degree of freedom oscillator and the turbulence as a stochastic process. We obtain general asymptotic approximation for the moment Lyapunov exponent, g (p), and the Lyapunov exponent, lambda, for a four-dimensional system with one critical mode and another asymptotically stable mode driven by a small intensity stochastic process. These results, pertaining to p th moment stability and almost-sure stability, explain how the stochastic components that couple the stable and the critical modes play an important role in determining whether a noisy excitation can stabilize or destabilize the oscillatory critical mode. They are then applied to a prototypical flow induced oscillation model to justify the experimental results.