$$1/f^{\alpha }$$ 1 / f α Low Frequency Fluctuations in Turbulent Flows

Abstract

We report the experimental observation of low frequency fluctuations with a spectrum varying as \(1/f^{\alpha }\) in three different turbulent flow configurations: the large scale velocity driven by a two-dimensional turbulent flow, the magnetic field generated by a turbulent swirling flow of liquid sodium and the pressure fluctuations due to vorticity filaments in a swirling flow. For these three systems, \(1/f^{\alpha }\) noise is shown to result from the dynamics of coherent structures that display transitions between a small number of states. The interevent duration is distributed as a power law. The exponent of this power law and the nature of the dynamics (transition between symmetric states or asymmetric ones) select the exponent \(\alpha \) of the \(1/f^{\alpha }\) fluctuations.