Influence of the fluid density on the statistics of power fluctuations in von Kármán swirling flows

Abstract: Here we report experimental results on the fluctuations of injected power in confined turbulence. Specifically, we have studied a von K\'arm\'an swirling flow with constant external torque applied to the stirrers. Two experiments were performed at nearly equal Reynolds numbers, in geometrically similar experimental setups. Air was utilized in one of them and water in the other. With air, it was found that the probability density function of power fluctuations is strongly asymmetric, while with water, it is nearly Gaussian. This suggests that the outcome of a big change of the fluid density in the flow-stirrer interaction is not simply a change in the amplitude of stirrers' response. In the case of water, with a density roughly 830 times greater than air density, the coupling between the flow and the stirrers is stronger, so that they follow more closely the fluctuations of the average rotation of the nearby flow. When the fluid is air, the coupling is much weaker. The result is not just a smaller response of the stirrers to the torque exerted by the flow; the PDF of the injected power becomes strongly asymmetric and its spectrum acquires a broad region that scales as $f^{-2}$. Thus, the asymmetry of the probability density functions of torque or angular speed could be related to the inability of the stirrers to respond to flow stresses. This happens, for instance, when the torque exerted by the flow is weak, due to small fluid density, or when the stirrers' moment of inertia is large. Moreover, a correlation analysis reveals that the features of the energy transfer dynamics with water are qualitatively and quantitatively different to what is observed with air as working fluid.