Interscale energy transfer in a propeller-driven homogeneous and isotropic turbulence generation device

Abstract

We investigate the interscale energy dynamics of nearly homogeneous isotropic turbulence (HIT) generated in a spherically forced, propeller-driven device. From a spatial perspective, by employing the Kármán-Howarth-Monin (KHM) framework, we analyze the scale-by-scale energy transfer without isotropy assumptions. In contrast to other forcing strategies, where regions with inverse and forward cascades often coexist in scale space, we show that spherical forcing produces a purely forward energy cascade across the entire scale space. While the energy distribution remains highly isotropic and orientation-averaged structure functions align with Kolmogorov's two-thirds law, the energy flux exhibits a directional dependence, suggesting a higher sensitivity to residual forcing asymmetries. Regarding the temporal dynamics, the reduced mean flow generated by this device allows us to investigate the temporal variability in conditions where Taylor's frozen turbulence hypothesis does not apply. Our results provide experimental validation of Tennekes' Eulerian frequency spectrum, where intermediate scales evidence an inertial-convective range with statistics determined by the integral velocity scale and the dissipation rate. Finally, we adopt a global approach to investigate whether the main turbulent scales can be linked to external experimental parameters. We propose a framework that captures the propeller frequency dependence of the main turbulent variables obtained in our measurements and those of previously reported HIT chambers. These findings contribute to the understanding of how external forcing influences the complex interscale energy dynamics of turbulent flows from a spatial, temporal, and global perspective.