Characterization of turbulence in inhomogeneous anisotropic flows
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We introduce a global quantity $δ$ that characterizes turbulent fluctuations in inhomogeneous anisotropic flows. This time-dependent quantity is based on spatial averages of global velocity fields rather than classical temporal averages of local velocities. $δ(t)$ provides a useful quantitative characterization of any turbulent flow through generally only two parameters, its time average $\bar δ$ and its variance $δ_2$. Properties of $\bar δ$ and $δ_2$ are experimentally studied in the typical case of the von Kármán flow and used to characterize the scale by scale energy budget as a function of the forcing mode as well as the transition between two flow topologies.