Martin Obligado
Centrale Lille Institut

The study of turbulent flows continues to challenge researchers. For instance, within the global effort to increase the generation of alternative energy, the study of the flow downstream of one or multiple turbines has drawn significant attention from the turbulence community due to its complexity. It involves turbulent wakes, their interactions, and their coupling with the background turbulent flow.

Many recent advances in the modelling of turbulent flows have yet to be adapted for such studies. To advance this research, a deeper understanding of the inner structure of turbulence, the energy cascade, is required. This phenomenon governs how energy is transferred from large to small scales and how it is ultimately dissipated. It has been found to play a crucial role in defining key properties of turbulent wakes, such as their velocity deficit and their streamwise spreading behaviour.

In this seminar, I will discuss recent advances in turbulence research, particularly relevant to wind energy applications. I will present experimental and theoretical evidence demonstrating the existence of a non-canonical energy cascade observed across a broad range of flows, including grid turbulence, turbulent boundary layers, and the turbulent axisymmetric wake. I will explore how this alternative cascade may result in turbulent wakes exhibiting scaling laws different from those predicted by standard models, such as the Richardson–Kolmogorov cascade. Moreover, I will illustrate how an oscillating freestream velocity influences this effect, as dissipation follows a hysteresis cycle linked to the unsteady term in the Kármán–Howarth equation.

Furthermore, I will introduce a newly discovered empirical law relating the energy cascade to small-scale intermittency in turbulent wakes and other inhomogeneous flows. Our findings, based on an extensive range of flows and experimental conditions, reveal a relationship between the dissipation constant, which characterises the energy cascade, and the intermittency factor, which quantifies deviations from self-similarity within the inertial range. Interestingly, while no prior theoretical expectation exists for a direct correlation between these two parameters, our results show that one evolves as the inverse of the other, potentially establishing a new universal law for turbulent flows.