Characterisation of streak dynamics in Couette-Poiseuille flow using orthogonal wavelet decomposition.

It is known that the flow dynamics of transitional wall-bounded shear flow can be decomposed into the large and small scales. Typically, this decomposition can be performed using a two-dimensional spatial Fourier transform (e.g. Duguet & Schlatter PRL, 2013; Klotz et al. JFM, 2021). Taking Couette-Poiseuille flow as a recently introduced new canonical shear flow, we propose an alternative way with orthogonal discrete Meyer wavelet decomposition typically applied in atmospheric context (Yano et al. J. Atmos. Sci., 2001). We show that this decomposition allows us to extract and characterise not only the large-scale flow, as it has been done with the Fourier transform, but also the dynamics of small-scale streaks. Specifically, we characterise the "waviness of the streaks" related to the non-linear Waleffe process that has been proposed as the mechanics sustaining the turbulent fraction at small time-scales, which is known to be a notoriously difficult task.