Identity of attached eddies in turbulent channel flows with bidimensional empirical mode decomposition

Bidimensional empirical mode decomposition (BEMD) is used to identify attached eddies in turbulent channel flows and quantify their relationship with the mean skin-friction drag generation. BEMD is an adaptive, non-intrusive, data-driven method for mode decomposition of multiscale signals especially suitable for non-stationary and nonlinear processes such as those encountered in turbulent flows. In the present study, we decompose the velocity fluctuations obtained by direct numerical simulation of channel flows into BEMD modes characterized by specific length scales. Unlike previous works (e.g. Flores & Jiménez, Phys. Fluids, vol. 22(7), 2010, 071704; Hwang, J. Fluid Mech., vol. 767, 2015, pp. 254–289), the current approach employs naturally evolving wall-bounded turbulence without modifications of the Navier–Stokes equations to maintain the inherent turbulent dynamics, and minimize artificial numerical enforcement or truncation. We show that modes identified by BEMD exhibit a self-similar behaviour, and that single attached eddies are mainly composed of streaky structures carrying intense streamwise velocity fluctuations and vortex packets permeating in all velocity components. Our findings are consistent with the existence of attached eddies in actual wall-bounded flows, and show that BEMD modes are tenable candidates to represent Townsend attached eddies. Finally, we evaluate the turbulent-drag generation from the perspective of attached eddies with the aid of the Fukagata–Iwamoto–Kasagi identity (Fukagata et al., Phys. Fluids, vol. 14(11), 2002, pp. L73–L76) by splitting the Reynolds shear stress into four different terms related to the length scale of the attached eddies.