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

In nature, wall-bound turbulence is a common occurrence. This high dimensional, nonlinear dynamical system of interacting eddies of different sizes was first studied in the early 1960’s. The pioneering works first observed that the mean streamwise velocity in turbulent boundary layers exhibited a wall-normal logarithmic dependence hence it was hypothesized that the sizes of the energy-containing motions in the so-called logarithmic layer (log layer) were proportional to the distance to the wall. The energy-containing motions was first modeled by Townsend (1976) with the “attached-eddy” theory. Over the years, more and more evidence has emerged suggesting the existence of attached eddies in wall turbulence. However, to identify the attached eddies from instantaneous flow-fields is still a challenging work. Recently, the bidimensional empirical mode decomposition (BEMD) has been used to identify attached eddies in turbulent channel flows and quantify their relationship with the mean skin-friction drag generation.

This technique 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. Unfortunately, a thorough review of existing literature reveals that the self-similar and geometrical properties of the BEMD modes have not been investigated.

Fundamentally, the question of practical importance has been how attached eddies work individually and cooperatively to generate mean skin-friction drag. This alone is can be regarded as one of the most relevant quantities in aero- and hydrodynamics. However, owing to the difficulty of discerning and extracting individual attached eddies, only a small number of studies have attempted to address this issue to date. To this end, a group or researchers from the School of Aeronautics and Astronautics at Shanghai Jiao Tong University: Cheng Cheng (PhD candidate), Dr. Weipeng Li and Dr. Hong Liu, in collaboration with Dr. Adrián Lozano-Durán at the Center for Turbulence Research, Stanford University, USA, proposed to utilize a novel data analysis technique to identify attached eddies and quantify their contributions to the mean skin-friction drag generation. Their work is currently published in Journal of Fluid Mechanics.

This study was inspired by the fact that, in spite of the achievements of decades worth of research, the identification of individual eddies from the continuum of multiscale dynamical processes, and consequently the investigation of their dynamics, still remains a challenging task. Consequently, the researchers sought to decompose the velocity fluctuations obtained by direct numerical simulation of channel flows into BEMD modes characterized by specific length scales. Technically, they employed BEMD in turbulent channel flows to decompose the velocity fluctuations in the homogeneous directions (x-z) and provide a comprehensive investigation of wall-attached eddies.

The authors were able to show that modes identified by BEMD exhibited a self-similar behavior, and that single attached eddies were mainly composed of streaky structures carrying intense streamwise velocity fluctuations and vortex packets permeating in all velocity components. In addition, they reported that the second-order moment of each mode was consistent with the attached eddy theory by Townsend (1976).

In summary, the study demonstrated a systematic approach to identify attached eddies from DNS data by using BEMD. Remarkably, the findings were consistent with the existence of attached eddies in actual wall-bounded flows and showed that BEMD modes were tenable candidates to represent Townsend attached eddies. Overall, in an interview with Advances in Engineering, Professor Weipeng Li emphasized that the geometrical and statistical properties of attached eddies obtained in their work may aid the development of the attached eddy model and ultimately help improve its predictability.