Bivariate 2D empirical mode decomposition for analyzing instantaneous turbulent velocity field in unsteady flows

We introduce and demonstrate the bivariate two-dimensional empirical mode decomposition (bivariate 2D-EMD) for the decomposition of a turbulent instantaneous velocity field to separate spatial large-scale organized motion from random turbulent fluctuations. To validate this approach, it was applied to an experimental homogeneous and isotropic turbulent flow (HIT), perturbed by a synthetic Lamb–Oseen vortex that mimics the feature of organized motion. Through different test cases, the scale, the amplitude and the position of the synthetic vortex with respect to the turbulent velocity field were changed. By applying an energy criterion on the modes which resulted from the decomposition process, the initial HIT flow was separated from synthetic perturbation. It is important to point out that in this approach the decomposition as well as the distinction of different parts of the flow are free from any prior and objective assumptions and it requires just one instantaneous velocity field of the flow under analysis. The proposed methodology could be used for analyzing 2D velocity fields obtained from experimental measurement or CFD in different configurations (in-cylinder flow, channel flows, etc.).