Separation of Unsteady Scales in a Mixing Layer Using Empirical Mode Decomposition

Abstract

Empirical mode decomposition has been shown to be a valuable data analysis tool in a wide array of technical fields, and it has recently emerged as a useful technique for studying complex fluid flows. This technique is useful for separating relevant unsteady spatiotemporal scales from a signal through an adaptive, iterative data-processing algorithm. Traditionally, empirical mode decomposition has been used to study time-dependent single-dimensional signals, though it can also be useful for studying multidimensional flowfield data. For the current study, unsteady velocity measurements were acquired across the initial development region of a turbulent-plane mixing layer using time-resolved particle image velocimetry. Empirical mode decomposition was applied to the resulting velocity field measurements to decompose the flowfield into several unsteady modes. Single-dimensional empirical mode decomposition was used to understand the time-frequency behavior of the flow associated with the formation and pairing process of large-scale vortical structures. The resulting spectrogram clearly displayed a periodic influence of large-scale vortex structures produced by the Kelvin–Helmholtz instability, which also exhibited a phase relationship with the vortex pairing mechanism. A multidimensional empirical mode decomposition analysis was also conducted, which allowed the unsteady velocity field to be decomposed into scale-based modes with dependence on , , and dimensions. This analysis allowed the influence of small-scale turbulent structures within the flowfield to be separated from those associated with large-scale vortical structures produced by the Kelvin–Helmholtz instability.