Application of a self-organizing map to identify the turbulent-boundary-layer interface in a transitional flow

Existing methods to identify the interfaces separating different regions in turbulent flows, such as turbulent/nonturbulent interfaces, typically rely on subjectively chosen thresholds, often including visual verification that the resulting surface meaningfully separates the different regions. Since machine learning tools are known to help automate such classification tasks, we here propose to use an unsupervised self-organizing map (SOM) machine learning algorithm as an automatic classifier. We use it to separate a boundary layer undergoing bypass transition into two distinct spatial regions, the turbulent boundary layer (TBL) and non-TBL regions, the latter including the laminar portion prior to transition and the outer flow which possibly contains weak free-stream turbulence. Both regions are separated by the turbulent boundary layer interface (TBLI). The data used in this study are from a direct numerical simulation and are available on an open database system. In our analysis of one snapshot in time, every spatial point is characterized by a 16-dimensional vector containing the magnitudes of the components of total and fluctuating velocity, magnitudes of the velocity gradient tensor elements, and the streamwise and wall-normal coordinates, all normalized by their global standard deviation. In an unsupervised fashion, the SOM classifier separates the points into TBL and non-TBL regions, thus identifying the TBLI without the need for user-specified thresholds. Remarkably, it avoids including vortical streaky structures that exist in the laminar portion prior to transition as well as the weak free-stream turbulence in the turbulent boundary layer region. The approach is compared quantitatively with existing methods to determine the TBLI (vorticity magnitude, cross-stream velocity fluctuation). Also, the SOM classifier is cast as a linear hyperplane that separates the two clusters of data points, and the method is tested by finding the TBLI of other snapshots in the transitional boundary layer data set, as well as in a fully turbulent boundary layer with similar levels of free-stream turbulence. Variants in which the approach failed are also summarized.