An Objective Scheme for Turbulent Spot detection in Transitional Boundary Layers using Gaussian Mixture Model

Boundary layer (BL) transition is characterized by the emergence of concentrated zones of turbulence, called Turbulent Spots. Detecting these spots remains challenging as existing methods rely on subjective thresholds, empirical constants, or DNS-specific tuning.

We propose an objective scheme that incorporates automatic thresholding using BL thickness (δ₉₉), Pre-multiplied Wavelet Energy (PMWE) and Gaussian Mixture Model (GMM) to detect turbulent spots. For fixed wall-normal (y/δ₉₉) and spanwise locations, the compiled time series of streamwise velocity fluctuations (u′) from all streamwise locations serves as input, capturing the full laminar-to-turbulent transition. The detector function, viz. ∂u′/∂t, accentuates high-frequency bursts, while the criterion function, viz. frequency-averaged 〈PMWE〉, suppresses laminar noise. The δ₉₉ scaling encodes laminar-to-turbulent evolution of the BL in streamwise direction, and a log-transform amplifies cluster separation. A three-component GMM fitted on log(1+δ₉₉〈PMWE〉) is used for partitioning the dataset. Combining the transitional and turbulent clusters produces a turbulent/non-turbulent binary map.

The method demonstrates excellent performance on the freestream-turbulence and roughness induced transition datasets. This framework eliminates subjectivity, respects wall-normal variation of transitional intermittency and offers a robust tool for turbulent spot detection.